Multiple scattering of flexural waves from a cylindrical inclusion in a semi-infinite thin plate

In this paper, image method and wave function expansion method are applied to investigate the multiple scattering of flexural waves and dynamic stress concentration from a cylindrical inclusion in a semi-infinite thin plate, and the analytical solution of this problem is obtained. The semi-infinite plate with roller-supported boundary is considered, and the image method is used to satisfy the boundary condition. The addition theorem for Bessel functions is employed to accomplish the translation of wave fields between different local coordinate systems. As an example, the numerical results of dynamic stress concentration factors around the inclusion are graphically presented and analyzed. Analysis shows that the angular distribution of the dynamic stress around the inclusion shows great difference when the distance between the inclusion and the semi-infinite edge is different. The effects of the elastic modulus, density, Poissonʹs ratio, and the thickness of the inclusion on the shadow side of the inclusion are greater when the distance between inclusion and the semi-infinite edge is small. In the region of lower frequency, the effects of the elastic modulus, density, Poissonʹs ratio, and the thickness of the inclusion on the dynamic stress are little. Comparisons with other existing models are also discussed.