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

Abstract

In this paper, a semi-analytical approach is proposed to solve the scat- tering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinitethinplatewithmultiplecircularholes. Thenull-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynamic kernels of plate are expanded into degenerate forms and further the rotated degen- erate kernels have been derived for the general exterior problem. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. 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-staticresults of a plate with one or multiple circular holes are compared with the static data of finite element method (FEM) using ABAQUS. Numerical results indicate that the DMCF of two holes is apparently larger than that of one hole when two holes are close to each other. Fictitious frequency appeared in the external problem can be suppressed by using the more number of Fourier series terms. The effect of distance between the centers of holes on dynamic moment concentration factors is also investigated by using the proposed method. Keyword: scattering,flexuralwave, dynamicmoment concentration,biHelmholtz equation, null-field boundary integral equation, degenerate kernel, Fourier series