University of Southern California Dissertations and Theses

Experimental study of acoustical characteristics of honeycomb sandwich structures

(USC Thesis Other)

Experimental study of acoustical characteristics of honeycomb sandwich structures

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

EXPERIMENTAL STUDY OF ACOUSTICAL CHARACTERISTICS OF

HONEYCOMB SANDWICH STRUCTURES

by

Portia Renee Peters

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATERIALS SCIENCE)

May 2009

Copyright 2009 Portia Renee Peters

ii
DEDICATION

I would like to dedicate this work to my parents, Jerome and Brenda
Peters, for always loving me and supporting me in everything that I do. I love you
both very much. I would also like to dedicate this work to every teacher that has
inspired me to stretch my possibilities.

iii
ACKNOWLEDGEMENTS

I would like to thank my wonderful advisor, Dr. Steven Nutt, for
providing me with his guidance and motivation throughout my graduate school
career. His constant support, fun demeanor, and wealth of knowledge contributed
to an awesome research environment.
I thank the M.C. Gill Corporation, National Science Foundation East Asia
and Pacific Summer Institutes Program, Japan Society for the Promotion of
Science, and the USC Viterbi School of Engineering Dean’s Office for their
generous financial support of this research.
I sincerely thank Dr. Shankar Rajaram and Matt Sneddon for their insight
and technical expertise in regards to my research. I was truly blessed to have such
a supportive and knowledgeable team to work with. I also thank my colleagues in
the Composites Center for contributing to a fun research group that knows how to
party!
My special thanks to Mark Serridge, Lance Presnall, and Tony Spica of
Bruel & Kjaer for their technical support. I thank Dr. Hongbin Shen of the M.C.
Gill Corporation for always supplying me with the materials I needed to complete
my research.
Thank you to my family and friends that have always supported me and
encouraged me to be my very best. Last, but certainly not least, I want to thank
my Lord and Savior, Jesus Christ for giving me the talent to pursue the dreams he
placed in my heart and for sacrificing himself for my salvation. I can do all things
through Christ who strengthens me (Philippians 4:13).
iv
TABLE OF CONTENTS

DEDICATION ii

ACKNOWLEDGEMENTS iii

LIST OF TABLES vi

LIST OF FIGURES vii

ABSTRACT ix

Chapter 1: INTRODUCTION 1
1.1 Honeycomb Sandwich Structures for Aerospace 1
Applications
1.2 Acoustics of Honeycomb Sandwich Structures 2
1.3 Motivation 3
1.4 Scope of Dissertation 6

Chapter 2: BACKGROUND 8
2.1 Loss Factors 8
2.2 Acoustic Absorption 9
2.3 Wave Speeds 9
2.4 Coincidence Frequency 9
2.5 Transmission Loss 10

Chapter 3: MEASUREMENTS OF LOSS FACTORS OF 11
HONEYCOMB SANDWICH STRUCTURES
3.1 Introduction 11
3.2 Experimental Set-Up 14
3.2.1 Oberst Beam Method 14
3.2.2 Suspended Beam Method 17
3.3 Results and Discussion 19

v
Chapter 4: ACOUSTIC ABSORPTION CHARACTERISTICS 26
OF OPEN-WEAVE FOAM-FILLED HONEYCOMB
SANDWICH STRUCTURES
4.1 Introduction 26
4.2 Experimental Set-Up 28
4.2.1 Method 28
4.2.2 Materials 29
4.3 Results and Discussion 31
4.3.1 Initial Testing 31
4.3.2 Testing of Varying Foam Densities 34

Chapter 5: SEMI-ACTIVE VIBRATION SUPPRESSION OF 39
HONEYCOMB SANDWICH STRUCTURES
5.1 Introduction 39
5.2 Experimental Set-Up 41
5.3 Results and Discussion 46

Chapter 6: MEASUREMENTS OF WAVE SPEEDS OF 52
HONEYCOMB SANDWICH STRUCTURES
6.1 Introduction 52
6.2 Experimental Set-Up 54
6.2.1 Method 54
6.2.2 Materials 56
6.3 Results and Discussion 58
6.3.1 Modal Analysis 58
6.3.2 Transmission Loss 62

Chapter 7: CONCLUSIONS 66

REFERENCES 73

BIBLIOGRAPHY 80

vi
LIST OF TABLES

Table 3-1: List of beams tested and their properties. Panel designs 16
described and TL results presented in reference [39].

Table 4-1: Materials used in the acoustic absorption testing. 29

Table 4-2: Masses of the sandwich structures. 30

Table 5-1: Acoustic damping (PSD) and vibration suppression 46
(FRF) measurements when the measurement system
did not affect the data.

Table 5-2: Acoustic damping (PSD) and vibration suppression 46
(FRF) measurements when the measurement system
did affect the data through being connected.

Table 6-1: Dimensions and material properties of honeycomb 55
sandwich beams.

vii
LIST OF FIGURES

Figure 3-1: The experimental test apparatus included a shaker table 14
with a center mounted composite beam.

Figure 3-2: A modified version of the suspended beam set-up for 17
highly damped samples.

Figure 3-3: The loss factors for the five composite sandwich beam 19
samples.

Figure 3-4: The loss factor comparison between samples C and MP. 21

Figure 3-5: The loss factor comparison between samples G and C. 22

Figure 3-6: The loss factor comparison between samples C and 23
SSS-2.

Figure 3-7: The loss factor comparison between samples G and H. 24

Figure 4-1: The two-microphone set-up for measuring the absorption 27
of acoustical materials. Schematic is not drawn to scale.

Figure 4-2: (a) Traditional facesheet versus (b) Open-weave facesheet. 29

Figure 4-3: The normal incidence acoustic absorption for the closed 31
facesheet samples in the large tube (100-1600 Hz).

Figure 4-4: The normal incidence acoustic absorption for closed 31
facesheet samples in the small tube (500-6400 Hz).

Figure 4-5: The normal incidence acoustic absorption for the 32
open-weave facesheet samples in the large tube
(100-1600 Hz).

Figure 4-6: The normal incidence acoustic absorption for the 33
open-weave facesheet samples in the small tube
(500-6400 Hz).

Figure 4-7: Normal incidence acoustic absorption for open-weave 34
facesheet samples in the large tube (100-1600 Hz).

Figure 4-8: Normal incidence acoustic absorption for the open-weave 34
facesheet samples in the small tube (500-6400 Hz).

viii
Figure 5-1: Schematic of subfloor test chamber experiment set-up. 41

Figure 5-2: Accelerometers and piezoelectric transducers attached to 42
honeycomb sandwich panel mounted on subfloor source
chamber.

Figure 5-3: Block diagram of energy-recycling semi-active vibration 43
suppression method.

Figure 5-4: Shunt circuit with measurement system attached. The 47
measurement system is indicated by the R
M
resistor in
this circuit.

Figure 6-1: Schematic of experimental set-up. 53

Figure 6-2: Wave speeds of beams with carbon fiber laminate skins 57
and honeycomb core.

Figure 6-3: Wave speeds of beams with glass fiber laminate skins 59
and honeycomb core.

Figure 6-4: Transmission loss of panels with carbon fiber laminate 61
skins and honeycomb core.

Figure 6-5: Mass law deviation (MLD) of panels with carbon fiber 61
laminate skins and honeycomb core.

Figure 6-6: Transmission loss of panels with glass fiber laminate 62
skins and honeycomb core.

Figure 6-7: Mass law deviation (MLD) of panels with glass fiber 62
laminate skins and honeycomb core.

ix
ABSTRACT

Loss factor measurements were performed on sandwich panels to
determine the effects of different skin and core materials on the acoustical
properties. Results revealed inserting a viscoelastic material in the core’s mid-
plane resulted in the highest loss factor. Panels constructed with carbon-fiber
skins exhibited larger loss factors than glass-fiber skins. Panels designed to
achieve subsonic wave speed did not show a significant increase in loss factor
above the coincidence frequency. The para-aramid core had a larger loss factor
value than the meta-aramid core.
Acoustic absorption coefficients were measured for honeycomb
sandwiches designed to incorporate multiple sound-absorbing devices, including
Helmholtz resonators and porous absorbers. The structures consisted of
conventional honeycomb cores filled with closed-cell polyurethane foams of
various densities and covered with perforated composite facesheets. Honeycomb
cores filled with higher density foam resulted in higher absorption coefficients
over the frequency range of 50 – 1250 Hz. However, this trend was not observed
at frequencies greater than 1250 Hz, where the honeycomb filled with the highest
density foam yielded the lowest absorption coefficient among samples with foam-
filled cores.
The energy-recycling semi-active vibration suppression method (ERSA)
was employed to determine the relationship between vibration suppression and
acoustic damping for a honeycomb sandwich panel. Results indicated the ERSA
x
method simultaneously reduced the sound transmitted through the panel and the
panel vibration. The largest reduction in sound transmitted through the panel was
14.3% when the vibrations of the panel were reduced by 7.3%.
The influence of different design parameters, such as core density, core
material, and cell size on wave speeds of honeycomb sandwich structures was
experimentally analyzed. Bending and shear wave speeds were measured and
related to the transmission loss performance for various material configurations.
The shear modulus of the core showed maximum influence on the wave speeds of
the samples, while cell size did not have a significant influence on wave speeds or
on transmission loss. Skin material affected wave speeds only in the pure bending
regime. Honeycomb sandwich structures with a subsonic core and thus reduced
wave speed showed increased transmission loss compared to samples without a
subsonic core.

1
Chapter 1: INTRODUCTION

This chapter presents an introduction to the acoustical characteristics of
honeycomb sandwich structures. In section 1.1, the choice of using honeycomb
sandwich structures in aerospace applications is discussed. Section 1.2 gives an
overview of the acoustics of honeycomb sandwich structures in applications such
as airplane floors and satellite decks. The motivation for this work and the
potential impact of the results is outlined in section 1.3. The scope of this research
and a brief outline for the remaining chapters is presented in section 1.4.
In this dissertation, a honeycomb sandwich structure refers to a material in
which a stiff orthotropic core with a honeycomb construction is sandwiched
between two thin skins and bonded together with a thin layer of adhesive. Other
terms used to describe honeycomb sandwich structures are honeycomb
composites and honeycomb sandwiches. Also, note that transmission loss refers to
sound transmission loss in all cases. Acoustic absorption coefficients are also
known as noise reduction coefficients.

1.1 Honeycomb Sandwich Structures for Aerospace Applications

Lightweight honeycomb sandwich structures are used in a wide variety of
aerospace applications because a high stiffness to weight ratio is desired.
Honeycomb sandwich structures are designed for mechanical performance, but
have poor acoustical performance. As a result, continual efforts are made to
improve acoustical performance without compromising the amount of payload the
structure can carry. An advantage of using honeycomb sandwich structures is the
2
ability to easily tailor the material for a specific application. The material and
structural parameters of the skins, cores and core fillings can be suited to fit the
requirements of a wide variety of specific applications.
The two applications of honeycomb sandwich structures that were studied
in this research were commercial airplane floors and satellites. In commercial
airplanes, honeycomb sandwich structures are primarily used for floors in
passenger compartments and for fuselage linings. In satellite applications, the
material is widely used for the thrust tube, deck panel, and substrate of the
satellite. The honeycomb sandwich structure core is usually comprised of either a
meta-aramid (Nomex
®
) or para-aramid (Kevlar
®
) paper. Aluminum honeycomb
cores and balsa wood can also be used as core materials. The skins are typically
laminated composites of fibers such as carbon or glass and a thermoset resin such
as phenolic or epoxy. The core to skin thickness ratio is usually 10:1 but can be
altered for acoustical and mechanical optimization.

1.2 Acoustics of Honeycomb Sandwich Structures

Airplane floor panels and satellite substrates act as both a noise
transmission path, transmitting a majority of the noise, and as a secondary noise
source by radiating noise as a response to the multiple sources of excitation. The
floors and substrates are typically subjected to airborne noise excitation and
structural vibration excitation [1-4]. Airborne noise is generated by the noise from
the engines, the aerodynamic boundary layer, and the airframe vibrations. For the
airplane floors, the airborne noise from these sources excites the floors from the
3
lower lobe of the fuselage. For satellite substrates, the airborne noise excites the
substrates from the pressure field generated by the propulsion system. The
primary source of vibratory excitation is the connection between the sandwich
structures and the main body, which is the fuselage for floor panels and the
satellite frame for the substrates. The vibratory excitation leads to vibration
response of the structure and noise radiation. The airborne noise of interest is
between 315 Hz – 10 KHz and the structural vibrations of concern are in the
frequency range of 10 Hz – 1 KHz. However, the airborne noise and structural
vibrations are inter-twined, making discrimination of the individual contribution
of the two types of excitation and their responses virtually impossible [5].

1.3 Motivation

Airplane manufacturers are facing increased demand for faster, lighter,
and more fuel-efficient planes. Satellite and launch vehicle support teams have an
increased need to minimize the damage to delicate hardware that is caused by
acoustic and vibratory damage to the substrate during the course of the mission.
The solution to both of these problems is to use more composite materials in the
construction, including honeycomb sandwich structures, because they have high
stiffness and low weight. Unfortunately, the properties that make the honeycomb
sandwich structures desirable from a structural standpoint are the same properties
that tend to exacerbate noise and vibration problems for satellites and in airplane
cabins. Noise presents a serious threat to mechanical and electrical systems by
producing excessive vibration, which causes stress and damage by fatigue. The
4
primary motivation for satellite applications is to ensure the survivability of the
delicate hardware attached to the substrate while the motivation for airplane
manufacturers is the comfort and safety of the passengers in the airplane cabin.
There is motivation for developing and implementing noise control
measures for aerospace applications as effectively as possible. However, these
noise control measures must take into account certain constraints such as cost,
weight, mechanical requirements, safety regulations, restricted access and damage
vulnerability. There is a large amount of literature, too much to list here, available
for mechanical performance studies as well as theoretical studies on acoustic
performance of honeycomb sandwich structures [6-11]. However, few studies
have comprehensively investigated, through the use of experimental data, the
impact of material and structural parameters of honeycomb sandwich panels on
acoustic performance [12-14]. This present work attempts to address acoustic
issues for aerospace applications, specifically airplane floors and satellite
substrates through experimental work.
Noise and vibration can originate from one source and yet have multiple
pathways in which to excite a structure. Hence, the most efficient approach to
expanding noise control solutions is to have a comprehensive study of the
individual parameters that affect acoustic and vibration performance.
Understanding the individual acoustic properties of honeycomb sandwich
structures allows for a more robust approach to manipulating those properties to
produce the optimal material for aerospace applications.
5
Damped panels transmit less noise near the critical frequency [15]. This
trait can be exploited to reduce the amount of noise transmitted from a vibrating
panel. The loss factor is a measure of the amount of damping in a system.
Therefore, exploring how to increase the loss factor should lead to honeycomb
sandwich structure designs that produce quieter panels. This is one of the
motivations for this work.
The open construction of the honeycomb core affords opportunities to
implement lightweight solutions to control noise by combining multiple types of
absorbers within the sandwich structure. Mechanical properties of foam-filled
cores have been tested [8-11] but the acoustic properties were unknown. Porous
absorbers and Helmholtz resonators are combined in this work to test the acoustic
performance of the foam-filled core.
Damping of mechanical vibrations can also reduce structure-borne sound
and noise transmission through the honeycomb sandwich structure. Damping is a
common noise control solution; however, damping is usually associated with
additional weight. The energy-recycling semi-active (ERSA) method is
lightweight and was shown to be an effective method to reduce vibrations [16-
18]. Thus, the motivation for this work is to apply the ERSA method as a noise
control solution because it can damp vibrations and noise while minimizing the
amount of additional weight.
Studying wave speed characteristics of honeycomb sandwich structures
provides insight for noise control solutions because acoustical performance
6
depends on these characteristics. The key to designing honeycomb panels for
noise control is to maintain a subsonic bending wave speed (e.g., two-thirds the
speed of sound) in the sandwich panel over as great a frequency range as possible
[13,19,20]. These are multiple motivations for this work that merited
experimental verification.

1.4 Scope of Dissertation

The primary focus of this study is the acoustic properties of honeycomb
sandwich structures – loss factors, acoustic absorption, transmission loss, and
wave speed – for applications in airplane floors and satellite construction. The
acoustic properties measured address airborne and structure-borne noise. The
frequency range of interest for the entire study is 50 Hz – 10 kHz unless otherwise
stated. This frequency range covers the typical frequency range of interest for the
applications. The results presented in this dissertation are based on experimental
data only. All test samples were provided by the M.C. Gill Corporation with the
exception of the ERSA study in which the sandwich panel was from a different
manufacturer but of the same design. The aim of this study is for practical
solutions for the industry while simultaneously advancing the understanding of
acoustics and vibrations in the field of engineering and materials science.
Chapter 2 of this dissertation gives a brief background of the acoustical
properties studied in this work. The influence of a mid-plane damping layer, skin
material, wave speed, and core material on loss factors of honeycomb sandwich
structures is presented in Chapter 3. In Chapter 4, the efficacy of Helmholtz
7
resonators combined with porous absorbers in honeycomb sandwich structures for
increasing acoustic absorption is analyzed. The quantitative relationship between
vibration suppression and acoustic damping when the ERSA vibration
suppression method is employed with a honeycomb sandwich panel is determined
in Chapter 5. The following chapter, Chapter 6, presents the influence of wave
speeds on the transmission loss of honeycomb sandwich panels when skin
material, core material, and core cell size are varied. Chapter 7 has a few
concluding remarks and describes the scope for future work.

8
Chapter 2: BACKGROUND

The study of noise and vibration control in structures is a complex issue
because there are several parameters that affect vibroacoustic response. This
complexity is magnified in composite structures such as honeycomb sandwich
structures. Solutions for noise control are often accompanied with a trade-off in
weight, mechanical stability, or cost. Also, the structural response tends to be
frequency dependent, which is another factor to consider when finding a solution
for noise and vibration control. This research is primarily focused on three
individual noise control solutions – damping (through add-on materials and semi-
active vibration control), absorptive materials, and manipulating core wave
speeds. The purpose of this chapter is to serve as a quick orientation for future
students who might choose to conduct research in this area.

2.1 Loss Factors
Loss factor is a measure of the amount of damping in a structure.
Damping is the conversion of mechanical energy of a vibrating structure into
thermal energy, which is then transmitted into the environment of the structure.
The higher the loss factor, the higher the damping. There are several techniques
used to quantify the amount of damping in a structure. The two used in this study
are the half-power bandwidth method and the suspended beam method.

9
2.2 Acoustic Absorption
The acoustic absorption coefficient is defined as the ratio of absorbed
energy to incident energy. The incident energy must equal the sum of the reflected
energy, the transmitted energy, and the absorbed energy due to the conservation
of energy. Absorption coefficients range from 0 (no absorption) to 1 (complete
absorption). Acoustic absorption is frequency-dependent. Materials that have
higher absorption coefficients tend to have a porous construction. Absorbers such
as Helmholtz resonators also increase the absorption coefficient of materials.

2.3 Wave Speeds
The two types of waves studied in this work are bending and shear waves.
Bending waves are dispersive because the wave velocity is not constant and the
spatial form of the wave changes with time. Bending wave speeds are frequency
dependent and exhibit a parabolic dependence on frequency when plotted. Shear
waves are non-dispersive because the wave velocity is constant and the spatial
form of the wave remains constant with time. Shear wave speeds are not
frequency dependent and fall along a straight line when plotted [21].

2.4 Coincidence Frequency
The coincidence frequencies are the frequencies at which the wave speed
of the panel matches the speed of sound in air. The lowest of the coincidence
frequencies is called the critical coincidence frequency. Above the critical
coincidence frequency there is an efficient exchange of energy taking place
10
between the wave speeds of the honeycomb sandwich structure and the wave
speed of air. Ideally, for noise control moving the coincidence frequency to higher
frequencies delays this range of efficient energy exchange and thus results in
improved acoustical properties of the honeycomb structure.

2.5 Transmission Loss
The type of excitation, the frequency of excitation, and the nature and
geometrical configurations of the structure dictate the transmission of sound and
vibration in a structure. Structural response to vibration excitation is
predominantly due to resonant modes [1, 2, 5]. Sound transmission loss is one of
the primary metrics used to evaluate the acoustical performance of honeycomb
sandwich structures. Transmission loss (TL) is defined as the difference between
incident energy and the transmitted energy through a material or structure – it is
also an indication of the acoustic performance of the material as a noise barrier
between two spaces.

11
Chapter 3: MEASUREMENTS OF LOSS FACTORS OF HONEYCOMB
SANDWICH STRUCTURES

3.1 Introduction

Lightweight sandwich panels are used in applications that require high
specific stiffness and strength, such as aircraft flooring, naval vessels, and
transportation vehicles. However, the use of sandwich panels frequently results in
undesirable levels of noise transmission. As a result, continual efforts are made to
improve acoustical performance without compromising mechanical performance
of panel systems. While there are multiple approaches to mitigating noise,
damped panels transmit less noise near the critical frequency [15]. These traits
can be exploited to reduce the noise generated from a vibrating panel. Ultimately,
the reduction of noise also depends on the noise source. However, by exploring
noise control measures that increase the loss factor of sandwich structures through
passive damping controls, it should be possible to design and produce quieter
panels without sacrificing strength, thereby reducing noise levels in passenger
cabins. This correlation between a higher damping factor and decreased noise
generation has been shown in mechanical gears made from composite materials
[22]

and this current study is aiming to show this correlation for honeycomb
sandwich panels.
Understanding the acoustic behavior of the component materials of sandwich
panels can lead to approaches that mitigate the sound transmitted without adding
significant additional weight. Knowledge of the loss factor of component
12
materials can be used to develop designs of new sandwich panels with superior
acoustic properties.
Since the late 1950s, vibro-acoustic properties of sandwich structures have
been widely studied. For example, the Ross-Ungar-Kerwin model constituted a
pioneering theory for studying damping in sandwich structures [23-26]. Kerwin
also determined the effectiveness of viscoelastic material on damping [23],

and
expressions for the loss factors of structures with two or three components were
presented by Ungar. Ungar later reexamined and refined his previous loss factor
equations to account for the vibration energy of highly damped systems [25, 26].
Finally, Mead and Markus furthered the study of damping by formulating an
approximate method for determining both loss factors and resonant frequencies
for honeycomb structures [27] and formulating a 6
th
-order differential equation of
motion derived in terms of transverse displacement for a sandwich beam with a
viscoelastic core [28].
More recent advances include experiments to determine loss factors for
honeycomb sandwich panels with composite face sheets [29], combining
honeycomb and viscoelastic material to affect damping and vibration control [30],
and determining the effects of thickness and delamination on damping in
honeycomb [6]. The effects of different honeycomb core geometries have also
been explored for possible noise control and structural improvements [31,32]. Li,
et al determined the loss factor for composite sandwich beams using the modal
bandwidth method, which can be used to determine the damping for a single
13
mode [6], while Nilsson conducted a study of wave propagation, loss factors, and
transmission loss for sandwich plates [33]. Finally, He and Rao presented an
analytical model for the transverse and longitudinal vibrations in sandwich beams
[7], and Shi et al were able to use inverse methods to determine material
parameters in beams [34].
However, these studies, like most others, were based on theoretical models
or experiments that focused solely on the mechanics of the structure. Shorter [35]
performed an analytical study on wave propagation and damping for honeycomb
sandwich structures using viscoelastic laminates, and Ghinet, Atalia, and Osman
[36] studied the effects of materials on the transmission loss of curved honeycomb
sandwich panels. However, few attempts have been made to quantify the impact
of material choice on the loss factors of honeycomb sandwich structures. In the
present work, we investigate the influence of material choice on the damping of
honeycomb sandwich panels through experimental data. As an extension of this
experiment, one of the samples chosen uses an unconventional method of
increasing the loss factor. A panel was designed and produced with a damping
layer in the mid-plane rather than placing the damping layer on the skin-core
interface. The damping layer was placed in the center of the core as a proof of
concept experiment demonstrating that exposing the damping material to
maximum shear force would result in maximum damping.

14
3.2 Experimental Set-Up

In this study, data was acquired from Oberst beam [37] measurements (for
lightly damped materials) and from suspended beam tests (for highly damped
materials). Loss factors were subsequently calculated using these data.

3.2.1 Oberst Beam Method

The classical method for measuring damping characteristics of materials is
the Oberst method, which involves exciting a cantilever beam clamped at one end.
Problems arise from the effects of clamping conditions on the dynamic
characteristics of cantilever type composite structures (Hwang et al) [38]. These
clamping condition limitations prompted us to seek an excitation method less
sensitive to boundary conditions, which led to the adoption of a free-free
configuration illustrated in Fig. 3-1.

Figure 3-1: The experimental test apparatus included a shaker table with a center mounted
composite beam.

15
Eqn (3-1) is the ratio of the dynamic response of the free-free beam by the
imposed motion, Eqn (3-2) is the definition of the beta term, and Eqn (3-3) is the
definition of the omega term used to predict the modes. These equations were
derived using the compact model of the beam equation [37], and illustrate that the
free-free beam excitation method is similar to the traditional cantilever technique.
In fact, a cantilever beam has the same dynamical behavior as a free-free beam
with twice the length, excited in the center. Thus, the equations are suitable for
measurement of structural damping properties. For the free-free beam, only the
even modes will be excited, although the slope and relative displacement to the
imposed motion are void at the center. Therefore, the modal behavior will be
similar to a clamped beam [37].

)] sin( ) [sinh(
) 2 / cos( ) 2 / cosh( 1
) 2 / sin( ) 2 / sinh(
2
1
)] cos( ) [cosh(
) 2 / cos( ) 2 / cosh( 1
) 2 / cos( ) 2 / cosh(
2
1
) , (
x x
L L
L L
x x
L L
L L
x H
β β
β β
β β
β β
β β
β β
ω
+
+
−
+
+
+
+
=
(3-1)

EI
A
2
4
ω ρ
β = (3-2)

4
2
2
) (
L
Ek
L
n n
ρ
β ω = where (βL)
n
2
= (
2n−1
π
L)
2
(3-3)

In the above equations, H is the ratio of the dynamic response of the beam divided
by the imposed motion, x is the position, ω is the excitation frequency, L is the
length of the beam, ρ is the mass density of the beam, A is the cross-section area,
E is the elastic modulus, I is the second moment of area of the beam, k is the wave
number, and n is mode number.
16
The experimental set-up is shown in Fig. 3-1. Lightweight aluminum
mounting bobbins were bonded to the midpoint of the composite beam samples.
The beam was then attached to an electro-dynamic shaker by a threaded rod. The
composite beam samples used in this experiment were approximately 900 mm ×
50 mm × 10 mm. The apparatus was first tested using an aluminum reference
beam with these same dimensions. The measured modes of the reference beam
were within 1% of the predicted modes calculated using Eqn (3-3). Damping
measurements were performed for five honeycomb sandwich beams, listed in
Table 3-1. The lay-up for each of the samples was 2 plies unidirectional, 0/90, and
the volume fraction of the composite material of the skin for all samples was
~50%. The sample notation corresponds to the panels used by Rajaram et al

[39,40]. The samples were tested at room temperature (22°C) to simulate aircraft
interiors, the primary application for these materials.
Sample
Name
Skin Type Core
Material
Special
Properties
Layer
Thickness
skin/core/skin
(mm)
Young’s
Modulus
(Nm
-2
)
G Glass/Epoxy Nomex
®
0.5/9/0.5 20x10
9

H Glass/Epoxy Kevlar
®
0.5/9/0.5 20x10
9

C Carbon Nomex
®
0.5/9/0.5 100x10
9
MP Carbon Nomex
®
Mid-plane
damping
layer
0.5/9/0.5

Damping layer
= 0.5
100x10
9

SSS-2 Carbon Nomex
®
Subsonic
core
0.5/9/0.5 100x10
9

Table 3-1: List of beams tested and their properties. Panel designs described and TL results
presented in reference [39].

17
A white noise signal was used to drive the shaker, which then excited the
midpoint of the beam through a line displacement. Both the tip motion and the
center motion were measured using lightweight (0.65 gram) accelerometers
placed at the midpoint and one end of the beam. Data was collected using
commercial software (PULSE, B&K, Inc.) using a 10 kHz frequency span and a
resolution of 1600 lines. The software employs a dual FFT and modal bandwidth
measurement in the analysis. The loss factor values were obtained using
commercial software (PULSE, B&K), which used the half-bandwidth method for
calculations. All results were the average of three trials for each sample, and each
trial varied by less than 1.5%. This method was used for all samples with the
exception of Sample MP, for which the suspended beam method was used.

3.2.2 Suspended Beam Method

In some cases (particularly those with high-frequency/high damping),
resonant modes were ill defined when using the Oberst beam method. For such
cases, an alternate testing apparatus was designed and built, as shown in Fig. 3-2.
This method generally yields accurate results for ηk
⊥
l > 10 where η is the loss
factor, k
⊥
is the real part of the wave number, and l is the length of the beam [3].
The ηk
⊥
l value for Sample MP reached this minimum threshold because the end
of the beam had good sand termination. For test articles with lower loss factors,
the half-value bandwidth method used in the Oberst beam method yields accurate
results (when ηk
⊥
l is less than approximately two). The sample sizes remained the
same as the Oberst beam method.
18

Figure 3-2: A modified version of the suspended beam set-up for highly damped samples.
The suspended beam method was used for the sandwich beam with a
viscoelastic layer inserted in the middle (Sample MP). The suspended beam
apparatus (Fig. 3-2) was built to capture the velocities at predetermined positions
based on Eqn (3-4) [3].
[ ]
′ =
−
D
v v
x x
o
o
10
2
1
2
1
log /
( )
(3-4)
η
λ
=
′ D
136 .
(3-5)

In these equations η is the loss factor , D’ is the reduction in vibration level
per unit length, λ is the bending wavelength, v
o
and v
1
are the initial and final
velocities respectively, and x
o
and x
1
are the initial and final positions
respectively. Vibration was measured using a non-contact laser vibrometer. The
19
top of the beam was loosely connected to the supporting frame, and the end of the
beam was embedded in sand to help minimize the reflection of waves. The
surface velocity was measured at one centimeter increments along the beam.
These measurements were then used in Eqns (3-4)-(3-5) to calculate the loss
factor. All results were the average of three trials for each sample, with each trial
within 3% of the other results.
The two methods used in this study differ in the fact that the Oberst beam
method provided a direct measurement of the loss factors, while the suspended
beam method relied on distances and velocities to calculate the loss factor. There
was not a direct correlation between the two methods because the suspended
beam method was constructed specifically for highly damped samples, which
could not be measured using the Oberst beam method. Therefore, a reference
sample for both methods was not feasible, since a damping treatment would be
required in order to test the sample using the suspended beam method.
3.3 Results and Discussion

The loss factor values for the five samples are shown in Fig. 3-3. Four of
the samples showed similar loss factors of 0.01 – 0.03, which were large relative
to Aluminum (0.003). The sample beams also showed a weak dependence on
frequency, with mild perturbations around 1500 Hz, near the coincidence
frequency, which is the frequency at which the wavelength of the panel equaled
the wavelength of the speed of sound in air. The coincidence frequency values
20
were taken from a previous study on transmission loss, in which identical
materials were used [39]. Sample MP, which featured a mid-plane damping layer,
yielded the largest loss factor values.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
100 1000 10000
1/3 Octave Band Center Frequency (Hz)
Loss Factor
G
H
C
MP
SSS-2

Figure 3-3: The loss factors for the five composite sandwich beam samples.
Sample MP featured a viscoelastic sheet inserted at the mid-plane of the
honeycomb core to increase damping. The panel was constructed by slicing a
panel identical to sample C through the mid-plane, then bonding the damping
sheet between the halves using brush-on epoxy. The addition of the viscoelastic
sheet added 0.5 mm to the thickness of the sample. The mid-plane coincides with
the maximum shear force in the beam when a bending load is applied. The effect
of the damping layer was assessed by comparing the damping properties with a
conventional sandwich beam featuring identical skin and core materials (sample
C). The comparison between samples C and MP is shown in Fig. 3-4, a plot of
the loss factor as a function of frequency. The mid-plane damping layer increased
the loss factor of the beam by up to 233%. Fig. 3-4 also shows that the damping
curve for sample MP is similarly parallel to the control panel C over the entire
21
frequency spectrum, demonstrating that the damping from the mid-plane
viscoelastic layer is independent of frequency. This behavior indicates that the
operative damping mechanism is unlike constrained layer damping (CLD), in
which the usual frequency dependent behavior of the viscoelastic core [41] would
be apparent. However, the data shows that the loss factor is independent of
frequency, thus indicating free layer damping.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
100 1000 10000
1/3 Octave Band Center Frequency (Hz)
Loss Factor
C
MP

Figure 3-4: The loss factor comparison between samples C and MP.

The moments for shear stress are zero at the surface of the skin and
maximum at the interface of the skin and core. The shear stress is constant
through the thickness of the core, which carries the entire shear load when a
bending moment is applied [42]. Because the core carries the entire shear load, it
is less likely that the core will constrain the viscoelastic layer. Thus, the data
supports the assertion that the damping effect shown by the MP sample is free
layer damping. The enhancement in damping could also be attributed to the beam
22
acting as two smaller sandwich structures sharing the mid-plane layer as a face
sheet. While the damping is significantly increased with Sample MP, the bending
stiffness was markedly reduced because of the lower shear stiffness of the core
[43].
0
0.01
0.02
0.03
0.04
0.05
0.06
100 1000 10000
1/3 Octave Band Center Frequency (Hz)
Loss Factor
G
C

Figure 3-5: The loss factor comparison between samples G and C.
Comparison of samples G and C revealed the effect of skin material on
damping, as shown in Fig. 3-5. Sample G featured glass/epoxy face sheets, while
sample C featured carbon face sheets. Sample C showed a consistently higher
loss factor than panel G over the entire frequency range. However, it is commonly
accepted that glass fibers have higher damping than carbon fibers [44]. The
apparently contradictory findings shown here can be attributed to two possible
causes. First, the fibers used in the construction of the panel as well as the fiber
treatment and type of adhesives used in the sandwich panel can affect acoustic
properties [45]. In the case of transmission loss, details such as these are minor
relative to the overwhelming structural effects. However, in loss factor
23
measurements, material properties play a larger role, because the dynamic
behavior of the sandwich structure is governed by the individual components of
the panel at mid-to-high frequencies [21]. Second, the material structure of the
carbon skin could be responsible for the higher loss factor than the glass-epoxy
skin. The turbostratic structure of carbon fibers features well-aligned basal planes
which are only weakly bonded, allowing for interplanar sliding. Similar enhanced
damping is observed in other C-based structures, such as carbon nanotube-
reinforced epoxies, and certain cast irons containing graphitic flakes.
Sample SSS-2 featured a thinner core and thicker face sheets than
conventional sandwich designs, thus achieving a subsonic shear wave speed of
approximately two-thirds the speed of sound. Although this is a mechanical
modification rather than a material modification, the results provide insight into
the effect of wave speed on loss factors. This insight can be used to design
materials with varying wave speeds to reduce noise. Testing the subsonic panel
for loss factor was an extension of previous work [39,40]

that showed subsonic
cores could increase the transmission loss of a panel by several decibels. A
subsonic core increases the coincidence frequency and should thus, in principle,
impart superior acoustical performance. However, the subsonic panel exhibited a
lower loss factor than the control panel, as shown in Fig. 3-6. This finding can be
understood by noting that wave speed and damping are distinct parameters and do
not necessarily follow similar trends.
24
0
0.01
0.02
0.03
0.04
0.05
0.06
100 1000 10000
1/3 Octave Band Center Frequency (Hz)
Loss Factor
C
SSS-2

Figure 3-6: The loss factor comparison between samples C and SSS-2.

Sample H featured a para-aramid (Kevlar
@
) core, which was stiffer and
stronger than conventional core materials. This panel yielded loss factor values
that were greater than those of reference sample G, which featured a conventional
meta-aramid (Nomex
@
) core (Fig. 3-7) particularly beyond 3 KHz. The difference
in the loss factors stems from the different inherent stiffness of the meta- and
para-aramid cores. The higher stiffness of Sample H arises from the use of para-
aramid fiber paper, as opposed to meta-aramid fiber paper. In the sandwich
structure, the stiffer para-aramid cores impart a lower modal density to the panel
beyond the coincidence frequency, compared to meta-aramid cores of similar
density [39,46]. This lower modal density enhances the panel damping [39]. The
magnitude of the increase is comparable to the difference in mechanical
properties of the constituent materials since the para-aramid structure can be
molecularly aligned and gives high strength as opposed to the meta-aramid
structure, which cannot be molecularly aligned and has poor strength.
25
0
0.01
0.02
0.03
0.04
0.05
100 1000 10000
1/3 Octave Band Center Frequency (Hz)
Loss Factor
G
H

Figure 3-7: The loss factor comparison between samples G and H.

26
Chapter 4: ACOUSTIC ABSORPTION CHARACTERISTICS OF OPEN-
WEAVE FOAM-FILLED HONEYCOMB SANDWICH STRUCTURES

4.1 Introduction

Honeycomb sandwich structures are widely used in aerospace applications
due to the combination of high stiffness, high strength, and ultra-low weight.
However, sandwich structures are poor noise absorbers, and may in fact generate
noise efficiently by self-resonance. Because of the primary importance of
mechanical efficiency, most sandwich structures are designed for optimal stiffness
and weight, while relatively little attention is focused on noise mitigation [47].
Improving the acoustic performance of these structures has important potential
benefits, including reducing cabin noise in passenger aircraft.

Theoretical and experimental studies have been undertaken to investigate
the acoustic properties of various sandwich panels. For example, Renji et al
determined the modal density of honeycomb sandwich panels while investigating
vibration behavior under acoustic excitation [48] and measured the loss factors to
determine the dissipation of energy throughout the structure [30]. In subsequent
work, Cheong and Zheng predicted the vibroacoustic performance of the
honeycomb sandwich panels in close-fitting enclosures [49]. Additional studies
have reported the transmission loss characteristics of honeycomb sandwich panels
[2,13,19,50], and recent reports have described investigations of the mechanical
properties of foam-filled honeycomb cores [8-11]. Most of the recent studies have
addressed the mechanical behavior of sandwich structures with foam-filled cores,
27
although in one study, the acoustic absorption coefficient of different sandwich
structures was measured [11]. The absorption coefficient is defined as the ratio of
absorbed energy to incident energy on the structure.
There are three distinct types of absorbers: porous absorbers, panel
absorbers, and resonators. Porous absorbers allow air to flow into a cellular
structure. Panel absorbers are non-rigid, non-porous materials that are usually
placed over an air space, vibrating in a flexural mode in response to sound
pressure. Resonators act to absorb sound in a narrow frequency range and include
perforated materials as well as materials that have openings such as holes and
slots. Helmholtz resonators are a classic example of this type of absorber.
The open nature of honeycomb sandwich structures affords opportunities
to implement multiple types of absorbers with minimal weight penalties. In this
study, we consider sandwich designs that incorporate both porous absorbers and
an array of Helmholtz resonators. Foam inserted within honeycomb cells creates
the porous absorber, while the individual cells within the honeycomb core
constitute an array of resonators. Helmholtz resonators are typically comprised of
a cavity and a port. Within the honeycomb sandwich structure, the HC cells
defined cavities, while the ports were created by the apertures in the open-weave
facesheets. Here we analyze the efficacy of Helmholtz resonators combined with
porous absorbers in honeycomb sandwich structures for increasing acoustic
absorption. Direct measurements of absorption coefficients are performed with an
impedance tube following standard protocols.

28
4.2 Experimental Set-Up

4.2.1 Method

The noise reduction coefficient, widely accepted as the measure of
acoustic absorption, was measured for multiple prototype sandwich structures.
The noise reduction coefficient of the samples was measured using an acoustic
impedance tube in accordance with two standard protocols (ASTM E1050 [51]
and ISO 10534-2 [52]). The two standards are similar and describe a two-
microphone, transfer function method of measuring absorption of acoustical
materials. The two-microphone method is shown schematically in Fig. 4-1. The
impedance tube used for the measurements featured interchangeable tubes (29 and
100 mm diameters) for high and low frequency ranges (Bruel and Kjaer 4206
Impedance Tube) [53].

Figure 4-1: The two-microphone set-up for measuring the absorption of acoustical materials.
Schematic is not drawn to scale.

Disk-shaped samples were cut from sandwich panels. The sample sizes
were 29 mm and 100 mm in diameter for the small and large tubes, respectively,
29
and the sample thickness was 13 mm in both cases. The small diameter tube was
used to measure the absorption coefficient across the frequency range of 500 Hz
to 6400 Hz, while the large tube used for measurements from 100 Hz to 1600 Hz.
The effect of air gaps [54-55] around the sample was minimized by precise CNC
machining of the material for each tube size. Measurements were conducted three
times on each sample, remounting the sample between trials. Multiple retests
were performed to determine the effect of sample placement in the tube, and the
results revealed variations of less than 1% between each trial.

4.2.2 Materials

The materials tested in this experiment were honeycomb sandwich
constructions as described in Table 4-1. The honeycomb core (Gillcore® HD132)
was made from aramid paper impregnated with phenolic resin, with a cell size of
5 mm in width and 4 mm in height with a density of 48 mg/cm
3
. The honeycomb
cores were filled with ultra-low-density polyurethane foam and designated
“FISTS” [56]. The cores were bonded to two face sheets, one of which was a
conventional fiberglass composite 0.5 mm thick, and one of which was an open
weave glass fabric composite featuring a grid of square 3 x 3 mm apertures. The
grid of apertures effectively formed an array of Helmholtz resonators.
The samples were situated in the impedance tube such that the facesheet
with the open-weave glass fabric was exposed to the sound source. For
comparison, control samples with conventional composite face sheets were
included, as shown in Fig. 4-2a and Fig.4- 2b.
30

(a) (b)
Figure 4-2: (a) Traditional facesheet vs. (b) Open weave facesheet . The diameter of each sample
shown is 100 mm.

Sample
Name
Skin Material Core Material Other
Closed Glass-Epoxy
Facesheet
HD-132 No foam
ClosedLow Glass-Epoxy
Facesheet
HD-132 FISTS Low Density Foam
ClosedHigh Glass-Epoxy
Facesheet
HD-132 FISTS High Density Foam
Open Open Weave
Glass Fabric
HD-132 No foam
OpenLow Open Weave
Glass Fabric
HD-132 FISTS Low Density Foam
OpenHigh Open Weave
Glass Fabric
HD-132 FISTS High Density Foam
Sample 0 Open Weave
Glass Fabric
HD-132 No foam
Sample 1 Open Weave
Glass Fabric
HD-132 FISTS 12.8 mg/cm
3
foam
Sample 2 Open Weave
Glass Fabric
HD-132 FISTS 8.0 mg/cm
3
foam
Sample 3 Open Weave
Glass Fabric
HD-132 FISTS 4.8 mg/cm
3
foam
Sample 4 Open Weave
Glass Fabric
HD-132 FISTS 3.2 mg/cm
3
foam
Sample 5 Open Weave
Glass Fabric
HD-132 FISTS 3.2 mg/cm
3
foam
Table 4-1: Materials used in the acoustic absorption testing

31
Sample Open and Sample 0 featured similar configurations but were
manufactured using different procedures. Likewise, samples 4 & 5 featured foam
of identical density, but were processed using different methods. Table 4-2 lists
the masses of the samples. The foam-filled sample with the greatest foam density
showed a 6.3% increase in mass for the 29 mm sample and a 10.3% increase for
the 100 mm sample, compared to the sample with empty cells.
Sample Name 29 mm Mass (g) 100 mm Mass (g)
Closed 1.057 12.151
ClosedLow 1.108 13.093
ClosedHigh 1.139 13.111
Open 1.057 12.151
OpenLow 1.108 13.093
OpenHigh 1.139 13.111
Sample 0 1.073 12.042
Sample 1 1.141 13.280
Sample 2 1.121 12.982
Sample 3 1.108 12.704
Sample 4 1.123 12.672
Sample 5 1.094 12.452
Table 4-2: Masses of the sandwich structures.

4.3 Results and Discussion

4.3.1 Initial Testing

The initial test matrix included eleven samples, of which three featured the
perforated, open-weave facing. The frequencies of greatest interest for noise
control in commercial aircraft are those above the coincidence frequency for
honeycomb sandwich structures, which typically falls in the range of 1000-2000
Hz [13]. The absorption coefficients for the samples were measured for the
frequency range from 50-6400 Hz to characterize the global trend. As expected,
the samples with conventional, non-perforated facesheets exhibited low acoustic
32
absorption coefficients (i.e. less than 0.1 over the entire frequency range), as
shown in Fig. 4-3 and Fig. 4-4. These samples represent conventional
honeycomb structures and constitute a baseline or reference point for comparison.
0
0.01
0.02
0.03
0.04
0.05
0.06
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
One-Third Octave Band Center Frequency (Hz)
Closed
ClosedLow
ClosedHigh

Figure 4-3: The normal incidence acoustic absorption for the closed facesheet samples in the large
tube (100 – 1600 Hz).
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
One-Third Octave Band Center Frequency (Hz)
Closed
ClosedLow
ClosedHigh

Figure 4-4: The normal incidence acoustic absorption for closed facesheet samples in the small
tube (500 – 6400 Hz).

33
The results for samples featuring open-weave face sheets (with and
without foam-filled cells) are shown in Fig. 4-5 and Fig. 4-6. Because the
absorption coefficients for the lower frequencies measured in the large impedance
tube were much less than for the higher frequencies measured in the small tube,
the scale range has been reduced to portray the large tube results more clearly.
With a reduced scale in Fig. 4-5, it appears that the samples filled with high-
density foam have a slightly higher absorption coefficient than the samples filled
with low-density foam, in contrast to the results shown in Fig. 4-6. However, the
difference in acoustic coefficient values is within experimental error and is
considered negligible. When the plots are matched up by frequency, it is clear that
the low frequency data from the large tube is consistent with the high-frequency
data from the small tube between the overlap areas of 500-1600 Hz.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
100 125 160 200 250 315 400 500 630 800 1000 1250 1600
One-Third Octave Band Center Frequency (Hz)
Open
OpenLow
OpenHigh

Figure 4-5: The normal incidence acoustic absorption for the open-weave facesheet samples in
the large tube (100 – 1600 Hz).

34
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300
One-Third Octave Band Center Frequency (Hz)
Open
OpenLow
OpenHigh

Figure 4-6: The normal incidence acoustic absorption for the open-weave facesheet samples in
the small tube (500 – 6400 Hz).

Overall, the data from the initial testing of the samples showed that lower-
density foams yielded larger acoustic absorption coefficients than higher-density
foams at frequencies greater than 1800 Hz. At frequencies below 1800 Hz, the
differences among the absorption coefficients for the foam-filled samples were
minimal. These tests also confirmed that standard composite facesheets exhibited
acoustic absorption coefficients in the lower range of 0.05 – 0.15. However, the
data also indicated that further investigation was required to establish the
relationship between the foam density and the absorption coefficients of the
honeycomb structures.

4.3.2 Testing of Varying Foam Densities

Six samples (Samples 0-5) were prepared to investigate the relationship
between foam density and acoustic absorption coefficients. A sample without
foam filling was also included for reference. The results of these trials are shown
in Fig. 4-7 & Fig. 4-8. As expected, the sample without foam filling exhibited the
lowest acoustic absorption coefficient over all frequencies.
35
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
One-Third Octave Band Center Frequency (Hz)
Sample 0
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5

Figure 4-7: Normal incidence acoustic absorption for open-weave facesheet samples in the large
tube (100 – 1600 Hz).

0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300
One-Third Octave Band Center Frequency (Hz)
Sample 0
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5

Figure 4-8: Normal incidence acoustic absorption for the open-weave facesheet samples in the
small tube (500-6400 Hz).

For frequencies below 1250 Hz, Sample 1, which was filled with the
highest density foam (12.8 mg/cm
3
), yielded the highest absorption coefficient,
while Sample 2, with a foam density of 8.0 mg/cm
3
, yielded the second highest
absorption coefficient. The HC samples filled with foams of density 4.8 mg/cm
3
36
and 3.2 mg/cm
3
had the next highest absorption coefficients. Filling the
honeycombs with higher density foam resulted in higher absorption coefficients
over the lower frequency range of 500 – 1250 Hz. Note that the absorption
coefficients for cores filled with foams of different density were indistinguishable
at frequencies below 315 Hz.
At frequencies greater than 1250 Hz, there was an apparent shift in the
trend between foam density and acoustic absorption coefficient, as shown in Fig.
4-8. At these higher frequencies, cores filled with the highest density foam
showed the lowest absorption coefficient (among samples with foam-filled cores).
Samples 2-5 yielded the highest absorption coefficients (0.94), which were
reached in the range of 4000 – 5000 Hz (see Fig. 4-8). Throughout this frequency
range, Samples 3 and 5 showed the greatest coefficient values. In fact, Samples 3
and 5 showed almost identical behavior, despite the fact that the core densities
varied by 1.6 mg/cm
3
. Sample 4, on the other hand, which had a core density
identical to Sample 5, showed absorption coefficients greater than Samples 3 and
5 (by up to 0.25).
The apparent change in the dependence of absorption coefficient on foam
density between the lower frequency range and the higher frequency range is
counterintuitive. In general, higher density cores tend to be associated with higher
absorption coefficients at higher frequencies because the denser porosity of the
foam offers more resistance to sound waves [57]. Hence, samples 2-5 would be
expected to show inferior acoustic absorption characteristics at higher
37
frequencies. However, the reverse was in fact observed. These results indicated
that the absorption coefficients could be expected to decrease for higher density
foams at higher frequencies. This counterintuitive behavior can also indicate an
upper frequency limit on the effectiveness of combining porous absorbers with
Helmholtz resonators. Combining these noise control techniques is best suited for
the lower frequency range, which is often the range of interest for aerospace and
automotive applications.
The measured absorption coefficients showed a strong dependence on
frequency - coefficients increased with increasing frequency, as shown in Fig. 4-7
and Fig. 8. At 2250 Hz, the absorption coefficient for the HC sample filled with
high-density foam (12.8 mg/cm
3
) intersects with the data curves from the HC
samples filled with lower density foams, and falls below these foams for higher
frequencies (Fig. 4-8). The sample with the highest foam density showed weaker
frequency dependence than the lower density samples. Also, at higher
frequencies, the absorption coefficients of Samples 2-5 converged to a similar
value. This behavior is consistent with the theoretical predictions of Wang and
Torng [58] that described the propagation of sound through porous materials, as
well as the work of Smith and Parrott, who found that the resistance to the sound
pressure waves increases when the bulk density increases [59]. The results
reported here demonstrate that frequency and material density are two critical
factors affecting acoustic absorption characteristics of honeycomb sandwich
structures.
38
The improvements in acoustic absorption achieved here resulted from
combining two measures – porous absorbers and Helmholtz resonators in the
form of foam-filled cells with a perforated facesheet in a sandwich structure.
Filling the HC cells with closed-cell foam increased the acoustic absorption of all
samples by as little as 3% in the lower frequencies, and up to 100% at the higher
frequency range, as expected [60-61]. On the other hand, the resonators increased
absorption by 233% at lower frequencies, and by as much as 371% at the higher
frequencies when filled with foam. The shape of the honeycomb cell resulted in
a broad bandwidth due to the wide cavity of the cell in comparison to the narrow
opening of the facesheet weave. The array of Helmholtz resonators, formed by the
grid of apertures created by the perforated facesheets, multiplied the effect of the
absorbent action intrinsic to a single resonator.
The effectiveness of the two measures (resonators and absorbers) is well
documented in previous work, although the relative effectiveness of each measure
is an open question. Replacing the standard facesheet with the open-weave
perforated facesheet (as shown by the comparison between Sample Closed and
Sample Open) produced a greater increase in absorption coefficient than filling
the honeycomb cells with foam (as shown by the comparison between Sample
Open and Sample Open High). A consideration for future studies would be to
explore the effect of filling the HC cells with open-cell foam as opposed to
closed-cell foam. Open-cell foams should allow the air mass within the
honeycomb cells to resonate through the cavity of the cell unconstrained by the
cell walls of the foam.
39
Chapter 5: SEMI-ACTIVE VIBRATION SUPPRESSION OF
HONEYCOMB SANDWICH STRUCTURES

5.1 Introduction

During the powered flight phase of a rocket launch, the structure experiences
severe vibrations that constitute a significant design factor for satellites and on-
board electrical components. Damping measures that reduce launch vibrations
will improve the reliability of the on-board systems and reduce development
costs. Damping of mechanical vibrations can also reduce structure-borne sound
and noise transmission through the vibrating structure. Passive measures to
mitigate vibrations and noise, such as additions of viscoelastic materials, are
common techniques, but the addition of weight makes it less practical for
aerospace applications. Consequently, there has been increasing interest in semi-
active vibration control using piezoelectric materials, which transform electrical
energy into strain energy and vice versa. These materials can be embedded in a
structure and used to suppress vibration, either as an actuator, a sensor, or a
transducer.
Methods to suppress vibrations can be classified as active, passive, or semi-
active, and the relative effectiveness of these methods, including the possibility of
combining the methods, has been reported [62-65]. Active vibration suppression
methods typically employ piezoelectric actuators powered by an external power
source and may be unstable. Passive methods generally are more stable and less
costly than active methods, but tend to have poorer damping performance.
Attempts have been made to improve passive damping by using piezoelectric
40
materials shunted with a passive electrical circuit [66], as well as by applying
passive damping methods to two-dimensional structures [67-68]. A quite different
approach to enhance damping involves shunting a piezoelectric transducer on an
inductive shunt circuit for a short time at each peak of a strain yielded in the
transducer by a vibration [69]. By briefly shunting the transducer, the polarity of
the stored charge is reversed by the effect of the counter electromotive force of
the inductor, and the restored charge generates a vibration-suppressing force. As a
result, the energy stored in the transducer is recycled rather than immediately
dissipated. This is the underlying principal of the energy-recycling semi-active
(ERSA) method [16,17,70], which is simple, lightweight, and stable. The ERSA
method differs from the conventional semi-active method [71]

because the
electrical energy transformed by the piezoelectric transducers is re-used, and is
not dissipated. The approach is described and reviewed in the work by Onoda,
Makihara, and Minesugi [18].
When considering vibration suppression methods, it is important to choose a
method that supports the launch environment and is also reliable, lightweight,
compact, and has a power resource that does not detract from the launch. The
ERSA method meets these criteria because system parameters are controlled
without an external energy source, and the method is more stable than active
methods, while delivering superior damping performance compared to passive
methods.

41
Honeycomb sandwich structures are widely used in launch structures, such
as the thrust tube, deck panel, and substrate of the satellite. Honeycomb sandwich
structures are also used in commercial aircraft and in various applications where
high stiffness and minimal weight are required. However, sandwich panel
designs, which optimize high stiffness and low weight, result in efficient sound
radiators. The broadband acoustical excitation of a structure generally results in a
predominant forced response at the excitation frequencies and a relatively small
resonant vibration response. These responses affect the amount of sound
transmitted through the panel by changing the vibration pattern of the panel in
relation to the panel at rest. In the present work, we employ the ERSA method to
reduce the amount of sound transmitted through a sandwich panel by reducing
panel vibrations at a targeted frequency, the first natural mode of the structure.
The purpose of this study is to determine the quantitative relationship between
vibration suppression and acoustic damping when the ERSA vibration
suppression method is employed with a honeycomb sandwich panel. The ERSA
method is expected to simultaneously reduce the sound transmitted through the
panel and the panel vibration.

5.2 Experimental Set-Up

The sandwich panel was comprised of thin fiberglass face sheets and an
aramid paper honeycomb core (Nomex
@
). The panel dimensions were 500 mm x
400 mm. The piezoelectric materials used for the ERSA method were PZT
(Pb(ZrTi)O
3
) ceramics 40 mm × 10 mm × 0.5 mm.
42

Figure 5-1: Schematic of subfloor test chamber experiment set-up.

The experimental setup featured a subfloor source chamber, which
produced a normal incidence source field [72-73]. A schematic of the testing
apparatus is shown in Fig. 5-1. The panel was clamped on all four sides, and
microphones were positioned such that the distance between any reflecting
surface (i.e. the honeycomb sandwich panel) was at least 1/4
th
the wavelength of
the lowest frequency tested. For these experiments, the microphones were placed
0.195 m above and below the center of the panel to measure the incident and the
transmitted sound. Locations for the accelerometers and piezoelectric transducers
on the panel were determined by modal analysis. The targeted mode for vibration
suppression was the first bending mode for panel excitation at 280 Hz. The 20
piezoelectric transducers were positioned to maximize the vibration suppression
of the panel for the first mode shape, and the accelerometers were positioned to
effectively measure the magnitude of the panel response when excited by acoustic
43
pressure. The sensor transducer was positioned to measure the phase of the
vibration mode at the maximum displacement of the panel. These arrangements
are shown in Fig. 5-2. The accelerometers and transducers were bonded to the
panel with a thin layer of adhesive to avoid unfavorable load translations between
the panel and the transducer. The transducers were bonded at similar positions on
opposite surfaces of the panel to capture the full bending motion of the panel
during acoustic excitation. Thus, similar displacements of opposite sign occurred
in each transducer pair.

Figure 5-2: Accelerometers and piezoelectric transducers attached to honeycomb sandwich panel
mounted on subfloor source chamber.

An electrical circuit was employed with a 10× ratio between the first
natural frequency of the honeycomb panel (280 Hz) and the first natural
44
frequency of the electrocircuit (2800 Hz) [16,17,18]. The 10× ratio allowed the
charge stored in the transducers to be moved quickly. Switching was executed at
the maximum displacement of the panel, and thus the charge generated a force
that worked to suppress the vibration. The control performance degraded as the
time to move the charge increased. A slow-moving charge decreased the duration
of the force that suppressed the vibrations. Therefore, it was necessary to increase
the natural frequency of the electrical circuit to a much higher frequency than the
frequency of the controlled mode. The capacitance and resistance of the group of
transducers were measured to confirm that values were within the expected range,
which was derived from individual measurements from a single transducer. The
phase difference between the voltage of the sensor transducer and a group of
transducers was measured, and the control system was adjusted to determine an
optimized switching timing.

Figure 5-3: Block diagram of energy-recycling semi-active vibration suppression method.

45
The ERSA method is depicted in the block diagram in Fig. 5-3. The
continuous ERSA process consisted of six basic steps: (1) the panel was excited
by white noise sound waves from the speakers, which had a frequency range of 46
Hz – 20 kHz, within the chamber, (2) the sensor transducer generated a voltage,
(3) the sensor transducer voltage was sent to the computer via an A/D converter,
(4) the switching timing was calculated by the control software, (5) the switching
timing signal was sent to a shunt circuit, and (6) the group of transducers was
semi-actively controlled.
Power spectral density data was acquired from the microphones inside and
outside the subfloor source chamber to measure the acoustic damping as defined
by the power carried by the acoustic wave. The sensor transducer generated a
voltage that controlled the switching timing of the ERSA circuit. The five
accelerometers monitored the vibration response of the panel, while the
piezoelectric transducers suppressed vibrations. The transducers were controlled
by the circuitry used in the semi-active method was recycling the energy. At 280
Hz, the first resonant mode of the panel, voltage versus time data was collected to
verify that the ERSA circuit was operating efficiently.
Previous studies have shown that transducer connections can influence the
extent of damping for the ERSA method [16,17]. Thus, in the present work,
transducers were divided into multiple sets. Transducers within a set were
connected in parallel, and all sets were connected in series. The control efficiency
was assessed by changing the number of transducers in a set while keeping the
total number of transducers constant. The voltage measurement system for the
46
group of transducers can also affect the extent of damping when the configuration
is close to an all-series format. Therefore, experiments for such configurations
were performed with and without the use of the measurement system. The
combinations included all transducers set in series (with and without measurement
system), 10 parallel groups in series (with and without measurement system), 5
parallel groups in series, and 4 parallel groups in series. A configuration was also
tested without the ERSA components for use as a control sample. The ERSA
damping approach failed to suppress vibrations for configurations with less than 4
parallel groups connected in series. Each configuration was tested three times.

5.3 Results and Discussion

Power spectral densities (PSD) for the sound intensity pressures of the two
microphones were calculated to compare the sound intensity pressure between the
inside of the chamber and the outside of the chamber. This measurement provided
an indication of the degree of acoustic damping in the system. The frequency
response function (FRF) was calculated using the sound pressure measured by the
inside microphone and the acceleration measured by the accelerometer placed at
the center of the panel to obtain the relation between the sound pressure and the
induced dynamic behavior of the sandwich structure. The FRF value was
calculated using the real and imaginary parts of the frequency response, and the
magnitude had units of G/Pa. The FRF calculations provide insight into the extent
of vibration suppression achieved by ERSA damping in the present system.
47
The PSD and FRF data are summarized in Tables 5-1 and 5-2. The data
effectively relate the extent of vibration suppression and acoustic damping
achieved employing the ERSA method. For example, lower PSD values indicate
reduced sound transmission through the panel, while lower FRF values indicate
that the magnitude of the panel vibrations resulting from the applied sound waves
decreased. The maximum displacement occurred at the center of the panel
because of the shape of the first mode. Consequently, the amplitude values
acquired from the accelerometer located at this position were used to quantify the
degree of vibration suppression.
PSD (W/Hz) PSD Change FRF (G/Pa) FRF Change
No Control 0.161 -- 9.41 --
Series 0.138 -14.3% 8.72 -7.3%
10 Groups 0.147 -8.7% 9.02 -4.1%
5 Groups 0.154 -4.3% 9.16 -2.7%
4 Groups 0.168 4.3% 9.35 -0.6%
Table 5-1: Acoustic damping (PSD) and vibration suppression (FRF) measurements when the
measurement system did not affect the data.

PSD (W/Hz) PSD Change FRF (G/Pa) FRF Change
Series 0.168 4.3% 9.38 -0.3%
10-Groups 0.156 -3.1% 9.12 -3.1%
Table 5-2: Acoustic damping (PSD) and vibration suppression (FRF) measurements when the
measurement system did affect the data through being connected.

The measurement system for the voltage of the group of the transducers
affected the amount of vibration suppression and consequently the amount of
acoustic damping when the circuits were configured in an all-series format or in
the 10-groups format shown in Tables 5-1 and 5-2. The decrease in vibration
suppression was attributed to the low input impedance of the nominal A/D
48
converter in the measurement system. The A/D converter employed capacitors to
measure the voltage. Normally, the amount of the charge dissipated by the
capacitors is smaller than the charge flowing in the circuit. However, because the
amount of charge flowing in the circuit used in this experiment was extremely
small, the test results were affected by the charge dissipated by the A/D converter.
The primary effectiveness of the ERSA system stems from the potential to store a
maximum charge in the transducers to suppress vibration. Therefore, when some
of this charge is diverted and used to power the measurement system, the potential
to suppress the vibrations is correspondingly reduced. This is evident in the
tabulated data (Tables 5-1 and 5-2), because the wasted charge degrades the
control efficiency. This affects both the all-series and the 10-group configurations
more than the 5- or 4-group configurations because there is less charge flowing
through the system when it is at or near an all-series format. The 5- and 4-group
circuits have sufficient charge in the system to power the measurement system as
well as the components of the ERSA system. To eliminate the problem of charge
degradation, the measurement system was disconnected during measurements,
resulting in a 14.3% reduction in the PSD and a 7.3% reduction in the FRF.
Subsequently, the measurement system was connected only when collecting time
history data of the voltage of the transducer group to verify that the ERSA system
was operating as designed (Fig. 5-4). Note that the measurement system was not
an intrinsic part of the ERSA system.
49

Figure 5-4: Shunt circuit with measurement system attached. The measurement system is
indicated by the R
M
resistor in this circuit.

A trend became apparent when examining the results from the different
configurations (not including the series and 10-group when the measurement
system is used). As the circuit configuration approached an all-parallel
configuration, the PSD and FRF measurements indicated decreases in acoustic
damping and vibration suppression. The all-parallel configuration was not tested
because the voltage produced was insufficient to power the ERSA components.
Circuits predominantly connected in series produced higher voltage and less
charge flow through the circuit, while circuits connected in parallel produced
higher charge flow through the circuit and less voltage. When the circuits were in
a configuration that produced insufficient voltage to power the system, vibration
suppression was reduced because the available voltage was restricted by the
diode’s forward voltage, the lower limit of voltage that allowed current to flow
50
forward in a diode. Consequently, the available voltage for vibration suppression
was decreased by this forward voltage. Ideally, the forward voltage should be
zero, but the circuit produced a forward voltage that required the system to
produce at least 3-4 volts to overcome this forward voltage. The two options
available for increasing the voltage produced were to increase the number of
series connections or to increase the output of the speakers. In the present
experiments, the speaker output was held constant to produce self-consistent
results throughout all trials.
A direct relationship was observed between the amount of acoustic
damping and the amount of vibration suppression for the honeycomb sandwich
structure. The most efficient configuration resulted in a 14.3% reduction in the
PSD and a 7.3% reduction in the FRF. Other ERSA configurations also produced
reductions in sound transmission and panel vibrations. The average ratio of the
increase in acoustic damping to the increase in vibration suppression was
approximately 2:1, as shown in Table 5-1. These ratios were achieved by the
configurations that were not adversely affected by the measurement system. The
exception was the 4-groups configuration, which did not conform to the 2:1 ratio
exhibited by other samples. Note that for this particular configuration, the voltage
in the shunt circuit approached the lower limit set by the forward voltage of the
circuit. The increase in sound transmission produced by the 4-group configuration
is not completely understood, and awaits further investigation.

51
One limitation encountered with the experimental ERSA setup was the
relatively slow speed with which the computer acquired and processed the data.
Computer speed limited the response speed of the switches and consequently
limited the capacity to suppress vibrations using the ERSA system. However,
implementing the ERSA system led to a maximum 14.3% increase in acoustic
damping when vibrations were suppressed by 7.3%. Faster processing hardware
may well enable greater acoustic damping and vibration suppression.

52
Chapter 6: MEASUREMENTS OF WAVE SPEEDS OF HONEYCOMB
SANDWICH STRUCTURES

6.1 Introduction

Lightweight honeycomb (HC) sandwich structures are used in a wide
variety of applications where high stiffness and low weight is desired. These
structures typically feature orthotropic HC cores bonded to high-modulus
laminate skins. HC sandwich structures are designed for mechanical performance,
but generally have poor acoustical performance because they are optimized for
high stiffness and low weight. As a result, approaches are sought to improve
acoustical performance without compromising the mechanical performance of the
structures [12-14].
Basic understanding of wave speed characteristics of HC sandwich structures
provides useful insight for noise control solutions. For example, knowledge of the
frequency-dependent wave speed is useful for designing noise control solutions
for a given load-bearing structure [21]. Furthermore, Davis analyzed the wave-
speed dependence of transmission loss (TL) for HC panels and concluded that the
key to increasing the TL of HC panels was to achieve a subsonic bending wave
speed (e.g., two-thirds the speed of sound) for the greatest possible frequency
range [20]. Such reports indicate the potential utility of wave speed data for
differentiating various damping treatments and other means of noise mitigation.
HC sandwich structures exhibit frequency-dependent dynamic behavior
that influences the structural response to acoustic excitation [15]. The wave
speeds are controlled in different frequency regimes by different components of
53
the structure. There are three distinct regimes – pure bending, core shear, and
facesheet bending - each associated with different frequency ranges [2]. Pure
bending of the entire structure occurs at low frequencies and is controlled by
stiffness and resonance. Core shear occurs at mid-frequencies and is mass-
controlled. At higher frequencies, facesheet bending occurs and this region is
controlled by wave coincidence and stiffness. The wave speed in the structure
does not abruptly change from one regime to the next as frequency changes. For
aerospace applications, the primary concern lies in the low-to-mid-frequency
ranges. Therefore, in the present study we focus on bending and shear wave
speeds.
Sound transmission loss is one of the primary metrics used to evaluate the
acoustical performance of honeycomb sandwich structures. Transmission loss
(TL) is defined as the difference between incident energy and the transmitted
energy through a material or structure – it is also an indication of the acoustic
performance of the material as a noise barrier between two spaces. Klos, et al
demonstrated the acoustical benefit, as measured by transmission loss, of reducing
the wave speed for transverse vibration in HC sandwich panels [74]. Rajaram, et
al observed that core shear wave speed has a strong influence on transmission loss
[13]. Davis performed statistical energy analysis on HC structures and concluded
that radiation efficiency is a function of the bending wave speed in the structure
[20]. These findings demonstrate a need to validate the analytical predictions
through systematic measurements of wave speeds in HC structures.

54
Although wave speeds can be calculated using various approaches,
measurements of wave speeds are rarely reported because of the associated
experimental difficulties. Possible approaches to measuring wave speeds include
(1) direct measurement of a wave over a period of time and (2) propagation phase
measurements [75]. However, these methods involve inherent limitations because
bending waves are dispersive and it is difficult in practice to distinguish which
wave (bending or shear) is being measured. Furthermore, the reverberant
vibration field interferes with direct measurements [21]. The wave-speed
measurement method employed in the present study allows one to distinguish the
wave being measured. In addition, propagation phase measurements are not used,
thus avoiding the influence of the reverberant vibration field.
The purpose of this work is to validate the influence of wave speeds,
particularly shear wave speeds, on the transmission loss of HC panels predicted
by the analyses of both Kurtze and Watters [19] and Davis [20]. In this study, we
measure the bending wave speeds of HC structures with different design
parameters and distinguish the transition between panel bending and shear wave
motion. The wave speeds for the HC structures are then compared to previously
published TL measurements performed on identical structures.

6.2 Experimental Set-Up

6.2.1 Method

Wave speed measurements were performed on HC beams using the modal
approach. A shaker was used to excite the beams with a random noise signal. An
55
impedance head was attached to the shaker to measure the input force, and a laser
vibrometer was used to collect velocity data along the surface of the beams. The
beam vibration velocity was measured at 64 equally spaced locations along the
beam. The schematic of the test apparatus is shown in Fig. 6-1. Suspending the
beams from the supporting structure with lightweight string

simulated the free-
free boundary condition [3]. A homogenous aluminum reference beam was tested
to calibrate the measurement set-up. The measured natural frequencies of the
reference beam were within 3-5% of calculated values [76].

Figure 6-1: Schematic of experimental set-up.

Modal analysis is based on the relationship between the modal shape and
the wavelength, which is equal to wave speed divided by frequency. A simple
formula relates the speed of both bending and core shear waves to the measured
n
th
resonance frequency, f
n
, for a beam of length L, as shown in Eqn. (6-1).

c f
f L
n
n
n
( )=
2
(6-1)

56
A critical aspect of modal analysis measurements is measuring both the
modal shape and the vibration spectrum. The modal shape identifies the modal
orders of the individual modal frequencies and serves as a means to monitor and
distinguish the desired wave types (i.e., bending and shear modes as opposed to
torsional modes). The utility of the modal analysis method diminishes at
frequencies above 3kHz, where it becomes difficult to distinguish individual
modes.

6.2.2 Materials

The material properties and dimensions of the eight commercial-grade HC
beam samples are listed in Table 6-1. Beams A-D and SSS-2 featured composite
skins of carbon fiber/phenolic, while beams F-H featured composite skins of glass
fiber/epoxy. All beams featured hexagonal HC cores made from a pararamid fiber
paper (Nomex
®
), except for beams D and H, which featured cores made of an
aramid fiber paper (Kevlar
®
). Beam SSS-2 featured an unusual core designed for
a subsonic shear wave speed (two-thirds the speed of sound). This beam was
tested to validate the predictions of Davis [20]

and to compare with the results of
Rajaram [13]. The 6061-T6511 aluminum reference beam was 914.4 × 50.8 ×
12.7 mm. The HC sandwich beams were 927.1 mm long, 50.8 mm wide, and 10.2
mm thick. Narrow beams were chosen to facilitate identification of modal shapes
and measurements.

57
Panel Skin Core Cell
Size
(m)
p
c
(kg/m
3
)
t
c
(m)
p
sk

(kg/m
3
)
t
sk

(m)
G
c

x10
6
Nm
-
2
E
sk

x10
9
Nm
-
2
A Carbon Nomex 0.004 144 0.0096 1600 0.0003 108 100
B Carbon Nomex 0.003 80 0.0096 1600 0.0003 63 100
C Carbon Nomex 0.003 48 0.0096 1600 0.0003 32 100
D Carbon Kevlar 0.004 72 0.0096 1600 0.0003 115 100
F Glass Nomex 0.004 144 0.0096 1900 0.0003 108 20
G Glass Nomex 0.003 48 0.0096 1900 0.0003 42 20
H Glass Kevlar 0.004 72 0.0096 1900 0.0003 115 20
SSS-
2
Carbon Nomex 0.004 28.8 0.0087 1600 0.0006 18 100
Table 6-1: Dimensions & material properties of honeycomb sandwich beams

58
6.3 Results and Discussion

6.3.1 Modal Analysis
The wave speeds were measured for two categories of sandwich structures
– one with carbon laminate skins and the other with glass fiber laminate skins.
Within each category, simple core parameters, including core density, cell size,
and skin material, were varied to determine the effects on wave speeds. In
addition to the two primary categories, a subsonic panel was produced to test the
analytical predictions of Davis and to compare with the TL measurements
reported by Rajaram [13,20]. The wave speeds were plotted with respect to Mach
speed to illustrate differences between the subsonic and supersonic samples. The
speed of sound in air was assumed to be 549 km/hr to normalize the wave speeds
to the Mach speed.
The wave speeds of the beams with carbon skins and HC cores of different
density and materials are presented in Fig. 6-2. The samples all exhibit increases
in wave speed with increasing frequency, which is indicative of bending waves.
Bending waves are dispersive and the wave speeds exhibit a parabolic
dependence on frequency, while shear waves are non-dispersive and exhibit a
linear dependence [21]. The Sample SSS-2 exhibits a transition from a parabolic
dependence to a linear dependence at frequencies above 1500 Hz. Therefore, the
transition from bending to shear waves for the Sample SSS-2 was identified by
the point on the wave speed versus frequency plot where the parabolic
dependence changed to a linear dependence. Samples A-D exhibited a continuous
parabolic curve, indicating that bending wave speeds occurred for frequencies

59
below 3000 Hz. These results are consistent with predictions that the bending to
shear wave speed transition for similar specimens occurred at ~3500 Hz [21].
0
1
2
0 500 1000 1500 2000 2500 3000
Frequency, Hz
Sample A
Sample B
Sample C
Sample D
SS
Air

Figure 6-2: Wave speeds normalized to Mach speed of beams with carbon fiber laminate skins
and honeycomb core.

The results presented in Fig. 6-2 show that the core shear modulus
strongly affected the wave speed trends. The influence of the core material was
evaluated by comparing Sample D, constructed with the high-shear-modulus
Kevlar
®
core, to Samples A-C, which featured Nomex
®
cores, which exhibited
relatively lower shear moduli. In general, cores with higher shear moduli yield
higher wave speeds [13]. The wave speeds for Sample D were greater than those
of Samples A-C. The subsonic core of Sample SSS-2 had the lowest core shear
modulus and thus exhibited the slowest wave speeds of this group of samples. On
the other hand, Sample D (with the high-modulus Kevlar core) displayed the
fastest wave speeds. Samples A, B and C had intermediate values of core shear

60
moduli, and yielded wave speeds that were intermediate between those of
Samples D and SSS-2. The wave speed values for Samples A-C were similar
even though their shear moduli were 108 × 10
6
Nm
-2
, 63 × 10
6
Nm
-2
, and 32 × 10
6

Nm
-2
respectively because the transition from panel bending regime to core shear
regime did not occur within the measured frequency range. The skin and core
thicknesses for these samples were identical. Therefore, in this frequency range,
the wave speeds would also be similar regardless of the shear moduli of the cores.
Samples A and B were analyzed to determine the influence of core cell
size on wave speeds. Sample A had a larger cell size and higher core density
compared to Sample B. The wave speeds for these samples were similar across
the frequency range tested. The results led to the conclusion that core cell size did
not have a significant effect on wave speed.
The wave speeds of the second family of three beams with glass fiber
laminate skins and honeycomb cores are shown in Fig. 6-3. Samples A-D featured
carbon fiber laminate skins and showed steeper slopes for wavespeeds at low
frequencies and approached Mach speeds at ~700 Hz. In comparison, the
wavespeeds of samples F, G and H, which featured glass fiber laminate skins,
showed lower slopes and approached Mach speeds at frequencies greater than
1000 Hz. Samples F, G and H had cores comparable to Samples A-D, and all
panels had similar dimensions, from which we infer that the skin material strongly
influenced the wave speed at low frequencies. In particular, the stiffer carbon
laminate skins resulted in higher wave speeds compared to the glass fiber
laminate skins. The wave speeds in Fig. 6-3 also showed a parabolic shape, which

61
indicates bending waves for Samples F, G, and H. The panel bending regime
controlled wave speeds in this range, and consequently the wave speed values
were similar despite the different core shear moduli.
0
1
2
0 500 1000 1500 2000 2500 3000
Frequency, Hz
Sample F
Sample G
Sample H
Air

Figure 6-3: Wave speeds normalized to Mach speed of beams with glass fiber laminate skins and
honeycomb core.

Samples F and G were evaluated to assess the influence of core cell size
on wave speeds. Sample F had a larger cell size and higher core density compared
to Sample G. The wave speeds for these samples were similar across the
frequency range tested. The results indicate that the cell size did not significantly
affect wave speeds. These results were consistent with results from the carbon
skin samples.
Samples F and H were also considered to assess the influence of core
material on wave speeds. Sample F consisted of a Nomex core, while Sample H
had a Kevlar core. The wave speeds for Sample H were greater than the wave

62
speeds for Sample F, indicating that higher core shear modulus results in faster
wave speeds. The wave speeds were similar for Samples F and G although the
shear moduli of the cores were different.
The difficulty in differentiating modal shapes at frequencies above 3000
Hz was a limitation of the modal analysis method. Consequently, this method had
a limited frequency range and the transition from bending to shear wave speeds
for the samples could not be measured using this method as that transition occurs
around 3200 Hz or higher. Sample SSS-2 was the exception to this limitation
because the subsonic core caused a bending to shear wave speed transition at a
lower frequency that occurred within the scope of this method.

6.3.2 Transmission Loss
The wave speed characteristics of honeycomb sandwich structures are
closely linked to the sound transmission loss characteristics. Rajaram measured
the transmission loss for the same set of honeycomb sandwich structures in Table
1 [13]. Fig. 6-4 shows the transmission loss for the panels with carbon skins and
Fig. 6-6 displays the transmission loss for the panels with glass skins. Because the
mass of the panels varied, the performance was evaluated using the mass law
deviation (MLD), defined as the difference between the measured transmission
loss and the mass law predicted transmission loss. A positive or higher value for
MLD indicates superior acoustical performance, while a negative or lower value
for MLD indicates inferior acoustical performance. These plots are displayed in
Fig. 6-5 and Fig 6-7 for carbon and glass skins respectively. There was little

63
variation in the MLD values for the supersonic samples. However, the MLD for
the subsonic sample was significantly greater than those of the supersonic
samples, while the wave speeds were significantly lower. Core cell size and skin
material had negligible effects on the measured values of TL and wave speed.
0
5
10
15
20
25
30
35
40
45
50
100 1000 10000
Frequency, Hz
Sample A
Sample B
Sample C
Sample D
Sample SSS-2

Figure 6-4: Transmission loss of panels with carbon fiber laminate skins and honeycomb core
[13].

-15
-10
-5
0
5
10
15
20
100 1000 10000
Frequency, Hz
Sample A
Sample B
Sample C
Sample D
Sample SSS-2

Figure 6-5: Mass law deviation (MLD) of panels with carbon fiber laminate skins and honeycomb
core [13].

64
The transmission loss measurements on similar panels resulted in several
key findings [13]. (1) Core density and transmission loss were inversely related,
as core density increased the transmission loss decreased. The comparison
between Samples A and C (carbon skins) and Samples F and G (glass skins)
demonstrated this relationship. (2) Samples with high shear modulus Kevlar cores
(Samples D and H) showed higher TL values at higher frequencies than the
samples with Nomex cores. (3) Skin material did not significantly influence the
panel TL. (4) Varying the cell size also did not significantly influence the panel
TL. (5) The subsonic core of Sample SSS-2 displayed the highest transmission
loss of all samples.
0
5
10
15
20
25
30
35
40
45
50
100 1000 10000
Frequency, Hz
Sample F
Sample G
Sample H

Figure 6-6: Transmission loss of panels with glass fiber laminate skins and honeycomb core [13].

65
-15
-10
-5
0
5
10
15
20
100 1000 10000
Frequency, Hz
Sample F
Sample G
Sample H

Figure 6-7: Mass Law Deviation (MLD) of panels with glass fiber laminate skins and honeycomb
core [13].

The present wave speed measurements are closely aligned with previously
reported TL measurements [13]. Overall, transmission loss increases with reduced
wave speeds, particularly when the wave speeds are reduced to subsonic levels,
which can be achieved by decreasing the shear modulus of the core. This
phenomenon is best illustrated by the behavior of the panel with the subsonic core
(Sample SSS-2), in which the transition from bending wave speeds to shear wave
speeds occurred at a lower frequency than the supersonic samples. This low-
frequency transition accounts for the superior transmission loss performance of
Sample SSS-2. By shifting the transition to shear wave speeds to a lower
frequency, the coincidence frequency is shifted to higher frequency. Past studies
have shown that delaying the onset of the coincidence frequency also reduces the
acoustic radiation from the panel [20].

66
Chapter 7: CONCLUSIONS

The conclusions are presented chapter wise and the vital conclusions are
listed towards the end of this chapter. The effect of material choice and structural
parameters on the loss factors of honeycomb sandwich structures was
investigated. Then the influence of open-weave construction and various foam
densities of honeycomb sandwich structures on acoustic absorption performance
were experimentally evaluated. The quantitative relationship between vibration
suppression and acoustic damping when the energy-recycling semi-active
vibration suppression method was employed with a honeycomb sandwich panel
was established. Finally, the analytical claims of Kurtze and Watters [19] and
Davis [20] were validated experimentally and showed that wave speeds,
particularly shear wave speeds, impacted the sound transmission loss of
honeycomb sandwich structures.
Prototype sandwich structures were fabricated and tested to assess the
effects of simple materials and structural parameters on the loss factor in Chapter
3. Sandwich beams that featured a mid-plane damping layer exhibited
substantially greater loss factors compared to the control reference sample, while
panels with carbon fiber skins had the greatest loss factor. Structures designed for
subsonic shear wave speeds did not exhibit increased loss factors. Of the panels
with aramid cores, the panel with the para-aramid core consistently showed the
greatest loss factor.

67
From a materials perspective, noise control of sandwich panels can be
strongly influenced by both additive materials, such as the mid-plane viscoelastic
material, and by the different skin materials. While the mid-plane damping layer
and the para-aramid core increased the loss factor, the subsonic core did not.
However, in past work the subsonic core resulted in substantially increased
transmission loss. Inserting the mid-plane layer demonstrated the potential of
judiciously placed damping materials. This approach could be extended to
applications such as automotive frames and panels and airplane fuselages. While
the focus of this work was on frequencies above the coincidence frequency,
increased damping at lower frequencies is expected to reduce transmission loss in
this mass-controlled frequency range.
The sections in chapter 4 led to the conclusion that open-weave
construction and various foam densities have a strong influence on acoustic
absorption performance of honeycomb sandwich structures. The open-weave
facesheet configuration showed the maximum improvement of acoustic
absorption. For frequencies below 1250 Hz, higher foam densities resulted in
higher absorption coefficients. Above 1250 Hz, that trend was less apparent as the
lower density foam filled cores produced higher absorption coefficients. Overall,
the open-weave foam-filled cells had greater absorption coefficients than the
control sample, which illustrates the effectiveness of combining porous absorbers
and resonators to improve acoustic performance.

68
Multiple types of absorbers can be incorporated into honeycomb sandwich
panels to increase sound absorption coefficients. For example, the open-weave
facesheet is a design element that can improve acoustic absorption and can be
applied to a variety of sandwich structure applications. Manipulating the flow of
sound waves through a sandwich structure can be used to adjust acoustic
properties, thereby reducing noise levels in passenger compartments, or
alternatively increasing resonator efficiencies for applications where sound
transmission is desirable, such as speaker and entertainment systems.
One of the challenges associated with use of open-weave facesheets in
sandwich structures is the potential loss of stiffness, strength, and impact
resistance. However, this challenge is not insurmountable, and for non-weight
bearing applications such as partitions and fuselage linings, open-weave
facesheets combined with foam-filled cores could provide a noise control solution
with minimal manufacturing adjustments.
In chapter 5, the energy-recycling semi-active (ERSA) method of
vibration suppression was employed to assess the influence of vibration
suppression on acoustic damping for a honeycomb sandwich panel. As expected,
suppression of panel vibrations was accompanied by reductions in the amount of
sound transmitted through the HC sandwich panels. Ultimately, it was the ERSA
system that increased the vibration suppression that increased the transmission
loss. The increase in acoustic damping (as measured by PSD), was typically twice
the increase in vibration suppression (as measured by FRF), indicating that the
ERSA method was more effective in achieving acoustic damping. However,

69
vibration suppression and acoustic damping are related phenomena, and vibration
suppression undoubtedly contributed to the increase in acoustic damping by
reducing the structure-borne noise. Airborne noise accounted for another source
of sound transmission through the panel. The circuit configuration determined the
effectiveness of the ERSA method, because the available voltage was limited by
the forward voltage of the diode. If the forward voltage of the diode could be
minimized, there could be even more efficient configurations possible. The data
from this study suggests that improvements to an all-series configuration could
yield even higher acoustic damping and vibration suppression. The measurement
system also affected the degree of vibration suppression and acoustic damping for
series and 10-group circuit configurations because the charge flowing through the
system in these configurations was less than in others.
The results demonstrate the potential for future noise reduction strategies
that recycle waste energy to actively suppress noise and vibrations in lightweight
structures. Sandwich panels can be efficient resonators, and this can be
problematic for aerospace and astronautic structures. However, they also afford
opportunities to incorporate ERSA system components and mitigate the noise and
vibration problems inherent in such applications. The present findings illustrate
the potential to design honeycomb sandwich panels that utilize the ERSA method
to achieve specific reductions in noise and vibration. ERSA damping is a
lightweight and effective noise control solution that requires little space, and thus
there is reason to pursue this approach in aerospace and automotive structures.

70
Chapter 6 dealt with the influence of core type, skin type, and cell size of
HC sandwich beams on acoustic wave speeds. The shear modulus of the core
showed maximum influence on the wave speeds of the samples, while cell size
did not have a significant influence on the wave speeds or on the transmission
loss. For sandwich structures with comparable core and skin thickness, the skin
modulus influenced the wavespeeds at low frequencies. For example, samples
with carbon fiber laminate skins approached the Mach speeds at about 700 Hz
while structures with glass fiber laminate skins approached Mach speeds at
frequencies above 1000 Hz. These observations are consistent with the Kurtze
and Watters model [19], which predicts that bending motion of the panel controls
the wave speed at lower frequencies. The sample with the subsonic core displayed
the slowest wave speeds and a transition from bending to shear wave speeds at
1500 Hz. In comparison, the samples with supersonic cores showed transitions to
shear wave speed at 3000 Hz or greater.
This work experimentally demonstrates that HC cores with lower shear
modulus values translate into slower wave speeds and superior acoustical
performance. These results validate the analytical predictions of Davis [20],
whose work was based on the Kurtze and Watters model [19], that TL can be
increased by designing HC structures with reduced shear wave speeds.

The results
are also consistent with the TL measurements of identical HC structures with
subsonic cores [13]. The subsonic core showed a major difference in acoustical
performance and can be used to improve the design process for commercial

71
aircraft, automotive interiors, and other applications where lightweight yet quiet
features are required.
The experimental set-up used in Chapter 6 offers an alternative method for
evaluating the acoustic properties of honeycomb sandwich structures. The results
demonstrate a direct correlation between wave speed and transmission loss for
HC structures. Thus, the method described for measuring wave speeds can
potentially replace more expensive and bulky anechoic chambers as a way of
measuring acoustic behavior. The method also provides a cost-effective and
practical substitute for acoustic measurements in impedance tubes.
The following are the vital conclusions of this research on honeycomb
sandwich structures:
o Adding a mid-plane damping layer to sandwich structures results
in substantially greater loss factors.
o Porous absorbers combined with resonators improve the acoustic
absorption of honeycomb sandwich structures.
o The energy-recycling semi-active vibration suppression system is
an effective method of increasing acoustic damping.
o HC cores with lower shear modulus values result in increased
transmission loss.
Overall, noise control requires a comprehensive perspective and solutions that
encompass transmission loss, damping, acoustic absorption, vibration
suppression, and wave speed control. The work presented in this dissertation
confirms that the acoustical performance of sandwich structures is influenced by a

72
variety of components that are independently linked. Weight penalties must also
be considered when designing acoustically superior panels as a component that
improves the acoustic properties could decrease the mechanical performance of
the sandwich structure. Investigating materials and their combination of properties
can also be manipulated to produce the optimal material for aerospace
applications. This dissertation is mostly a compilation of the journal publications
and conference papers that resulted from this work [22,77-80].

73
REFERENCES

[1] Norton, M.P. (1989) Fundamentals of Noise and Vibration Analysis for
Engineers, Cambridge: University Press.
[2] Fahy, F. (1985) Sound and Structural Vibration Radiation, Transmission
and Response, New York: Academic Press, New York.
[3] Cremer, L., Heckl, M., and Ungar, E.E. (1973) Structure-Borne Sound, 4
th

ed., Berlin: Springer-Verlag.
[4] Junger, M.C., and Fiet, D. (1972) Sound, Structures and Their Interaction,
Boston: M.I.T. Press.
[5] Rajaram, S. (2005) Experimental Study of Acoustical Behavior of Flat
Honeycomb Sandwich Panel, unpublished thesis (Ph.D.), University of Southern
California.
[6] Li, Z. and Crocker, M.J. (2006) ‘Effects of thickness and delamination on
the damping in honeycomb-foam sandwich beams’, Journal of Sound and
Vibration, 294, 473-485.

[7] He, S. and Rao, M.D. (1993) ‘Vibration and damping analysis of multi-
span sandwich beams with arbitrary boundary conditions’, Journal of Sound and
Vibration, 164(1), 125-142.

[8] Vaidya, A.S., Vaidya, U.K. and Uddin, N. (2008) ‘Impact response of
three-dimensional multifunctional sandwich composite’, Materials Science and
Engineering:A, 472(1-2), 52-58.

[9] Hosur, M.V., Abdullah, M., and Jeelani, S. (2005) ‘Manufacturing and
low-velocity impact characterization of foam filled 3-D integrated core sandwich
composites with hybrid face sheets’, Composite Structures, 69(2), 167-181.

[10] Sorokin, S.V. and Grishina, S.V. (2004) ‘Analysis of wave propagation in
sandwich beams with parametric stiffness modulations’, Journal of Sound and
Vibration, 271(3-5), 1063-1082.

[11] Chen, W. and Wierzbicki, T. (2001) ‘Relative merits of single-cell, multi-
cell and foam-filled thin-walled structures in energy absorption’, Thin-Walled
Structures, 39(4), 287-306.

[12] Wang, T., Sokolinsky, V., Rajaram, S., and Nutt,S. (2005) ‘Assessment of
sandwich models for the prediction of sound transmission loss in unidirectional
sandwich panels’, Applied Acoustics, 66, 245-262.

74
[13] Rajaram, S., Wang, T. and Nutt, S. (2006) ‘Sound transmission loss of
honeycomb sandwich panels’, Noise Control Engineering Journal, 54(2), 106-
115.

[14] Rajaram, S. and Nutt, S. (2006) ‘Measurement of sound transmission
losses of honeycomb partitions with added gas layers’, Noise Control Engineering
Journal, 54(2), 101-105.

[15] Renji, K. and Nair, P.S. (1997) ‘Critical and coincidence frequencies of
flat panels’, Journal of Sound and Vibration, 205(1), 19-32.

[16] Minesugi, K. and Onoda, J. (2008) ‘Practical application of energy-
recycling semi-active vibration suppression method to an actual satellite structural
model’, IAC-07-C2.5.09.

[17] Makihara, K., Onoda, J., and Tsuchihashi, M. (2006) ‘Investigation of
performance in suppressing various vibrations with energy-recycling semi-active
method’, Acta Astronautica, 58, 506-514.

[18] Onoda, J., Makihara, K., and Minesugi, K. (2003) ‘Energy-recycling semi-
active method for vibration suppression with piezoelectric transducers’, AIAA
Journal, 41(4), 711-719.

[19] Kurtze, G. and Watters, B.G. (1959) ‘New wall design for high
transmission loss or high damping’, J. Acoust. Soc. Am. 31(6), 739-48.

[20] Davis, E.B. (1997) ‘Designing honeycomb panels for noise control’,
American Institute of Aeronautics and Astronautics, J. AIAA-99-1917.
[21] He, H. and Gmerek, M. (1999) ‘Measurement and prediction of wave
speeds of honeycomb structures’, Fifth AIAA/CEAS Aeroacoustics Conference
and Exhibit, Bellevue, WA, AIAA Paper 99-1965.

[22] Senthilvelan, S. and Gnanamoorthy, R. (2006) ‘Damping characteristics of
unreinforced, glass and carbon fiber reinforced nylon 6/6 spur gears’, Polymer
Testing, 25, 56-62.
[23] Kerwin, E.M. (1959) ‘Damping of flexural waves by a constrained
viscoelastic layer’, Journal of the Acoustical Society of America, 31(7), 952-962.

[24] Ross, D., Ungar, E.E. and Kerwin, E.M. (1959) ‘Damping of plate flexural
vibrations by means of viscoelastic laminate’, Structural Damping, ASME, New
Jersey, 49-88.

[25] Ungar, E.E. (1962) ‘Loss factors of viscoelastically damped beam
structures’, Journal of the Acoustical Society of America, 34(8), 1082-1089.

75

[26] Ungar, E.E. and Kerwin, E.M. (1962) ‘Loss factors of viscoelastic systems
in terms of energy concepts’, Journal of the Acoustical Society of America, 34(7),
954-958.

[27] Mead, D.J. and Markus, S. (1970) ‘Loss factors and resonant frequencies
of encastre damped sandwich beams’, Journal of Sound and Vibration, 12(1), 99-
112.

[28] Mead, D.J. and Markus, S. (1969) ‘The forced vibration of a three-layer,
damped sandwich beam with arbitrary boundary conditions’, Journal of Sound
and Vibration, 10(2), 163-175.

[29] Renji, K. and Narayan, S. (2002) ‘Loss factors of composite honeycomb
sandwich panels’, Journal of Sound and Vibration, 250(4), 745-761.

[30] Jung, W.Y. and Aref, A.J. (2003) ‘A combined honeycomb and solid
viscoelastic material for structural damping applications’, Mechanics of
Materials, 35, 831-844.

[31] Stavroulakis, G.E. (2005) ‘Auxetic behaviour: appearance and engineering
applications’, Phys. Stat. Sol, 242(3), 710-720.

[32] Ruzzene, M. (2004) ‘Vibration and sound radiation of sandwich beams
with honeycomb truss core’, Journal of Sound and Vibration, 277, 741-763.

[33] Nilsson, A.C. (1990) ‘Wave propagation in and sound transmission
through sandwich plates’, Journal of Sound and Vibration, 138(1), 73-94.

[34] Shi, Y., Sol, H. and Hua, H. (2006) ‘Material parameter identification of
sandwich beams by an inverse method’, Journal of Sound and Vibration, 290,
1234-1255.

[35] Shorter, P. (2004) ‘Wave propagation and damping in linear viscoelastic
laminates’, The Journal of the Acoustical Society of America, 115, 1917-1925.

[36] Ghinet, S., Atalia, N., and Osman, H. (2005) ‘The transmission loss of
curved laminates and sandwich composite panels’, The Journal of the Acoustical
Society of America, 118, 774-790.

[37] Wojtowicki, J.L., Jaouen,L. and Panneton,R. (2004) ‘A new approach for
the measurement of damping properties of materials using the oberst beam’,
Review of Scientific Instruments, 75(8), 2569-2574.

76
[38] Hwang, H.Y., Hak, G.L., and Lee, D.G. (2004) ‘Clamping effects on the
dynamic characteristics of composite machine tool structures,’ Composite
Structures, 66, 399-407.

[39] Rajaram, S., Peters,P., Wang, T. and Nutt,S. (2006)‘Comparison of
acoustical performance of Kevlar vs Nomex honeycomb cores in sandwich
panels’, Proceedings of the Society for the Advancement of Material and Process
Engineering.

[40] Rajaram, S., Wang,T., Chui, Y., et al. (2005) ‘Measurement and prediction
of sound transmission loss for airplane floors’, Proceedings of the American
Institute of Aeronautics and Astronautics.

[41] Shih, Y.S., and Yeh,Z.F. (2005) ‘Dynamic stability of a viscoelastic beam
with frequency-dependent modulus’, International Journal of Solids and
Structures, 42(7), 2145-2159.

[42] Bitzer, T. (1997) Honeycomb Technology, London: Chapman & Hall.

[43] M.C. Gill Corporation, http://mcgillcorp.com/products/index.html

[44] Kyriazoglou, C. and Guild,F.J. (2006) ‘Finite element prediction of
damping of composite GFRP and CFRP laminates – a hybrid formulation –
vibration damping experiments and Rayleigh damping’, Composites Science and
Technology, 66, 487-498.

[45] Dunn, M., and Ledbetter,H. (2000) ‘Micromechanically-based acoustic
characterization of the fiber orientation distribution function of morphologically
textured short-fiber composites: prediction of thermomechanical and physical
properties’, Materials Science and Engineering A, 285 (1-2), 56-61.

[46] Paolozzi, A. and Peroni,I. (1996) ‘Response of aerospace sandwich panels
to launch acoustic environment’, Journal of Sound and Vibration, 196(1), 1-18.

[47] He, M.F. and Hu, W.B. (2008) ‘A study on composite honeycomb
sandwich panel structure’, Materials & Design, 29(3), 709-713.

[48] Renji, K., Nair, P.S. and Narayanan, S. (1996) ‘Modal density of
composite honeycomb sandwich panels’, Journal of Sound and Vibration, 195(5),
687-699.

[49] Cheong, T.W. and Zheng, L.W. (2006) ‘Vibroacoustic performance of
composite honeycomb structures’, Noise Control Engineering Journal, 54(4),
251-262.

77
[50] Ng, C.F. and Hui, C.K. (2008) ‘Low frequency sound insulation using
stiffness control with honeycomb panels’, Applied Acoustics, 69, 293-301.

[51] ASTM E1050, Standard test method for impedance and absorption of
acoustical materials using a tube, two microphones, and a digital frequency
analysis system.

[52] ISO 10534-2, Acoustics – Determination of sound absorption coefficient
and impedance in impedance tubes – Part 2: Transfer-function method.

[53] Bruel & Kjaer Impedance Tube Guide

[54] Cummings, A. (1991) ‘Impedance tube measurements on porous media:
the effects of air-gaps around the sample’, Journal of Sound and Vibration,
151(1), 63-75.

[55] Kino, N. and Ueno, T. (2007) ‘Investigation of sample size effects in
impedance tube measurements’, Applied Acoustics, 68, 1485-1493.

[56] M.C. Gill Technology, patent pending, www.mcgillcorp.com

[57] Hong, Z., Bo, L., and Guangsu, H. (2006) ‘Sound absorption behavior of
multiporous hollow polymer micro-spheres’, Materials Letters, 60, 3451-3456.

[58] Wang, C.N. and Torng, J.H. (2001) ‘Experimental study of the absorption
characteristics of some porous fibrous materials’, Applied Acoustics, 62, 447-459.

[59] Wang, C.N. and Cho,H.M. (2005) ‘Sound field of a baffled sound source
covered by an anisotropic rigid-porous material’, Applied Acoustics, 66 (7), 866-
878.

[60] Goransson, P. (2007) ‘Tailored acoustic and vibrational damping in
porous solids – Engineering performance in aerospace applications’, Aerospace
Science and Technology, 12(1), 26-41.

[61] Smith, C. and Parrott, T. (1983) ‘Comparison of three methods for
measuring acoustic properties of bulk materials’, Journal of the Acoustical
Society of America, 74(5), 1577-1582.

[62] Moheimani, S.O. (2003) ‘A survey of recent innovations in vibration
damping and control using shunted piezoelectric transducers’, IEEE Transactions
on Control Systems Technology, 11(4).

78
[63] Agnes, G.S. and Mall, S. (1999) ‘Structural integrity issues during
piezoelectric vibration suppression of composite structures’, Composites: Part B,
30, 727-738.

[64] Nguyen, C.H. and Pietrzko, S.J. (2007) ‘Vibroacoustic FE analysis of an
adaptive plate with PZT actuator/sensor pairs connected to a multiple-mode,
electric shunt system’, Finite Elements in Analysis and Design, 43, 1120-1134.

[65] Carneal, J., Giovanardi, M., et al, (2008) ‘Re-active passive devices for
control of noise transmission through a panel,’ Journal of Sound and Vibration,
309, 495-506.

[66] Hagood, N.W. and von Flotow, A. (1991) ‘Damping of structural
vibrations with piezoelectric materials and passive electrical networks’, Journal of
Sound and Vibration, 146(2), 243-268.

[67] Fein, O. (2008) ‘A model for piezo-resistive damping of two-dimensional
structures’, Journal of Sound and Vibration, 310, 865-880.

[68] Becker, J., Fein, O., et al (2006) ‘Finite element-based analysis of shunted
piezoelectric structures for vibration damping’, Computers and Structures, 84,
2340-2350.

[69] Richard, C., Guyomer, D., et al (2000) ‘Enhanced semi passive damping
using continuous switching of a piezoelectric device on an inductor’, Proceedings
of the SPIE Smart Structures and Materials Conference, SPIE Vol. 3989, Society
of Photo-Optical Instrumentation Engineering, Bellingham, WA, 288-299.

[70] Lesieutre, G.A., Ottman, G.K., and Hofmann, H.F. (2004) ‘Damping as a
result of piezoelectric energy harvesting’, Journal of Sound and Vibration, 269,
991-1001.

[71] Lin, Q., and Ermanni, P. (2004) ‘Semi-active damping of clamped plate
using PZT’, International Journal of Solids and Structures, 41, 1741-1752.

[72] Tsui, C.Y., Voorhees, C.R., and Yang, J.C.S. (1976) ‘The design of small
reverberation chambers for transmission loss measurements’, Applied Acoustics,
9, 165-175.

[73] Pallett, D.S., Pierce, E.T. and Toth, D.D. (1976) ‘A small-scale multi-
purpose reverberation room’, Applied Acoustics, 9, 287-302.

[74] Klos, J., Robinson, J. and Buehrle, R. (2003) ‘Sound transmission through
a curved honeycomb composite panel’, American Institute of Aeronautics and
Astronautics, J. AIAA, 2003-3157.

79

[75] Clark, N. and Thwaites, S. (1995) ‘Local phase velocity measurements in
plates’, Journal of Sound and Vibration, 187(2), 241-252.

[76] Blevens, R. (2001) Formulas for Natural Frequency and Mode Shape,
Florida: Krieger.

[77] Peters, P., Sneddon, M. and Nutt, S. (2009) ‘Measurements of loss factor
of honeycomb sandwich structures’, Noise Control Engineering Journal, Jan/Feb
Issue.

[78] Peters, P., Sneddon, M., and Nutt, S. (Feb 2009) ‘Acoustic absorption
characteristics of honeycomb sandwich structures’, Noise Control Engineering
Journal, In Review.

[79] Peters, P., Minesugi, K., Onoda, J., Nutt, S. (March 2009) ‘Semi-active
vibration suppression of honeycomb sandwich structures’, AIAA Journal, In
Review.

[80] Peters, P., and Nutt, S. (March 2009) ‘Wave speeds of honeycomb
sandwich structures: An experimental approach’, Applied Acoustics, In Review.

80
BIBLIOGRAPHY

Agnes, G.S. and Mall, S. (1999) ‘Structural integrity issues during piezoelectric
vibration suppression of composite structures’, Composites: Part B, 30, 727-738.

ASTM E1050, Standard test method for impedance and absorption of acoustical
materials using a tube, two microphones, and a digital frequency analysis system.

Becker, J., Fein, O., et al (2006) ‘Finite element-based analysis of shunted
piezoelectric structures for vibration damping’, Computers and Structures, 84,
2340-2350.

Bitzer, T. (1997) Honeycomb Technology, London: Chapman & Hall.

Blevens, R. (2001) Formulas for Natural Frequency and Mode Shape, Florida:
Krieger.

Bruel & Kjaer Impedance Tube Guide

Carneal, J., Giovanardi, M., et al, (2008) ‘Re-active passive devices for control of
noise transmission through a panel,’ Journal of Sound and Vibration, 309, 495-
506.

Chen, W. and Wierzbicki, T. (2001) ‘Relative merits of single-cell, multi-cell and
foam-filled thin-walled structures in energy absorption’, Thin-Walled Structures,
39(4), 287-306.

Cheong, T.W. and Zheng, L.W. (2006) ‘Vibroacoustic performance of composite
honeycomb structures’, Noise Control Engineering Journal, 54(4), 251-262.

Clark, N. and Thwaites, S. (1995) ‘Local phase velocity measurements in plates’,
Journal of Sound and Vibration, 187(2), 241-252.

Cremer, L., Heckl, M., and Ungar, E.E. (1973) Structure-Borne Sound, 4
th
ed.,
Berlin: Springer-Verlag.
Cummings, A. (1991) ‘Impedance tube measurements on porous media: the
effects of air-gaps around the sample’, Journal of Sound and Vibration, 151(1),
63-75.

Davis, E.B. (1997) ‘Designing honeycomb panels for noise control’, American
Insitute of Aeronautics and Astronautics, J. AIAA-99-1917.

81
Dunn, M., and Ledbetter,H. (2000) ‘Micromechanically-based acoustic
characterization of the fiber orientation distribution function of morphologically
textured short-fiber composites: prediction of thermomechanical and physical
properties’, Materials Science and Engineering A, 285 (1-2), 56-61.

Fahy, F. (1985) Sound and Structural Vibration Radiation, Transmission and
Response, New York: Academic Press, New York.
Fein, O. (2008) ‘A model for piezo-resistive damping of two-dimensional
structures’, Journal of Sound and Vibration, 310, 865-880.

Ghinet, S., Atalia, N., and Osman, H. (2005) ‘The transmission loss of curved
laminates and sandwich composite panels’, The Journal of the Acoustical Society
of America, 118, 774-790.

Goransson, P. (2007) ‘Tailored acoustic and vibrational damping in porous solids
– Engineering performance in aerospace applications’, Aerospace Science and
Technology, 12(1), 26-41.

Hagood, N.W. and von Flotow, A. (1991) ‘Damping of structural vibrations with
piezoelectric materials and passive electrical networks’, Journal of Sound and
Vibration, 146(2), 243-268.

He, H. and Gmerek, M. (1999) ‘Measurement and prediction of wave speeds of
honeycomb structures’, Fifth AIAA/CEAS Aeroacoustics Conference and
Exhibit, Bellevue, WA, AIAA Paper 99-1965.

He, M.F. and Hu, W.B. (2008) ‘A study on composite honeycomb sandwich panel
structure’, Materials & Design, 29(3), 709-713.

He, S. and Rao, M.D. (1993) ‘Vibration and damping analysis of multi-span
sandwich beams with arbitrary boundary conditions’, Journal of Sound and
Vibration, 164(1), 125-142.

Hong, Z., Bo, L., and Guangsu, H. (2006) ‘Sound absorption behavior of
multiporous hollow polymer micro-spheres’, Materials Letters, 60, 3451-3456.

Hosur, M.V., Abdullah, M., and Jeelani, S. (2005) ‘Manufacturing and low-
velocity impact characterization of foam filled 3-D integrated core sandwich
composites with hybrid face sheets’, Composite Structures, 69(2), 167-181.

Hwang, H.Y., Hak, G.L., and Lee, D.G. (2004) ‘Clamping effects on the dynamic
characteristics of composite machine tool structures,’ Composite Structures, 66,
399-407.

82
ISO 10534-2, Acoustics – Determination of sound absorption coefficient and
impedance in impedance tubes – Part 2: Transfer-function method.

Jung, W.Y. and Aref, A.J. (2003) ‘A combined honeycomb and solid viscoelastic
material for structural damping applications’, Mechanics of Materials, 35, 831-
844.

Junger, M.C., and Fiet, D. (1972) Sound, Structures and Their Interaction,
Boston: M.I.T. Press.
Kerwin, E.M. (1959) ‘Damping of flexural waves by a constrained viscoelastic
layer’, Journal of the Acoustical Society of America, 31(7), 952-962.

Kino, N. and Ueno, T. (2007) ‘Investigation of sample size effects in impedance
tube measurements’, Applied Acoustics, 68, 1485-1493.

Klos, J., Robinson, J. and Buehrle, R. (2003) ‘Sound transmission through a
curved honeycomb composite panel’, American Institute of Aeronautics and
Astronautics, J. AIAA, 2003-3157.

Kurtze, G. and Watters, B.G. (1959) ‘New wall design for high transmission loss
or high damping’, J. Acoust. Soc. Am. 31(6), 739-48.

Kyriazoglou, C. and Guild,F.J. (2006) ‘Finite element prediction of damping of
composite GFRP and CFRP laminates – a hybrid formulation – vibration damping
experiments and Rayleigh damping’, Composites Science and Technology, 66,
487-498.

Lesieutre, G.A., Ottman, G.K., and Hofmann, H.F. (2004) ‘Damping as a result of
piezoelectric energy harvesting’, Journal of Sound and Vibration, 269, 991-1001.

Li, Z. and Crocker, M.J. (2006) ‘Effects of thickness and delamination on the
damping in honeycomb-foam sandwich beams’, Journal of Sound and Vibration,
294, 473-485.

Lin, Q., and Ermanni, P. (2004) ‘Semi-active damping of clamped plate using
PZT’, International Journal of Solids and Structures, 41, 1741-1752.

Makihara, K., Onoda, J., and Tsuchihashi, M. (2006) ‘Investigation of
performance in suppressing various vibrations with energy-recycling semi-active
method’, Acta Astronautica, 58, 506-514.

M.C. Gill Corporation, http://mcgillcorp.com/products/index.html

M.C. Gill Technology, patent pending, www.mcgillcorp.com

83
Mead, D.J. and Markus, S. (1970) ‘Loss factors and resonant frequencies of
encastre damped sandwich beams’, Journal of Sound and Vibration, 12(1), 99-
112.

Mead, D.J. and Markus, S. (1969) ‘The forced vibration of a three-layer, damped
sandwich beam with arbitrary boundary conditions’, Journal of Sound and
Vibration, 10(2), 163-175.

Minesugi, K. and Onoda, J. (2008) ‘Practical application of energy-recycling
semi-active vibration suppression method to an actual satellite structural model’,
IAC-07-C2.5.09.

Moheimani, S.O. (2003) ‘A survey of recent innovations in vibration damping
and control using shunted piezoelectric transducers’, IEEE Transactions on
Control Systems Technology, 11(4).

Ng, C.F. and Hui, C.K. (2008) ‘Low frequency sound insulation using stiffness
control with honeycomb panels’, Applied Acoustics, 69, 293-301.

Nguyen, C.H. and Pietrzko, S.J. (2007) ‘Vibroacoustic FE analysis of an adaptive
plate with PZT actuator/sensor pairs connected to a multiple-mode, electric shunt
system’, Finite Elements in Analysis and Design, 43, 1120-1134.

Nilsson, A.C. (1990) ‘Wave propagation in and sound transmission through
sandwich plates’, Journal of Sound and Vibration, 138(1), 73-94.

Norton, M.P. (1989) Fundamentals of Noise and Vibration Analysis for
Engineers, Cambridge: University Press.
Onoda, J., Makihara, K., and Minesugi, K. (2003) ‘Energy-recycling semi-active
method for vibration suppression with piezoelectric transducers’, AIAA Journal,
41(4), 711-719.

Pallett, D.S., Pierce, E.T. and Toth, D.D. (1976) ‘A small-scale multi-purpose
reverberation room’, Applied Acoustics, 9, 287-302.

Paolozzi, A. and Peroni,I. (1996) ‘Response of aerospace sandwich panels to
launch acoustic environment’, Journal of Sound and Vibration, 196(1), 1-18.

Peters, P., Minesugi, K., Onoda, J., Nutt, S. (March 2009) ‘Semi-active vibration
suppression of honeycomb sandwich structures’, AIAA Journal, In Review.

Peters, P., and Nutt, S. (March 2009) ‘Wave speeds of honeycomb sandwich
structures: An experimental approach’, Applied Acoustics, In Review.

84
Peters, P., Sneddon, M., and Nutt, S. (Feb 2009) ‘Acoustic absorption
characteristics of honeycomb sandwich structures’, Noise Control Engineering
Journal, In Review.

Peters, P., Sneddon, M. and Nutt, S. (2009) ‘Measurements of loss factor of
honeycomb sandwich structures’, Noise Control Engineering Journal, Jan/Feb
Issue.

Rajaram, S. (2005) Experimental Study of Acoustical Behavior of Flat
Honeycomb Sandwich Panel, unpublished thesis (Ph.D.), University of Southern
California.
Rajaram, S. and Nutt, S. (2006) ‘Measurement of sound transmission losses of
honeycomb partitions with added gas layers’, Noise Control Engineering Journal,
54(2), 101-105.

Rajaram, S., Peters, P., Wang, T. and Nutt, S. (2006)‘Comparison of acoustical
performance of Kevlar vs Nomex honeycomb cores in sandwich panels’,
Proceedings of the Society for the Advancement of Material and Process
Engineering.

Rajaram, S., Wang,T., Chui, Y., et al. (2005) ‘Measurement and prediction of
sound transmission loss for airplane floors’, Proceedings of the American Institute
of Aeronautics and Astronautics.

Rajaram, S., Wang, T. and Nutt, S. (2006) ‘Sound transmission loss of
honeycomb sandwich panels’, Noise Control Engineering Journal, 54(2), 106-
115.

Renji, K. and Nair, P.S. (1997) ‘Critical and coincidence frequencies of flat
panels’, Journal of Sound and Vibration, 205(1), 19-32.

Renji, K., Nair, P.S. and Narayanan, S. (1996) ‘Modal density of composite
honeycomb sandwich panels’, Journal of Sound and Vibration, 195(5), 687-699.

Renji, K. and Narayan, S. (2002) ‘Loss factors of composite honeycomb
sandwich panels’, Journal of Sound and Vibration, 250(4), 745-761.

Richard, C., Guyomer, D., et al (2000) ‘Enhanced semi passive damping using
continuous switching of a piezoelectric device on an inductor’, Proceedings of the
SPIE Smart Structures and Materials Conference, SPIE Vol. 3989, Society of
Photo-Optical Instrumentation Engineering, Bellingham, WA, 288-299.

Smith, C. and Parrott, T. (1983) ‘Comparison of three methods for measuring

85
acoustic properties of bulk materials’, Journal of the Acoustical Society of
America, 74(5), 1577-1582.

Ross, D., Ungar, E.E. and Kerwin, E.M. (1959) ‘Damping of plate flexural
vibrations by means of viscoelastic laminate’, Structural Damping, ASME, New
Jersey, 49-88.

Ruzzene, M. (2004) ‘Vibration and sound radiation of sandwich beams with
honeycomb truss core’, Journal of Sound and Vibration, 277, 741-763.

Senthilvelan, S. and Gnanamoorthy, R. (2006) ‘Damping characteristics of
unreinforced, glass and carbon fiber reinforced nylon 6/6 spur gears’, Polymer
Testing, 25, 56-62.
Shi, Y., Sol, H. and Hua, H. (2006) ‘Material parameter identification of
sandwich beams by an inverse method’, Journal of Sound and Vibration, 290,
1234-1255.

Shih, Y.S., and Yeh,Z.F. (2005) ‘Dynamic stability of a viscoelastic beam with
frequency-dependent modulus’, International Journal of Solids and Structures,
42(7), 2145-2159.

Shorter, P. (2004) ‘Wave propagation and damping in linear viscoelastic
laminates’, The Journal of the Acoustical Society of America, 115, 1917-1925.

Sorokin, S.V. and Grishina, S.V. (2004) ‘Analysis of wave propagation in
sandwich beams with parametric stiffness modulations’, Journal of Sound and
Vibration, 271(3-5), 1063-1082.

Stavroulakis, G.E. (2005) ‘Auxetic behaviour: appearance and engineering
applications’, Phys. Stat. Sol, 242(3), 710-720.

Tsui, C.Y., Voorhees, C.R., and Yang, J.C.S. (1976) ‘The design of small
reverberation chambers for transmission loss measurements’, Applied Acoustics,
9, 165-175.

Ungar, E.E. (1962) ‘Loss factors of viscoelastically damped beam structures’,
Journal of the Acoustical Society of America, 34(8), 1082-1089.

Ungar, E.E. and Kerwin, E.M. (1962) ‘Loss factors of viscoelastic systems in
terms of energy concepts’, Journal of the Acoustical Society of America, 34(7),
954-958.

Vaidya, A.S., Vaidya, U.K. and Uddin, N. (2008) ‘Impact response of three-
dimensional multifunctional sandwich composite’, Materials Science and
Engineering:A, 472(1-2), 52-58.

86

Wang, C.N. and Chow, H.M. (2005) ‘Sound field of a baffled sound source
covered by an anisotropic rigid-porous material’, Applied Acoustics, 66 (7), 866-
878.

Wang, C.N. and Torng, J.H. (2001) ‘Experimental study of the absorption
characteristics of some porous fibrous materials’, Applied Acoustics, 62, 447-459.

Wang, T., Sokolinsky, V., Rajaram, S., and Nutt,S. (2005) ‘Assessment of
sandwich models for the prediction of sound transmission loss in unidirectional
sandwich panels’, Applied Acoustics, 66, 245-262.
Wojtowicki, J.L., Jaouen,L. and Panneton,R. (2004) ‘A new approach for the
measurement of damping properties of materials using the oberst beam’, Review
of Scientific Instruments, 75(8), 2569-2574.

Abstract (if available)

Abstract Loss factor measurements were performed on sandwich panels to determine the effects of different skin and core materials on the acoustical properties. Results revealed inserting a viscoelastic material in the core's mid-plane resulted in the highest loss factor. Panels constructed with carbon-fiber skins exhibited larger loss factors than glass-fiber skins. Panels designed to achieve subsonic wave speed did not show a significant increase in loss factor above the coincidence frequency. The para-aramid core had a larger loss factor value than the meta-aramid core.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

In situ process monitoring for modeling and defect mitigation in composites processing

PDF

Synthesis and mechanical evaluation of micro-scale truss structures formed from self-propagating polymer waveguides

PDF

Development of composite oriented strand board and structures

PDF

Defect control in vacuum bag only processing of composite prepregs

Asset Metadata

Creator Peters, Portia Renee (author)

Core Title Experimental study of acoustical characteristics of honeycomb sandwich structures

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Publication Date 04/28/2009

Defense Date 03/23/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Acoustics,composites,honeycomb sandwich structures,OAI-PMH Harvest,vibrations

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nutt, Steven R. (committee chair), Flashner, Henryk (committee member), Kassner, Michael E. (committee member)

Creator Email portia.peters@gmail.com,ppeters@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2134

Unique identifier UC1147845

Identifier etd-Peters-2689 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-224713 (legacy record id),usctheses-m2134 (legacy record id)

Legacy Identifier etd-Peters-2689.pdf

Dmrecord 224713

Document Type Dissertation

Rights Peters, Portia Renee

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu