Scattering of SH-waves by an interacting circular cavity and crack near the bimaterial interface

Abstract

The problems of SH-wave scattering, which is caused by half-space circular cavity near the bimaterial interface and crack of arbitrary length and arbitrary position, are studied in this paper based on the field of elastodynamics, and the methods of Green's Function, complex variables function, the method of crack-division and multi-polar coordinates are used here. Firstly, a suitable Green's function is constructed, which is the key technology of this problem. Two Green's functions are needed here: The first one is an essential solution of the displacement field for the elastic half-space containing a circular cavity and crack with arbitrary length and arbitrary position under the out-of-plane harmonic line-loads at an arbitrary point; The second Green' function is an essential solution of the displacement field for the elastic half space subjected to the out-of-plane harmonic line source loads at half space surface arbitrary point. The scattering of SH-wave by the crack at an arbitrary position and a circular cavity near the bimaterial interface is investigated, the problem can be regarded as harmony model: the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and a crack, and the other is a complete elastic half space. The horizontal surfaces of the two parts are loaded with unknown anti-plane forces in order to satisfy at the linking section. A series of Fredholm integral equations can be set up through continuity conditions. Then, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite integral equations, the analytical solution of displacement field and stress field of scattering of SH-wave by the crack and circular cavity near the bimaterial interface are given. Numerical examples are provided to show the influences of wave numbers, incident angle, the distance between the center of the circular cavity and horizontal surfaces, the distance between the center of the circular cavity and crack, the angle of crack, the length of crack, and parameter combinations of different media upon dynamic stress concentration factor (DSCF).