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

Abstract

The subject of scattering flexural wave in a thin plate with multiple circular inclusions under the incident flexural wave is studied in this paper. A semi-analytical approach is proposed to solve this problem which can be decomposed into several interior circular inclusion problems and an exterior plate problem subject to the incident wave. The scattered field in the associated exterior problem is solved by using the null-field integral formulation in conjunction with degenerate kernels, tensor transformation and Fourier series. All dynamic kernels of plate in the direct formulation are expanded into degenerate forms to avoid the integral singularity and further the rotated degenerate kernels have been derived to consider the general case of multiple circular inclusions. The proposed results for an infinite plate with one circular inclusion are compared with the available analytical solutions to verify the validity of the proposed method. To demonstrate the generality of the proposed method, the cases of multiple inclusions are studied and their quasi-static results are verified by static data of 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 exterior problem can be suppressed by using the more number of Fourier series terms. Numerical results show that the space between scatterers has the opposite effect on the near-field DMCF in comparison with the far-field scattering pattern.