A buried piezoelectric spherical particle incident upon by plane shear waves

Abstract

The dynamic electromechanical coupling in piezocomposites in response to wave propagation and scattering phenomenon is of great importance in engineering sciences, innovative technologies, and nondestructive evaluation. The present work is concerned with the scattering of shear waves by a spherical piezoelectric particle bonded to an infinitely extended isotropic elastic polymer matrix. The particle is assumed to have radial polling direction and spherically isotropic electromechanical properties. An incident shear wave propagates in the positive z-direction, while polarizes along the x-axis. The incident, scattered, and the transmitted electromechanical fields are analytically achieved by the utilization of spherical harmonics followed by the employment of the extended Frobenius series for the interior points of the particle to solve a set of four governing coupled differential equations for the displacement and the electric potentials. The set problem possesses a symmetry with respect to the xz-plane and as it will be shown the mentioned differential equations in conjunction with the particle-matrix interface conditions can be transformed into two systems of linear algebraic equations for the unknown constants which appeared in the Frobenius series. Verification is made in the special case of purely elastic isotropic particle. In the present formulation there is no restriction on the range of the frequency of the incident wave. The effect of the piezoelectric particle properties on the total scattering cross section is investigated. The dynamic stress concentration factors and the dynamic electric displacement concentration factor at the matrix-piezoelectric interface are calculated. Subsequently, the effect of the frequency of the incident wave on the maximum values of the dynamic stress concentration factors and the dynamic electric displacement concentration factor as well as their appurtenant locations are discussed and compared to those of the corresponding static cases.