Three-Dimensional Free Vibration Analysis of Multiphase Piezocomposite Structures

Abstract

Based on Hamilton’s principle, a three-dimensional semianalytical method for the analysis of free vibration of a structure composed of piezoelectric and elastic materials is developed. Computations of dynamical behavior including natural frequencies, and mode shapes are of interest. In this approach, the mechanical displacement and electric potential functions, in each region, are expressed as products of a three-dimensional (3D) base function and a 3D polynomial with unknown coefficients. The base functions over every domain are constructed with respect to the kinematical boundary conditions, geometry of the structure, and the geometry of that domain. These base functions satisfy the necessary continuities in the displacement field and electric potential at the interfaces, and at the same time accounting for possible discontinuities in their derivatives at the interfaces. The mode shapes will be decomposed in accordance to the presence of any symmetry plane. The robustness of the proposed approach is demonstrated through comparison with the finite element method as applied to the following problems: (1) A perforated thick plate made of piezoelectric and elastic layers and (2) an elastic plate containing a hole, whose exact solution is available. For the latter problem, the result of the present study is in good agreement with the exact solution. Also, an example of a thick PZT plate containing an elastic inclusion with a complex interface, and various types of boundary conditions is considered.