Scattering of flexural wave in thin plate with multiple holes by using the null-field integral equation method

Abstract

In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and dynamic moment concentration factors in an infinite thin plate with multiple circular holes by using the null-field integral formulation in conjunction with degenerate kernels and Fourier series. In the proposed approach, all the kernels in the direct formulation are expanded into degenerate forms. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. The scattering problem can be solved by decomposing it into two parts: incident wave field and radiation field. The radiation field is solved by using the proposed method and then the total field is obtained by adding it with the incident wave field. The results of dynamic moment concentration factors for the plate with one hole are compared with the analytical solution to verify the validity of the proposed method. For the cases of small wave number, the quasi-static results of a plate with one or multiple circular holes are compared with the static data of finite element method (FEM) using ABAQUS. The effect of distance between the centers of holes on dynamic moment concentration factors is also investigated by using the proposed method.