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This is to certify that the

thesis entitled
The Development of Low—frequency Piezoelectric Panels
for Active Noise Control Applications

presented by
Jonathan Iwamasa

has been accepted towards fulfillment
of the requirements for

Master of Science degeehiMeChanical Engineering

    

Major professor

0.7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

LIBRARY
Mlchlgan State
Unlverslty

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
‘ TO AVOID FINES return on or before date due.

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MSU to An Affirmative ActIon/Equel Opportunity Inetltmion
Wanna-9.1

     
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THE DEVELOPMENT OF LOW-FREQUENCY PIEZOELECTRIC PANELS FOR ACTIVE NOISE
CONTROL APPLICATIONS

BY

Jonathan Iwamasa

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1994

ABSTRACT

THE DEVELOPMENT OF LOW-FREQUENCY PIEZOELECTRIC PANELS
FOR ACTIVE NOISE CONTROL APPLICATIONS

BY

Jonathan Iwamasa

The active modification of sound levels in acoustic spaces is of
increasing interest. Active noise control is necessary for low
frequency noise reduction, since porous absorbers are ineffective. The
objective of this research is to develop a low frequency piezoelectric
polymer speaker panel for active noise control.

The acoustic response of prototype speakers was investigated and
optimized for low frequency response. Small-angle, multi-layered
speakers are more effective in producing low frequency acoustic power.
Multi-layer PVDF speaker response differs notably from the single-layer
speaker response.

An ll-speaker piezoelectric speaker panel was fabricated, which
produced enough low frequency acoustic power to be used in active noise
control applications and is capable of producing in excess of 90dB over
the range of 40-840Hz given an input white noise signal of 30 volts.
Future investigations may find that a speaker panel composed of many
smaller-diameter speakers is more effective than the current ll-speaker

panel.

 

In Memory of Robin Joy Theeuwes, 1968—1993

fii

ACKNOWLEDGEMENTS

This research was funded by the
State of Michigan Research Excellence Fund
and administered through the

Composite Materials & Structures Center at Michigan State University

iv

 

TABLE OF CONTENTS

LISTOP FIGURES0000000000000000000000000000000000000000000000000000000Vi

nommm0000000000.0000000000000000000000000000000000000000000000Vii

INTRODUCTION...........................................
PIEZOELECTRICITY.................................
ACOUSTICS........................................

PROTOTYPE AND PANEL DESIGN.............................

EXPERIMENTAL MEASUREMENT...............................

ACOUSTIC ANALYSIS......................................
PROTOTYPE SOUND CHARACTERISTICS..................
PANEL SOUND CHARACTERISTICS............... .......

CONCLUSIONS00000000000000000000000000000000000000000000

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........4

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.......16

.......19

000000021

LISTOFREFERENCESeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee0e00023

 

Figure

Figure
Figure
Figure

Figure

Figure
Figure

Figure

Figure

Figure
Figure
Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

2:

17

18

19

LIST OF FIGURES

The Piezoelectric Effect - Expansion Due to Applied
VOltage00000000000000.000000000000000000000000000 0000000000 02

Acoustic Emission00000000000000000000000000000000000000000003

Single-layer PVDF Configuration........ ....... . ........ .....3
Multi-layer PVDF configuration 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ....... 0 0 0 4
Power per Volume Squared vs. Frequency for a Monopole

source0000000000000000000000000000000000000000000000000000005

PVDF Speaker Cone................ ...... . .................. ..7
Static Displacement of PVDF Cone.................. .......... 8
Static Displacement Geometry of the Speakers Radial

Cross section0000000000000000000000000000000000 000000 00000009

Graphical Solution of Equation (17), the

Maximization/Minimization of Ah....... ..................... 10
Ah vs. Speaker Angle Given a = 2.76e-5 .... ................. 11
Speaker Angle for Minimum Ah vs. Strain............. ..... ..11
Prototype Design, Partial Section View ..................... 12
Speaker Panel Design. ......... . .............. . .......... ...14
Experimental Set-up......................... ............... 15
Sound Pressure vs. Incident Angle of S-degree, 3-

layer Speaker at 100Hz, SOOHz, and 1000Hz......... ......... 16

Frequency Response for 15-, 20-, 30-, and 45-degree

Speakers with l-layer.. ...... ... ..... ........... ......... ..17
Frequency Response for 5-, 15-, and 20-degree
Speakers0000000000000000000000000.00000000000 00000000000000 18
S-degree Single Speaker and ll-speaker Panel

Frequency Response....................... ...... . ........... 19
Speaker Panel System SPL Response Spectrum for 30

Volt White Noise Input Signal.......... .................... 20

NOMENCLATURE

A area

c speed of sound

d piezo strain constant
D diameter

E Youngs Modulus

f frequency

F force

G frequency response

h or H height

L length

P acoustic pressure

Po reference pressure (20uPa)
R radius

SPL Sound Pressure Level
t or T thickness

V volume of air displaced or voltage
Wa acoustic sound power
a angle of incidence

5 strain

p density of air

a stress

6 speaker angle

vfi

INTRODUCTION

The active modification of sound levels in acoustic spaces is of
increasing interest to both industry and government. In current
automobile industry surveys of customer response to vehicle designs, one
of the strongest indicators of customer approval is their perception of
the level of noise and vibration experienced while driving. The
development of new ways to design for reduced noise levels and control
of existing "noise, vibration and harshness" is a primary thrust in new
automotive design technology.

Active noise control is necessary for low-frequency noise
reduction, since porous absorbers, such as foam, are ineffective. A
porous absorber's thickness must be comparable to the wavelength of
sound for good sound absorption (Everest, 1989, p.177), therefore porous
absorbers are impractical at low frequencies due to the large
thicknesses necessary. For example, the wavelengths of BOOHz, SOOHz,
and 100Hz are 1.4ft, 2.3ft, and 11.3ft, respectively, and would require
these thicknesses to accomplish good sound absorption.

The objective of this research is to determine the feasibility of
a low—frequency piezoelectric polymer speaker panel for active noise
control. Active noise control by absorption requires large-area
coverage by the speakers. This necessitates a panel composed of several
individual speakers, and makes conventional speakers impractical due to

expense and weight. Polyvinylidene Fluoride (PVDF) piezoelectric

2

polymer film overcomes these-disadvantages. The cost of manufacturing
the film is low when manufactured in mass quantities, and it is a thin,
light-weight film capable of being easily cut and glued to facilitate
speaker fabrication, allowing large-area coverage. The active control
of noise requires acoustic generation of equivalent sound powers, and
although effective high-frequency piezoelectric speakers exist, no
practical low-frequency piezoelectric speakers have been developed.

It has been determined that a low-frequency piezoelectric speaker
is feasible through the design and fabrication of prototype speakers,
the analysis of the speakers' acoustic response, and the construction of
a low-frequency PVDF speaker panel. Before the design and fabrication
of PVDF speakers can be discussed, a basic understanding of
piezoelectricity and acoustics is necessary. This background is
presented in the following section, proceeded by the prototype and panel
design section, the experimental measurement section and a final section
on acoustic analysis.

PIEZOELECTRICITY

The piezoelectric effect is the property of a material to expand

and contract when a voltage is applied across its surface and,

conversely, to create a voltage when the sheet is strained. The basic

be L12
é '\ \s

 

 

 

 

Figure 1: The Piezoelectric Effect - Expansion Due to Applied Voltage

PVDF Sheet \ Acoustic Emission
CV1}

Clamped Edges

 

 

 

Figure 2: Acoustic Emission

equation describing the strain, 81, of a simply clamped sheet is:

V
83==GQI5FJ (1)

where £1==strain in the film's stretched
direction (or length)
d31==piezo strain constant
V==voltage applied across thickness
t = thickness of film
The subscripts refer to an axis defined by convention, where (3) denotes
the thickness direction, and (1) denotes the film's stretched, or
length, direction (Figure 1). The 31 subscript on the piezo strain
constant denotes expansion in the length direction, (1), when a voltage
is applied in the thickness direction, (3). This material expansion can
be converted to vibration, producing acoustic power (Figure 2).

Greater force can be generated with multi-layer PVDF designs. To

illustrate this, two piezoelectric configurations are examined. In the

 

The arrow indicates the
piezoelectric orientation. A
I positive voltage will cause film

 

l I I: To expansion, while a negative
I voltage will cause a contraction.

 

 

 

 

Figure 3: Single-layer PVDF Configuration

 

 

...,

 

.L I ET.

I’ ‘ . 1

 

 

 

Figure 4: Multi-layer PVDF Configuration

first, a voltage, V0, is applied across a single sheet of thickness To

(Figure 3). The strain is then,

V
6,=d3,7,°- (2)

with a corresponding force of,

Ed VA
Fo=oA=(E£1)A=——3}—°— (3)
0

where A is the cross-sectional area of the expanding edge. The
orientation of the film is such that a positive voltage will cause film
expansion, while a negative voltage will cause contraction.' In the
multi-layered system, the sheets of PVDF are glued together with
opposite piezoelectric orientation (Figure 4). The two-sheet interface
is grounded, and a voltage of V0 is applied across both sheets. The
strain in this case is the same amount of strain as the single-sheet

system:

V
gi=‘giag
o

(4)
the cross-sectional area, however, is doubled due to the increased
thickness. The force generated in the two-layer system, then, is twice
as much as the single-layer configuration.

ACOUSTICS

Large volume displacements of air are necessary for low-frequency

generation. The sound power level of a monopole, or point, sound source

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

25)
E2; 200 ”I",
~— \ lV’
:5, .5. .1
E r’
% § 100 "/
s ‘3
" 50
g e
0
10 100 10a) 10dx> 10axn
Frequency (Hz)

 

 

 

Figure 5: Power per Volume Squared vs. Frequency for a Monopole
Source

may be calculated from the net volumetric displacement of air of the
given sound source; As the frequency of sound decreases, the volume of
air displaced must increase in a squared-sense to keep the sound power
level constant. The ratio of sound power to volumetric displacement
squared varies linearly with frequency (Figure 5) (Crocker and Price,
1975, pp. 18-19).

The sound power can also be expressed as a function of the volume

of air displaced and frequency of sound as,

2
C

a

where Wa - acoustic sound power

;7= density of air

C’= speed of sound

V’= volume of air displaced
f'= frequency

Sound Pressure Levels (SPL) are used to quantify the sound power.

Sound power is measured as a surface integrated value of the sound

pressure, and can be found as,

m=llP(x,y>cbcay (a)

Sound pressure is commonly measured on a logarithmic scale in decibels.

The equation for Sound Pressure Level (SPL) is,

P2
SPL = 10 log (F) (7)

where the reference pressure, P0 = ZOuPa, is the ASA standard for the

smallest audible pressure.

PROTOTYPE AND PANEL DESIGN

The preliminary prototype design consisted of a 7cm x 15cm
rectangular section of PVDF mounted along its edges to a 3.0 inch
diameter cylindrical enclosure. Acoustic measurements were below
measurable levels at frequencies less than lOOOHz, and the speaker
profile was too large to accommodate a thin speaker panel. A new
prototype design was developed with these considerations in mind.

A cone shape was chosen as the prototype PVDF design because it is
easily fabricated, has a potentially flat profile, and has a symmetry
that does not restrict PVDF expansion when mounted. The individual
speakers must have a thin profile, because the final speaker panel
should be thin to conserve space. A cone-shaped speaker with a 3.0 inch
diameter and a 30-degree angle meets this criterion and is only 1.5 inch
in height (Figure 6). The diameter of 3.0 inch was chosen based on the
stiffness of the PVDF film; if the cone diameter is too large, the

structure is not self-supporting.

e—Eiel

 

D V
l_ 9
Top View Side View, Cross-section

Figure 6: PVDF Speaker Cone

7

 

-34

 

 

 

Figure 7: Static Displacement of PVDF Cone

Low frequency sound pressure will be mainly composed of air
displaced by the first vibrational mode of the cone. Higher modes will
generate less pressure because of the decrease in net displaced air
caused by simultaneous positive and negative cone motion. The static
displacement of this cone shape is shown in Figure 7. By examining the
cone displacement, we can determine the speaker parameters to
investigate to optimize the acoustic output.

The speaker angle is a parameter of interest in optimizing the
acoustic output. The greatest volume of air displacement, and thus the
largest acoustic output, will be generated when Ah is maximized
(Figure 7). The piezoelectric force, however, may not be sufficient to
produce the full strain that would occur in a simply clamped geometry.
Therefore, it is important to understand how Ah and the piezoelectric
force change with speaker angle.

The maximization of Ah as a function of 9 is dependent on the
geometry's strain. By examining the radial cross-section of the cone,
it can be seen that while the speaker cone of length, L, expands to
L+eL, both H and 9 change (Figure 8). The radius, R, is fixed due to
the clamped circumference and the symmetry boundary along the centerline

(Figure 7). Ah can be found by reducing the Pythagorean Equation, as

follows (Figure 8):
(H+Ah)2+R2=(L+gL)2 (a)
Ah=[(L+gL)2—R2]%—H (9)

To maximize Ah as a function of 9, Ah is normalized by the constant R,

and the derivative taken:

Ah l1,2 2 rally2 H
“IT-[ii] (1..) iii] 7 ‘1‘”
%:[(SCCZQ)(1+£)2-I]yz—tan6 <11)

vii-l 1

d6 = §[(secz 6l)(1+.e)2 - 11%[2 sec6(secc9* tan6)(1+£)2] — sec2 (9 (12)

 

The maximum/minimum solution of Ah occurs when the derivative is zero,

therefore Equation (12) is set equal to zero and simplified.

Sin

 

[(sec 22l9)(1+£) -1] /[(secz 6*tan0)(1'+8)2]—sec26 (13)

2
(sec 6*tan6))(21+8)‘/:_S _ ec29 (14)
[(56026)( 1+8) 1]2

R _i .,(___ Ref—l

Figure 8: Static Displacement Geometry of the Speaker's Radial Cross
Section

 

 

 

 

 

10

 

 

6.0E-05
4.0E-05 «
ZOE-05 -

 

0.0E+OO
-2.0E-05 -

Function Value

   

-4.0E-05 .
-6.0E-05

For given strain, a = 2.76e-5

 

 

 

O 10 20 30 40 50 60 7O 80 90
Gukgunfl

 

 

 

Figure 9: Graphical Solution of Equation (17),
the Maximization/Minimization of Ah

%

tani9(1+a)2 2 [(sec2 6)(l+.e)2 —1] (15)
tan26(1+a)4 =(sec26)(l+z:)2 —1 (16)
(1+£)4sin26+coszi9—(l+£)2=0 (17)

The maximum Ah, then, is dependent on the strain. Equation (17) is
solved graphically for e = 2.76e-5 in Figure 9, and is shown to be a
minimum by plotting Ah vs. 6 in Figure 10. The minimum is similarly
found for various strains, and plotted as a function of strain in
Figure 11.

Ah is minimized at a speaker angle of 45 degrees for the
piezoelectric strains generated by the prototype speakers. Choosing a
nominal value of 30 volts for safety purposes, the maximum strain
produced (assuming a simply clamped geometry) is:

(23 12 mm 30V)
e__ __
a - d3'V - V/m - 2 76e—5 18

’ z ’ 25e-6m ’ ' ‘ )

 

ll

 

 

 

 

 

 

 

ZHEAE
For given strain, 3 = 2.76e-5
sz45--
E:1£bE£6~-
.:
< 1rnscs«-
SNEABF~
0.00E+OO::::r::;:::;;;;::
O 15 a) 45 a) 75 a)

 

 

 

Figure 10: Ah vs. Speaker Angle Given 8: 2.76e-5

Referencing the graph of Ahmin vs. 8(Figure 11), it is seen that Ahmin
occurs at 45 degrees, even when the voltage is increased to 300 volts
(8 = 2.76e-4).

The optimum speaker angle is a compromise between maximizing the
calculated Ah, and generating enough force to cause this displacement.
Ah is at a minimum when the speaker angle is 45 degrees, and increases

as the speaker angle approaches both 0 and 90 degrees. Since

 

 

(Buhgnefi

 

 

 

 

 

 

 

Figure 11: Speaker Angle for Minimum Ah vs. Strain

12

small-angle speakers will be more conducive to a thin speaker panel
design, we will only consider speakers with an angle less than 45
degrees. In this situation, Ah is inversely proportional to 6. The
z—direction component of the force, F, equals F sin(9) and thus, is
proportional to 6. Therefore, if the speaker angle is small, the force
may not be great enough to generate the full displacement.

The number of PVDF layers is also a parameter of interest in
optimizing the acoustic output. As stated previously, multi-layer PVDF
designs can increase the amount of force generated. The acoustic output
may be increased with a multi-layer design, then, for small-angle
speakers where the small force generated limits the acoustic output.

The prototype speaker design in this research consists of a PVDF
cone mounted along the outer circumference to an enclosure (Figure 12).
The sealed speaker enclosure consists of a 3-inch diameter polyvinyl
pipe 8" tall, and is designed with a beveled angle to prevent initial
strains on the PVDF film and provide a uniform speaker geometry. Light
gage wires are used to prevent applied stress to the film, while barrier
strips are utilized to allow transfer from light gage wires to heavy
gage wire for electrical connections.

Electrical connections to PVDF film must insure low-contact

resistance in acoustic actuator designs to prevent electrical breakdown

PVDF Cone
Barrier Strip

Beveled Edge

to voltage source

 

Figure 12: Prototype Design, Partial Section View

13
due to the large voltages required to operate the actuators. PVDF film

is typically supplied with surface electrodes covering both sides of the
film. The surface electrodes allow voltages to be applied across the
entire area of the film. Wires soldered to copper foil with conductive
adhesive was used to connect electrical leads to the aluminum-electrodes
on the surface of the film used in this research. Electrical breakdown
occurred at high electric fields for a 2cm2 of copper foil. By
increasing the area of the copper foil, the contact resistance can be
reduced. The electrical connection using copper foil with conductive
adhesive, however, degrades over time due to decreased contact (acoustic
output decreased over a period of one month); therefore clamping the
copper foil is suggested to insure a consistent contact resistance over
time.

Arcing across the edges of the film at high voltages must be
prevented by increasing the dielectric constant between the top and
bottom surface electrodes. The dielectric constant defines the maximum
voltage per distance that can be applied in a given medium without
arcing. Arcing occurred at approximately 100 volts for 25pm film,
resulting in lower acoustic output, or even no acoustic output, due to
the electrical short created by the arcing between the two sides of the
film. Initially, glue covering the edges proved efficient at preventing
arcing up to approximately 300 volts. Additionally, removing the PVDF
surface electrodes along the edges prevents a voltage potential in this
area, thus preventing arcing. The surface electrodes near the edges may
be removed with dilute NaOH (Scott, Bloomfield, 1981, p. 80). Ferric
Chloride (FeCl3) has also been used as an etchant for nickel-aluminum

electrodes (C.-K. Lee, 1990, p. 438).

l4

Multi-layer speakers were fabricated using spray epoxy to bind the
PVDF layers together. It is important to use as little epoxy as
possible to prevent damping of the cone structure, and the associated
loss in acoustic power. A two-compound epoxy was initially used, but
could not be applied sufficiently thin to prevent a large damping of the
acoustic output; spray epoxy was found to be suitable for applying very
thin coats.

The speaker panel system consisted of an 18" x 30" x 4" speaker
case with a hinged, sealable back and a panel inset with 11 individual
speakers (Figure 13). The speaker case was made from high-grade
particle board to prevent energy-dissipative resonances within the
boards. The speaker case was made larger than necessary, so the speaker
could be filled in and the optimum volume determined. Air-impassable
foam was used to seal the hinged back with the speaker case. The
speaker panel was designed with 11 uniformly-spaced, beveled holes, and
the individual speakers were wired in parallel to prevent a single short
from effecting the entire system. Phono connector jacks were installed
to allow direct connection to a drive source, such as a stereo
amplifier, and a transformer within the speaker case was used to

increase the supplied voltage signal to usable piezoelectric levels.

 

 

o o 00 M 00
w 0 ©© °°°°¢
© ©   Q C) j

connector jacks

 

 

 

 

 

 

 

Figure 13: Speaker Panel Design

EXPERIMENTAL MEASUREMENT

A system to measure the sound pressure level characteristics was
devised utilizing a PC, a digital frequency analyzer, amplifier,
transformer, an acoustic microphone probe and the PVDF speakers
(Figure 14). The frequency analyzer supplied the acoustic measurement
capabilities and the drive voltage. The drive voltage was supplied at
both discrete frequencies and over specified frequency ranges to an
amplifier. The amplifier increased the signal power to usable levels,
while the transformer increased the voltage to drive the piezoelectric
speakers. The frequency analyzer was then used to measure the acoustic
pressure distribution and the frequency response of the system's
acoustic pressure to drive voltage, and this data was transferred to the
PC for further analysis. All measurements were obtained at 15cm from

speaker to microphone probe.

PC Frequency Amplifier
‘ Analyzer

Ca

 

 

 

lTr—‘j.

 

 

Microphone Probe PVDF Speaker

and Stand \ a: /_h Prototype
D—D Transformer

Figure 14: Experimental Set-up

 

 

 

ACOUSTIC ANALYSIS

PROTOTYPE SOUND CHARACTERISTICS

The prototype is non-directional at low frequencies, allowing
characterization of the sound power by sound pressure level measurements
at one point. The SPL was measured at 100Hz, 500Hz, and 100082 for a
between 0 and 90 degrees. The directional characteristics of a
S-degree, 3-layer speaker showed a maximum difference of only 3.5dB
throughout a 90-degree angle of incidence (Figure 15).

The sound pressure per volt frequency response for l-layer
prototypes had a repeatable curve shape as the speaker angle varied and
showed an increase in response for a 15—degree speaker over larger-angle
speakers. Actual spectral data are shown for four different l-layer

speakers in Figure 16. This data shows that the low frequency acoustic

 

700
600
5001
40.0 «~ 2A
3004~ l
200«~ (
100~» '
00 t i t t r t t t l

0 1O 20 30 40 50 60 70 80 90

 

SPL (as)
$2—

 

 

 

 

Angle of Incidence, (1 (degrees)

 

-—i—=KDHZ-1F—5GMt-—0—400}t

 

 

 

 

 

 

 

Figure 15: Sound Pressure vs. Incident Angle of 5-degree, 3—layer
Speaker at 100Hz, 500Hz, and 1000Hz

16

l7

 

 

 

 

    

 

 

0.007
QGEJ-
QMBJ'
% 0.004 "'
45 de rees
“- 0.003 ._ g
0002 d 4.:
. , a " 20 degrees
ooo1 « . .. v
' “sew if ' *" ~ 30 degrees
0 1 t i :7 '
«m an an up an
Frequency (Hz)

 

 

Figure 16: Frequency Response for 15-, 20-, 30-, and 45-degree
Speakers with 1-layer

response is approximately the same for speaker cones with an angle
greater than 20 degrees, and increases at angles smaller than 20
degrees. This increase in acoustic response is expected, but a decrease
in response at smaller cone angles is also expected; this data does not
indicate if, and when, the acoustic response begins to decrease with
angle.

A 5-degree, 1-layer speaker, however, develops structural
harmonics which reduce the acoustic output. A 5-degree, 1-layer speaker
was not stiff enough to provide a uniform cone shape, given the 3.0 inch
speaker diameter. Instead, the cone shape had a waviness characterized
by taut radial sections bounding relaxed film areas. This created
structural harmonics that diminished the energy and acoustic response.
Additionally, this non-uniform geometry was unstable and produced an
inconsistent frequency response.

Multi-layered PVDF speakers are able to remove the harmonics that
occur due to geometry non-uniformity. A S-degree speaker was ‘

investigated with 2, 3, 4 and 6 layers. Speaker cones of more than 6

18

layers were determined to be cost ineffective and not investigated. The
2-layer speaker had greater acoustic output, but harmonics-were still
present. For 3 layers and greater, the harmonics were not detected.
This multi-layer speaker data was used to select a 3-layer,
S-degree speaker as the speaker panel prototype. The 3-layer, S-degree
speaker produced more acoustic output than any of the single-layer
prototypes (Figure 17). The multi-layer frequency response is notably
different from the single-layer frequency response trend. Instead of a
smooth curve, drops in the frequency response appear at approximately
525Hz, 700Hz and 825Hz. The first mode of the speaker enclosure is
approximately 1,100Hz, and therefore, these peaks in frequency response
are not due to the enclosure resonances. The change in the frequency
response trend may instead be due to the characteristics of a
multi-layer PVDF system or the consistency of the spray epoxy used to
glue the layers of PVDF together. The multi-layer speaker data
collected, however, did not contain enough detail and are not sufficient

to present here.

 

can
0mm4-
34ayer
0.007 -- '
5 de rees \
0.006 .. g

 

 
   

 

_1—Iayer,
15 degrees
I
_1-layer,
20 degrees

 

 

 

«m an (mo 7m) an
Frequency (Hz)

 

 

Figure 17: Frequency Response for 5-, 15-, and 20—degree Speakers

l9
PANEL SOUND CHARACTERISTICS

The speaker panel produced a higher acoustic output with a general
frequency response shape comparable with that of the single speaker
frequency response (Figure 18). The increase in the magnitude of the
speaker panel frequency can be characterized over three different
regions. From 150Hz to 325Hz the response is increased by approximately
fourteen times the single speaker response, while the response is
increased by 6.5 and 3.5 times the individual speaker response over the
ranges of 325-550Hz and 550-840Hz, respectively. The general shape of
the panel frequency response is comparable to the one speaker response
with variations most notable by the shift in the low frequency response
drops at 525, 700, and 825Hz to drops at 485, 675, and 775Hz.

The speaker panel system design is successful and can generate
usable low frequency acoustic power. The sound pressure level spectrum
for a 30 volt input white noise signal of frequency span 40-840Hz is
shown in Figure 19. The total band SPL from 40-840Hz is 91.8dB. The

SPL is greater than 50dB for all frequencies above 150Hz, and the SPL is

 

 

0.035
0.030 ..
0.025 4~
0.020 4~
0015 A
0.010 i“
0.005 q
0.000

 
 
 
 
 
  

PNV

 

    

 

L ...A 4 1 L l
T 7 T

1&) 2a) 33) 4K) 5K) 68) 75) BK)
Frequency (Hz)

 

 

—Panel Response Single Speaker Response

 

 

 

 

Figure 18: 5—degree Single Speaker and ll-speaker Panel Frequency
- Response

20

 

 

70 1*
60+

SPL (re 2009a)
8

20 '1)-
10 ..

 

J

Total SPL band a

4‘

 

 

o 4 A;

 

Frequency (Hz)

0100200300400500600700800900

 

 

Figure 19: Speaker Panel System SPL Response Spectrum for 30 Volt
White Noise Input Signal

approximately 40dB or greater between 40Hz and 150Hz.

These levels are '

sufficiently high to further investigate the PVDF speaker panel for use

in an active noise control system.

CONCLUSIONS

The first stage of developing an acoustic PVDF active noise
control system has been successful. The speaker panel of eleven 3-layer
5-degree PVDF cones mounted on a speaker box of dimensions 18" x 30" x
4" produced in excess of 90dB from 40-840Hz given an input white noise
signal of 30 volts. This speaker's enclosure was overly large to allow
for later optimization of the speaker enclosure volume. The design
presented here requires only an amplifier connected in series with a
step transformer to drive the PVDF speakers. This speaker design and
the acoustic response show that it is feasible to create a PVDF speaker
panel with enough sound power for actual implementation of an active
noise control system.

'Small-angle, multi-layered speakers are more effective in
producing low-frequency acoustic power than large-angle, single-layered
speakers. The 3.0 inch diameter speakers investigated showed increased
acoustic response for a 15-degree speaker over the similar acoustic
responses of the 20-, 30- and 45-degree speakers. While these speakers
were stiff enough to provide a uniform geometry, a S-degree speaker
required at least 3 layers of PVDF to produce a stable speaker that did
not produce acoustic harmonics. The 3-layer, S-degree speaker produced
more low-frequency acoustic power than all of the 1-layer speakers
investigated.

Multi-layer PVDF speaker response differs notably from the

21

22

single-layer speaker response. The general shape of the 3-layer,
S-degree speaker had drops in frequency response at approximately 525,
700 and 825Hz, while all 1-layer speaker responses were characterized by
a smooth shape from 440-840Hz. Additionally, a greater number of layers
increased the acoustic power, but also changed the shape of the
frequency response. The change in frequency response as a function of
the number of PVDF layers requires future investigation.

A speaker panel composed of many smaller-diameter speakers may be
more effective than the current 11-speaker panel. By reducing the
speaker diameter, the effective stiffness of the cone is increased and
it may be possible to use single-layer speakers at angles as small as 5-
degrees without structural harmonics developing. This will reduce

manufacturing efforts associated with multi-layer constructions.

LIST 0!" REFERENCES

LIST OF REFERENCES

M.J.Crocker and A.J.Price CPC Noise & Noise Control, Volume I, 1975 CRC
Press, Inc.

F.A.Everest, The Master Handbook of Acoustics, Second Edition, 1989 Tab
Books.

C.-K.Lee 1990 Journal of Acoustical Society of America 87, 1144-1158.
Theory of laminated piezoelectric plates for the design of distributed
sensors/actuators. Part 1: Governing equations and reciprocal
relationships.

W.R.Scott and P.E.Bloomfield 1981 Ferroelectrics 32, 79-83. Durable lead
attachment techniques for PVDF polymer transducers with application to
high voltage pulsed ultrasonics.

23

GENERAL REFERENCES

B.Allik and T.Hughes 1970 International Journal for Numerical Methods in
Engineering Vol. 2, 151-157. Finite element method for piezoelectric
vibration.

B.Allik, K.M.Webman and J.T.Hunt 1974 Journal of Acoustical Society of
America 56, 1782-1791. Vibrational response of sonar transducers using
piezoelectric finite elements.

B.Armstrong and G.McMahon 1984 IEEE Proceedings 131, 275-279.

Discussion of the finite-element modelling and performance of ring-shell
projectors.

L.L.Beranek, Noise Reduction, 1960 McGraw-Hill Book Company.

R.D.Blevins, Formulas for Natural Frequency and Mbde Shapes, 1984 Robert
E. Krieger Publishing Company.

W.J.Cady, Piezoelectricity, 1964 Dover Publications.

G.Gerliczy and R.Betz 1987 Sensors and Actuators 12, 207-223. Solef
PVDF Biaxially Oriented Piezo- and Pyro-electric Films for Transducers.

W.L.Ghering, Reference Data for Acoustic Noise Control, 1978 Ann Arbor
Science Publishers Inc. ‘

N.Guo, P.Cawley, and D.Hitchings 1992 Journal of Sound and Vibration
159(1), 115-138. The finite element analysis of the vibration

characteristics of piezoelectric discs.

IEEE Recommended Practice for Loudspeaker Measurements, IEEE Std 219-
1975.

IEEE Standard on Piezoelectricity, IEEE Std 176—1978.

B.Jaffe, W.R. Cook and H. Jaffe, Piezoelectric Ceramics, 1971 Academic
Press.

Y.Kagawa and T.Yamabuchi 1976 IEEE Transactions on Sonics and
Ultrasonics SU-23(4), 379-385. Finite element approach for a
piezoelectric circular rod.

R.G. Kepler and R.A. Anderson 1978 Journal of Applied Physics 49, 1232--

1235. Ferroelectricity in polyvinylidene fluoride.

24

25

Kynar Piezo Film Technical Manual 1987 Pennwalt Corporation.

C.-K.Lee and F.C. Moon 1989 Journal of Acoustical Society of America 85,
2432-2439. Laminated piezopolymer plates for torsion and bending
sensors and actuators.

C.-K.Lee and F.C. Moon 1990 Journal of Applied Mechanics: Transactions
of the ASME 57, 434-441. Modal Sensors/Actuators.

W.P.Mason, ed., D.A. Berlincourt, D.R. Curran, and H. Jaffe,
Piezoelectric and Piezomagnetic Materials and Their Function in
Transducers, Physical Acoustics, vol. 1 - part a, 1964 Academic Press.

Measuring Sound 1984 Bruel & Kjaer.
L.Meirovitch, Elements of Vibration Analysis, 1986 McGraw-Hill.

P.V.Murphy and G. Maurer 1981 J.Audio Eng Soc 29, 364. Double acoustic
output device. TK5981.A83 (mere abstract for presentation at lkHz).

D.F.Nelson, Electric, Optic, and Acoustic Interactions in Dielectrics,
1979 John Wiley & Sons.

Piezoelectric SOLEF PVDF polyvinylidene fluoride films and sheets.
Solvay & Cie S.A.

T.D.Rossing, The Science of Sound, Second Edition, 1990 Addison-Wesley
Publishing Company.

S.N.Rschevkin, A Course of Lectures on the Theory of Sound, 1963 The
MacMillan Company. ~

L.J.Segerlind, Applied Finite Element Analysis, 2nd ed., 1984 John Wiley
& Sons.

G.M.Sessler, ed., M.G. Broadhurst, and G.T.Davis, Piezo- and
Pyroelectric Properties, Topics in Applied Physics, vol. 33 Electrets,
1980 Springer-Verlag. ~

G.M.Sessler 1981 Journal of Acoustical Society of America 70, 1596-1608.
Piezoelectricity in polyvinylidenefluoride.

R.R.Smith, J.T.Hunt and D.Barach 1973 Journal of Acoustical Society of
America 54, 1277-1288. Finite element analysis of acoustically
radiating structures with applications to sonar transducers.

H.Sussner 1976 Physics Letters 58A, 426-428. Physical interpretation of
the anisotropy and temperature dependence of the piezoelectric constants
of polyvinylidene fluoride.

M.Tamura, S.Hagiwara, S.Matsumoto, and N.Ono 1977 Journal of Applied
Physics 48, 513-521. Some aspects of piezoelectricity and
pyroelectricity in uniaxially stretched poly(vinylidene fluoride).

26

S.Tasaka and S.Miyata, 1981 Ferroelectrics 32, 17-23. The origin of
piezoelectricity in poly(vinylidene fluoride).

M.Toda 1981 Ferroelectrics 32, 127-133. Voltage-induced large amplitude
bending device - PVF2 bilayer - its properties and applications.

P.W.Van Der Wal, Loudspeakers and Loudspeaker Cabinets, 1966 Philips
Paperbacks.

T.T.Wang, J.M.Herbert, and A.M.G1ass, ed., The Applications of
Ferroelectric Polymers, 1988 Blackie & Sons Ltd.

I.M.Ward, Structure and Properties of Oriented Polymers, 1975 John Wiley
& Sons.

D.B.Weems, Designing, Building 5 Testing Your Own Speaker System, 1981
Tab Books.

R.T.Winnicki and S.E.Auyer 1977 Journal of Acoustical Society of America
61, 875-881. Geometric factors affecting hydrophone performance.

J.Zelenka, Piezoelectric Resonators and Their Applications, 1986
Elsevier Science Publishers.

 

 

 

 

                 

 

 

 

 

 

      

 

 

 

 

 

 

 

     

 

          

 

    

 

    

 

 

 

 

          

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

          

 

 

 

     

 

 

  

 

  

 

 

 
 

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