A note on a plate having a circular cavity excited by plane harmonic SH waves

Abstract

Abstract A solution for the plate having a circular cavity subject to plane harmonic SH waves, horizontally polarized shear waves, is presented in this paper. The method of solution involves series expansion of incident and reflected SH waves from the cavity and two free surfaces in terms of cylindrical wave functions and the image method, respectively. The image method proposed in this article is used to satisfy the boundary condition of the traction free surfaces on the plate. Then, the boundary condition of the cavity is applied to the solution having unknown coefficients. In order to simplify the problem, only the lowest mode is taken into account in the plate. The results obtained in this study provide important information about the behaviour of the plate near the discontinuity. Numerical results show that the distance between the upper surface and the nearest cavity boundary (at θ=0, r=a ) has primary effect. If the radius of the cavity is relatively small compared with the thickness of the plate, the solutions approach the full space's solutions for the cavity, well-known in literature. Also, those solutions for the plate correspond to the solutions of the plate without cavity. Dynamic stress concentration factors around the cavity and displacements in the cross-section of the plate are obtained near the cavity for various wave numbers. It is concluded that the presented solutions are partially analytical solutions, so they can be used for construction and verification of approximate numerical techniques such as the boundary element method (BEM), finite element method (FEM), finite difference method (FDM), etc.