Precise solutions of dynamic problems in stratified transversely isotropic piezoelectric materials

Abstract

Built upon the precise integration method (PIM) and dual vector technology, complete formulae for components of the electro-mechanical field in linearly elastic, stratified transversely isotropic piezoelectric materials subjected to dynamic axisymmetric mechanical and electrical loadings are acquired. It is assumed that between dissimilar adjacent layers perfect contact conditions are satisfied. Uniform axisymmetric forces exerted over a circular or semi-circular patch in the frequency domain are located at the exterior or interface of the layered system. Additionally, the introduced methodology is universal enough to account for any number of strata. Starting with partial differential equations of motion related to elastic displacements and the electric potential, and aided by the Hankel integral transformation and the technique of dual vector, a first-order ordinary differential governing matrix equation in the transformed domain is obtained. As a highly precise approach, the PIM is provided to compute the ordinary differential key equation for constructing the global stiffness matrix of the multilayered piezoelectric materials based on the continuous and compatible conditions between adjacent strata. As a result, the mechanical and electrical components with any conceived accuracy are gained. By dint of inverting the Hankel integral transformation, the dynamic axisymmetric electro-mechanical solutions are then transferred into the physical domain. Comparisons with finite element results implemented by the commercial software validate the accuracy and feasibility of the employed approach. Other numerical exercises are carried out to portray the role of parameters, form of prescribed loadings, frequency of excitation and thickness of layers on the elastodynamic axisymmetric solutions of the stratified piezoelectric materials.