On the Stress Field Caused by the Time Harmonic Force in the System Consisting of the Piezoelectric Covering Layer and Piezoelectric Half-Plane

Abstract

The Lamb problem is considered for the system consisting of the piezoelectric covering layer and orthotropic half-plane. The investigation is carried out within the framework of the piece-wise homogeneous body model by utilizing the exact equations of motion of the linear theory of electro-elasticity. The plane strain state is considered and it is assumed that between the covering layer and half-plane the perfect contact conditions satisfy. The boundary value problem under consideration is solved by employing Fourier exponential transformation with respect to the coordinate directed along the interface line. The algorithm proposed in a paper (Akbarov S, Ilhan N, Int J Solids Struct 46:3873, 2009) is developed to obtain numerical results on the normal stress distribution on the interface plane. Concrete results are presented and discussed for the piezoelectric materials PZT-5A, PZT-5H, PZT-4 and PZT-7A and orthotropic half-plane. The mechanical properties of the half-plane material are given through the mechanical constants of the PZT-5A, PZT-5H, PZT-4 and PZT-7A. It is established that the piezoelectricity of the covering layer causes to decrease of the absolute values of the normal stresses acting on the interface surface.