Models for simple closed-form analytical solutions for accurately predicting static deflections of circular thin-film piezoelectric microactuators are very useful in design and optimization of a variety of MEMS sensors and actuators utilizing piezoelectric actuators. While closed-form solutions treating actuators with simple geometries such as cantilevers and beams are available, simple analytical models treating circular bending-type actuators commonly used in MEMS applications are generally lacking. This paper presents a closed-form analytical solution for accurately estimating the deflections and the volume displacements of a circular multi-layer piezoelectric actuator under combined voltage and pressure loading. The model for the analytical solution presented in this paper, which is based on classical laminated plate theory, allows for inclusion of multiple layers and non-uniform diameters of various layers in the actuator including bonding and electrode layers, unlike other models previously reported in the literature. The analytical solution presented is validated experimentally as well as through a finite element solution and excellent experiment-model correlation within 1% variation is demonstrated. General guidelines for optimization of circular piezoelectric actuator are also discussed. The utility of the model for design optimization of a multi-layered piezoelectric actuator is demonstrated through a numerical example wherein the dimensions of a test actuator are optimized to improve the displaced volume by three-fold under combined voltage and resisting pressure loads.

1.
DeVoe
D. L.
and
Pisano
A. P.
,
1997
, “
Modeling and optimal design of piezoelectric cantilever microactuators
,”
J. Microelectromech. Syst.
,
6
(
3
), pp.
266
270
.
2.
Weinberg
M. S.
,
1999
, “
Working equations for piezoelectric actuators and sensors
,”
J Microelectromech Syst
,
8
(
4
), pp.
529
531
3.
Trolier-Mckinstry
S.
and
Muralt
P.
,
2004
, “
Thin film piezoelectrics for MEMS
,”
J. Electroceram.
,
12
(
1–2
), pp.
7
17
.
4.
Dobrucki
A. B.
and
Pruchnicki
P.
,
1997
, “
Theory of piezoelectric axisymmetric bimorph
,”
Sens. Actuators, A
,
58
(
3
), pp.
203
212
.
5.
Li
S.
and
Chen
S.
,
2003
, “
Analytical analysis of a circular PZT actuator for valveless micropumps
,”
Sens. Actuators, A
,
104
(
2
), pp.
151
161
.
6.
Timoshenko, S. and Woinowsky-Krieger, S., 1959, Theory of plates and shells, McGraw-Hill, New York.
7.
Morris
C. J.
and
Forster
F. K.
,
2000
, “
Optimization of a circular piezoelectric bimorph for a micropump driver
,”
J. Micromech. Microengineering
,
10
(
3
), pp.
459
459
.
8.
Reddy, J.N., 1997, “Classical and First-order Theories of Laminated Composite Plates,” in Mechanics of laminated composite plates: theory and analysis, CRC Press, Boca Raton.
9.
Jones, R.M., 1999, Mechanics of composite materials, Taylor & Francis, Philadelphia, PA.
10.
Cheng
Z.
,
Lim
C. W.
and
Kitipornchai
S.
,
1999
, “
Three-dimensional exact solution for inhomogeneous and laminated piezoelectric plates
,”
Int. J. Eng. Sci.
,
37
(
11
), pp.
1425
1439
.
11.
Lee
C. K.
,
1990
, “
Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships
,”
J. Acoust. Soc. Am.
,
87
(
3
), pp.
1144
1158
.
12.
Mitchell
J. A.
and
Reddy
J. N.
,
1995
, “
A refined hybrid plate theory for composite laminates with piezoelectric laminae
,”
Int. J. Solids Structures
,
32
(
16
), pp.
2345
2367
.
13.
Yang
S.
and
Ngoi
B.
,
1999
, “
General sensor equation and actuator equation for the theory of laminated piezoelectric plates
,”
Smart. Mater. Struct.
, (
3
), pp.
411
415
.
14.
Wang
B.
and
Rogers
C. A.
,
1991
, “
Laminate plate theory for spatially distributed induced strain actuators
,”
J. Composite Mater.
,
25
(
4
), pp.
453
468
.
15.
Chee
C. Y. K.
,
Tong
L.
and
Steven
G. P.
,
1998
, “
A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures
,”
J. Intell. Mater. Syst. Struct.
,
9
(
1
), pp.
3
19
.
16.
Prasad, S., Sankar, B., Cattafesta, L., Horowitz, S., Gallas, Q. and Sheplak, M., 2002, “Two-Port Electroacoustic Model of a Piezoelectric Circular Composite Plate,” 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 22–25 April 2002, Denver, Colorado, p. 1–9.
17.
American Piezo Ceramics, Inc., URL: http://www.americanpiezo.com
18.
ASM International, 1990, Metals handbook, ASM International, Materials Park, Ohio.
19.
Elka
E.
,
Elata
D.
and
Abramovich
H.
,
2004
, “
The electromechanical response of multilayered piezoelectric structures
,”
J. Microelectromech Syst.
,
13
(
2
), pp.
332
341
20.
Chang
S. H.
and
Du
B. C.
,
2001
, “
Optimization of asymmetric bimorphic disk transducers
,”
J. Acoust. Soc. Am.
,
109
(
1
), pp.
194
202
.
21.
Coorpender, S.J., Finkel, D., Kyzar, J., Sims, R., Smirnova, A.B., Tawhid, M., Bouton, C.E. and Smith, R.C., 1999, “Modeling and optimization issues concerning a circular piezoelectric actuator design,” American Society of Mechanical Engineers, Aerospace Division (Publication) AD, 59, pp. 199–204.
22.
Deshpande
M.
and
Saggere
L.
,
2005
, “
Modeling and Design of an Optically Powered Microactuator for a Microfluidic Dispenser
,”
J. Mech. Design
,
127
(
4
), pp.
825
836
.
23.
Delobelle
P.
,
Guillon
O.
,
Fribourg-Blanc
E.
,
Soyer
C.
,
Cattan
E.
and
Remiens
D.
,
2004
, “
True Young modulus of Pb(Zr,Ti)O3 films measured by nanoindentation
,”
Appl. Phys. Lett.
,
85
(
22
), pp.
5185
5187
.
24.
Espinosa
H. D.
,
Prorok
B. C.
and
Fischer
M.
,
2003
, “
A methodology for determining mechanical properties of freestanding thin films and MEMS materials
,”
J. Mech. Phys. Solids
,
51
(
1
), pp.
47
67
.
25.
Zhao
M.-.
,
Fu
R.
,
Lu
D.
and
Zhang
T.-.
,
2002
, “
Critical thickness for cracking of Pb(Zr0.53Ti0.47)O3 thin films deposited on Pt/Ti/Si(100) substrates
,”
Acta. Materialia
,
50
(
17
), pp.
4241
4254
.
26.
Wang, G., Sankar, B.V., Cattafesta, L.N. and Sheplak, M., 2002, “Analysis of a composite piezoelectric circular plate with initial stresses for MEMS,” 2002 ASME International Mechanical Engineering Congress and Exposition, Nov 17–22 2002, New Orleans, LO, pp. 339–346.
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