Elastodynamic response for the multi-layered transversely isotropic piezoelectric solid subjected to time-harmonic loads

Abstract

The precise integration algorithm (PIA) and the approach of dual vector form are utilized to explore the elastodynamic axisymmetric response of the multi-layered transversely isotropic piezoelectric medium. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the layered system. The elastic solid is under the action of axisymmetric mechanical or electrical time-harmonic loads prescribed either at the external surface or in the interior of the stratified medium. There is no limit of the thickness and number of layers to be considered. Based on the dual vector form and the Hankel integral transform, the governing equations of the cross-anisotropic piezoelectric material are conveniently turned into the standard ordinary differential matrix equation. The PIA is introduced to evaluate the first-order ordinary differential matrix equation with specified two-end boundary conditions. As PIA is a highly accurate method, any desired accuracy of dynamic piezoelectric solutions can be accomplished. In addition, the dual vector form of motion equation facilitates the combination of two neighboring layers into a new one and computational efforts could be reduced to a great extent. The true piezoelectric field is obtained by taking inversion of the Hankel integral transform. Finally, a comparison with the numerical solutions for stratified piezoelectric half-space is made to confirm the accuracy of the proposed procedure. Meanwhile, some numerical examples are also included to discuss the influence of loading positions, types of external forces, stratified characters and weak and thin interlayer on the dynamic response of the layered piezoelectric medium.