Acoustic Response of Piezoelectric
Membranes
A.S. Wixom, D.F. Bahr, M.J. Anderson
WSU REU 2010 – Materials Science and Engineering
• Total Harmonic Distortion (THD)
PRE-STRESS EFFECT
The acoustic response of piezoelectric membranes has been
shown to improve when bulged by a differential pressure.
Research to this point has been focused on transducers
using lead zirconate titanate (PZT) as the piezoelectric
layer.
•Pressure-deflection Curve is regressed to the equation
P  o w w
3
 o  d1
t
a
Et
  d2
4
(1  )a
2
OBJECTIVES
f  fR
f 
fB
f_bar = Normalized frequency
f = Frequency of interest
fR = Resonant frequency
fB = Lower half-bandwidth of resonance
An example of these values is shown below for both PVDF and PZT
transducers.
t = Membrane thickness
d1, d2 = Geometry constants
E = Young’s Modulus
ν = Poisson’s Ratio
σ = Initial stress in membrane
PVDF – 2C
•Results for several PVDF membranes and a PZT membrane
for comparison
PZT
fR
Displacement (μm/V)
where
P = Applied pressure
w = Center displacement of membrane
γo = Initial edge tension
δ = Sheet stiffness
a = Membrane span (radius)
•Develop transducers using the piezoelectric polymer
polyvinylidene flouride (PVDF)
THD has a strong dependence on resonance, so in order to compare
different transducers, a normalized frequency was defined.
fR
Displacement (μm/V)
INTRODUCTION
fB
fB
Frequency (Hz)
•Investigate the effect of pre-stress in the membrane on
acoustic response
Trans. ID γo (kPa/μm) δ (mPa/μm^3) σ (Mpa) E (Gpa)
2A
0.0062
0.484
3.85
5.29
2B
0.0116
0.473
7.24
5.18
2C
0.0215
0.447
13.4
4.89
PZT
0.2968
64.6
90.0
102
•Compare PZT and PVDF transducers
Frequency (Hz)
Restricting measurements to negative normalized frequencies,
those between -1 and 0 are within the resonance band with full
resonance occurring at 0. THD measurements for both PZT and
PVDF transducers at different normalized frequencies and pressures
were gathered.
•Silver ink painted onto the film is patterned to form
electrodes and leads
•Transducers are stretched to stress the membrane
Pre-Stress Peak - 500 Hz
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
2A
2B
2C
-10
Cut and patterned
transducer
being
stretched to produce
uniform biaxial stress
in the active area.
-5
0
Pressure (kPa)
5
Reduced pre-stress
results
in
an
increasing peak in
response due to a
smaller levels of
pressure differential
10
THD Comparison - 3 kPa
100
10
10
PVDF-2C
1
PZT
THD (%)
100
0.1
PVDF-2C
1
PZT
0.1
-2.5
-2
-1.5
-1
-0.5
0
-2.5
Normalized Frequency
-2
-1.5
-1
-0.5
0
Normalized Frequency
THD Comparison - 5 kPa
1000
THD (%)
•Sheets of 28 μm think PVDF film are cut into transducer
blanks
•Response to a harmonic input was measured at differing
pressurization levels
Displacement (μm/V)
TRANSDUCER CONSTRUCTION
THD (%)
THD Comparison - 1 kPa
100
PVDF-2C
10
PZT
1
-2.5
-2
-1.5
-1
-0.5
The PVDF transducer tends to
have slightly lower levels of THD.
The peak in the PZT THD is due to
the smaller resonance region
below
the
main
resonant
frequency.
0
Normalized Frequency
PVDF vs. PZT
•Frequency Response
Frequency (Hz)
•Testing is completed using the bulge testing apparatus to
pressurize the transducers
Frequency (Hz)
Pressure (kPa)
Frequency (Hz)
Pressure (kPa)
Pressure (kPa)
Pressure (kPa)
Mounted transducer
being tested on bulge
testing set-up.
Displacement (μm/V)
•A two part puck is used to mount and clamp the active area
of the transducer
CONCLUSION
PZT
Displacement (μm/V)
PVDF – 2C
Frequency (Hz)
PVDF has a lower resonant frequency as well as a lower overall response when
compared to PZT. The symmetry of layers in PVDF results in zero bending actuation
causing the dead spot to occur at zero pressure differential where the PZT occurs at
a slight negative pressure due to non-symmetrical layers.
Reduction of pre-stress in
piezoelectric membranes
produces a peak in acoustic response for low levels of
differential pressure. When comparing PVDF and PZT
transducers, we see that PVDF has a smaller response but it
also has less THD and therefore produces a cleaner signal.
Future work can be done examining the power required to
operate piezoelectric acoustic transducers. Also, the
sensitivity of piezoelectric membranes acting as free field
microphones should be investigated.
Thanks to Bruce Chang for getting me started on the bulge testing
equipment and to everyone in the MEMS lab who were there to bounce
ideas off of.
This work was supported by the National Science Foundation’s REU
program under grant number DMR-0755055.