Linear dynamics and distributed control of piezoelectric laminated continua have been intensively investigated in recent years. In this study, dynamics, electromechanical couplings, and control of thermal buckling of a nonlinear piezoelectric laminated circular plate with an initial large deformation are investigated. It is assumed that the transverse nonlinear component is much more prominent than the other two in-plane components—the von Karman type geometrical nonlinearity. In addition, the piezoelectric layers are uniformly distributed on the top and bottom surfaces of the circular plate. Accordingly, the control effect is introduced via an equivalent control moment on the circumference. Dynamic equations and boundary conditions including the elastic and piezoelectric couplings are formulated, and solutions are derived. Active control of plate’s nonlinear deflections, thermal buckling, and natural frequencies using high control voltages are studied, and their nonlinear effects are evaluated.

Issue Section:
Research Papers
Topics:
Buckling, Deflection, Dynamics (Mechanics), Couplings, Boundary-value problems, Deformation, Equations of motion
1.
Librescu
L.
,
1987
, “
Refined Geometrically Nonlinear Theories of Anisotropic Laminated Shells
,”
Quarterly of Applied Mathematics
, Vol.
XLV
, No.
1
, pp.
1
–
22
.
2.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley & Sons, Inc., New York.
3.
Pai
P. F.
,
Nafeh
A. H.
,
Oh
K.
, and
Mook
D. T.
,
1993
, “
A Refined Nonlinear Model of Piezoelectric Plate with Integrated Piezoelectric Actuators and Sensors
,”
Int. J. Solids Struct.
, Vol.
30
, pp.
1603
–
1630
.
4.
Sreeram, P. N., Salvady, G., and Naganathan, N. G., 1993, “Hysteresis Prediction for a Piezoceramic Material System,” Adaptive Structures and Material Systems, AD-Vol. 35, pp. 35–42, 1993 ASME WAM, New Orleans, LA, Nov. 28–Dec. 3, 1993.
5.
Tzou, H. S., 1993, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers, February 1993.
6.
Tzou, H. S., Anderson, G. L., Guran, A., Inman, D. J., and Natori, M. C., (Ed), 1996, Structronic Systems: Smart Structures, Devices and Systems, World Scientific Publisher. (To appear).
7.
Tzou, H. S., and Fukuda, ed, 1992, Precision Sensors, Actuators, and Systems, Kluwer Academic Publishers, Dordrecht/Boston/London, November 1992.
8.
Tzou
H. S.
, and
Zhou
Y.-H.
,
1995
, “
Dynamics and Control of Nonlinear Circular Plates with Piezoelectric Actuators
,”
Journal of Sound and Vibration
, Vol.
188
, No.
2
, pp.
189
–
207
.
9.
Yu, Y. Y., 1993, “Some Recent Advances in Linear and Nonlinear Dynamical Modeling of Elastic and Piezoelectric Plates,” Adaptive Structures and Material Systems, AD-Vol. 35, pp. 185–195, 1993 ASME WAM, New Orleans, LA, Nov. 28–Dec. 3, 1993.
10.
Zhou, Y. H., 1989, “Nonlinear Bending, Vibration and Buckling of Structures under Static Loads,” Ph.D. Dissertation, Lanzhou University.
11.
Zhou
Y. H.
,
Yeh
K. Y.
, and
Rimrott
F. P. J.
,
1994
, “
Theory of Vibrating Diaphragm Type Pressure Sensor
,”
AIAA J.
, Vol.
32
, No.
3
, pp.
633
–
638
.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.