Planar Free Vibrations of Off-Axis Piezoelectric Laminates
Publication: Journal of Engineering Mechanics
Volume 123, Issue 6
Abstract
The frequencies of free vibration and the through-thickness mode shapes for off-axis piezoelectric laminates in cylindrical bending are computed using an exact solution and an approximate discrete-layer theory. In the exact solution, the in-plane displacement and electrostatic potential functions for the case of simple support are selected to reduce the equations of motion and the charge equation into a system of ordinary differential equations. The unknown field distributions are found to be a function of eight unknown constants per layer and the resonant frequency. These are calculated using an iterative procedure. The discrete-layer approach uses one-dimensional approximation functions to represent the through-thickness behavior of the fields combined with analytic approximations in the axial direction. Example problems are studied for several geometric, material, and support conditions. For the case of simple support, excellent agreement is found between the two formulations.
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References
1.
Heyliger, P. R.(1994). “Static behavior of laminated elastic piezoelectric plates.”AIAA J., 32, 2481–2484.
2.
Heyliger, P. R., and Brooks, S. B.(1995). “Exact free vibration of piezoelectric laminates in cylindrical bending.”Int. J. Solids and Struct., 32(20), 2945–2960.
3.
Heyliger, P. R., and Saravanos, D.(1995). “Exact free vibrations of laminated plates with embedded piezoelectric layers.”J. Acoustical Soc. of Am., 98(3), 1547–1557.
4.
Heyliger, P. R., Pei, K. C., and Ramirez, G. (1994). “Discrete-layer piezoelectric plate and shell models for active tip-clearance control.”NASA Contractor Rep. G-NAG3-1520, Nat. Aero. and Space Admin., Washington, D.C.
5.
Jones, A. T.(1969). “Exact natural frequencies for cross-ply laminates.”J. Compos. Mat., 4, 476–491.
6.
Jones, A. T.(1971). “Exact natural frequencies for modal functions for a thick off-axis laminate.”J. Compos. Mat., 5, 504–520.
7.
Saravanos, D., and Heyliger, P. R.(1995). “Coupled layerwise analysis of composite beams with embedded piezoelectric sensors and actuators.”J. Intelligent Mat. Sys. and Struct., 6, 350–363.
8.
Pagano, N. J. (1970). “Influence of shear coupling in cylindrical bending of anisotropic laminates.”J. Compos. Mat., 4(July), 330–343.
9.
Parton, V. Z., and Kudrayavtsev, B. A. (1988). Electromagnetoelasticity. Gordon and Breach Science Publishers, New York, N.Y.
10.
Pauley, K. E., and Dong, S. B.(1976). “Analysis of plane waves in laminated piezoelectric plates.”Wave Electronics, 1, 265–285.
11.
Reddy, J. N.(1987). “A generalization of two-dimensional theories of laminated composite plates.”Communications in Appl. Numer. Methods, 3, 113–118.
12.
Reddy, J. N., and Robbins, D. H.(1993). “Modeling of thick composites using a layerwise laminate theory.”Int. J. Numer. Methods in Engrg., 36, 655–677.
13.
Tashiro, K., Tadokoro, H., and Kobayashi, M.(1981). “Structure and piezoelectricity of poly(vinylidene fluoride).”Ferroelectrics, 32, 167–175.
14.
Tiersten, H. F. (1969). Linear piezoelectric plate vibrations. Plenum Publishing Corp., New York, N.Y.
15.
Young, D., and Felgar, Jr., P. V. (1949). Tables of characteristic functions representing the normal modes of vibration of a beam. Univ. of Texas Publ. No. 4913, Univ. of Texas, Austin, Tex.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 123 • Issue 6 • June 1997
Pages: 604 - 611
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jun 1, 1997
Published in print: Jun 1997
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