Materials Characterization and Acoustic
Performance of Piezoelectric Membranes
Andrew Davis, Dr. David Bahr, Dr. Mike Anderson
WSU REU 2011 Materials Science and Engineering
Introduction & Objectives
Future Work
A new class of acoustic transducer with a polyvinylidene fluoride (PVDF)
membrane utilizing in plane tension and out of plane geometry shows
higher acoustic properties than un-stressed PVDF counterparts.
The polynomial used in the pressure deflection curve is a very good
approximation for isotropic materials, but PVDF is transversely isotropic
which means that there will be a degree of uncertainty in the results. It
is important to develop a cubic polynomial for transversely isotropic
membranes. The way to do this is by expanding upon the work done by
Timoshenko.
Goals:
•
Take into account the transversely isotropic nature of PVDF membranes.
•
Test membranes with uniaxial stress to determine properties.
Test acoustic performance when stressed parallel and perpendicularly
to the strain of manufacturing.
Nxy Ny

0
x
y
Nx Nxy

0
x
y
• Strain Components:
u 1   
x    
x 2  x 
2
 1   

y 
 
y 2  y 
2
u   
xy  

y x x y
• Secondary strain components:
Transducer mounted with leads
attached to measure amplitude
resonance.
This shows a typical pressure
deflection curve. The regression
shown in green has only a linear
and a cubic term.
From here the value of the elastic
modulus was calculated.
1
1
Nx Ny  y  Ny Nx 
x 
hE
hE
1
xy 
Nxy
hG
• Strain components combined to form stress function:



P0  N x 2  N y 2  2 N xy
0
x
y
xy
2
2
2
• The new polynomial will include the transversely isotropic stiffness
matrix with 5 engineering constants: two elastic modulus, two
Poisson's ratio, and one shear modulus.
• By assuming the coordinate system to be centered around the
center of the transducer, using boundary conditions, and symmetry
of strain, progress can be made toward developing the polynomial
that can be regressed to determine the elastic modulus of
transversely isotropic materials.
Acoustic Performance
Progression from circular transducer to an infinitely long
rectangle means that stress is added only in the direction of
the small side length.
Projections show that a
lower pre-stress would
allow initial experiments
to be run at relatively low
pressure situations.
Deflection (um)
• Stressing the membrane in the direction of original fabrication strain
produces a higher acoustic response than unstressed membranes or
membranes stressed perpendicularly to fabrication strain.
These figures show that as the pressure increases the resonating
frequency shifts upward drastically when the differential pressure
increases. This also confirms that the symmetry of PVDF cause zero
bending actuation at zero pressure, causing the drop.
Changing Pre-Stress to Observe Cubic Shape
Conclusion
• Using a rectangular transducer with an aspect ratio of around 5 it is
reasonable to assume that the stress is uni-axial and therefore directional
properties can be approximated.
When the rectangular transducer is stressed
nearly all of the stress is in the direction of the
small side as shown.
Differential Pressure (kPa)
•
• Equations of equilibrium for applied stress:
References
• J.J. Vlassak, W.D. Nix, “A new bulge test technique for the determination of
Young’s modulus and Poisson’s ratio of thin films”, Journal of Materials
Research, Vol. 7, No. 12, 3242-3246 (1992).
• S. Timoshenko, “Theory of Plates and Shells” (1959).
This “Gullwing” plot shows the lowest
response at zero differential pressure,
increases for a short range of pressure,
then the response drops drastically.
To all in the MEMS lab who answered questions
and gave advice, thanks.
This work was supported by the National Science
Foundation’s REU program under grant number
DMR-1062898