Technical Note: The Anti-plane Scattering of SH Waves by the Non-circular Cavity in an Infinite Strip

Abstract

ABSTRACT In this paper, the problem of dynamic stress concentration in the process of anti-plane motion caused by a single circular cavity in a strip medium and the non-circular cavity in a porous strip medium is studied. In the case of only a single circular cavity, a numerical calculating example is presented to solve scattering around a circular cavity with a given SH guided wave and describe dynamic stress distribution at the edge of a circular cavity. Then, the results of the finite element method and analytical method are used to verify each other. Firstly, a compatible guided wave is constructed in the elastic strip, which satisfies stress-free conditions in upper and lower boundaries. Secondly, the scattering of waves around a circular cavity is expressed as series form by the employed wave function expansion method, and compatible scattering guided waves resulting from the reflection of waves off the boundaries of the elastic strip is constructed by repeated image superposition. Lastly, the coefficients of the wave function expansion are determined based on the stress-free condition of circular boundaries with pre-given incident guided waves. In the case of the non-circular cavity in the medium, the scattering of guided waves from the cavity is solved by finite element analysis, the dynamic stress distribution factor around the edge of the cavity is given, and to discuss influences of wave frequency and cavity position. The conclusions of this paper are of great reference value to the selection and ultrasonic non-destructive testing of anti-seismic materials.