Three-dimensional vibration analysis of a piezothermoelastic cylindrical panel

In this work, based on three-dimensional piezoelectric thermoelasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel is presented. Displacement and electric potential functions are introduced in order to solve the equations of motion, Gauss equation and heat conduction equation. It is noticed that a purely transverse mode is independent of piezoelectric and pyroelectric effects and gets decoupled from rest of the motion. The equations for free vibration problem are further reduced to five second-order ordinary differential equations, after expanding the displacement, temperature change and electric potential functions with an orthogonal series. The dispersion relation for electrically-shorted/charge-free, thermally insulated/isothermal and simply supported cylindrical panel with stress-free edges have been obtained and discussed. A modified Bessel function solution with complex arguments is directly used for complex eigenvalues. In order to clarify the developed method and compare the results to the existing ones, numerical examples are presented for PZT-5A material, and the computed functions are illustrated graphically. (C) 2004 Elsevier Ltd. All rights reserved.