Three-dimensional vibration analysis of a transversely isotropic piezoelectric cylindrical panel

Abstract

In this work, based on three-dimensional piezoelectric elasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic cylindrical panel is presented. Three displacement potential functions are introduced so that the equations of motion and Gauss’ equation are uncoupled and simplified. It is noticed that a purely transverse (SH) mode is independent of piezoelectric effects and the rest of the motion. The equations for free vibration problems are further reduced to four second-order ordinary differential equations, after expanding the displacement and electric potential functions with an orthogonal series. The dispersion relations for an electrically shorted and charge free 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 to compare the results to the existing areas, numerical examples are presented and the computed functions are illustrated graphically.