Scattering of flexural wave in a thin plate with multiple inclusions by using the null-field integral equation approach

Abstract

The subject of scattering flexural wave in a thin plate with multiple inclusions subject to the incident wave is studied in this paper. A semi-analytical approach is proposed to solve this problem which can be decomposed into several internal inclusion problems and an external plate problem under the incident wave. The intensity of radiation field in the associated external problem can be derived by using the null-field integral formulation. The dynamic moment concentration factor (DMCF) around the circular inclusions, as well as the far field scattering pattern is determined. The numerical results for an infinite plate with one inclusion are compared with the available analytical solutions to verify the validity of the proposed method. For the cases of small wave number, the quasi-static results of an infinite plate with one or multiple circular inclusions are compared with static data of finite element method (FEM) using ABAQUS. Numerical results indicate that the DMCF of two inclusions is apparently larger than that of one when two inclusions are close to each other. Fictitious frequency appearing in the external problem can be suppressed by using the more number of Fourier series terms. The effects of space between inclusions on both the DMCF and the far scattering pattern are also investigated. It shows that the space between scatters has the opposite effect on the near field in comparison with the far field.