Abstract
In this paper, a semi-analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and Fourier series. All the kernels in the indirect formulation are expanded into degenerate form. By uniformly collocating points on the boundary, a linear algebraic system can be constructed. The direct searching approach is adopted to determine the natural frequency through singular value decomposition (SVD). After determining the unknown Fourier coefficients, the corresponding mode shape is obtained by using the indirect boundary integral formulations. The results of the annular plate, as a special case, are compared with the analytical solution to verify the validity of the present method. For the cases of circular plates with multiple circular holes, the results are also compared with those of finite element method (FEM) using ABAQUS. Besides, the effect of eccentricity of the hole on the natural frequencies is also considered. Good accuracy, high rate of convergence and computational efficiency are the main features of the present method due to the semi-analytical procedure.
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