Null-field integral equation approach for free vibration analysis of circular plates with multiple circular holes

Abstract

In this paper, a semi-analytical approach for eigenproblems of circular plate with multiple circular holes is presented. Natural frequencies and natural modes are determined by the null-field integral formulation in conjunction with degenerate kernels, tensor rotation and Fourier series. All the kernels in the direct formulation are expanded into degenerate (separable) form. By uniformly collocating points on the boundary and taking finite terms of Fourier series, a linear algebraic system can be constructed. The direct searching approach is adopted to determine the natural frequency through singular value decomposition (SVD). The result of the annular plate, as a special case, is compared with the analytical solution to verify the validity of the present method. For the cases of circular plates with an eccentric hole or multiple circular holes, eigensolutions obtained by the present method are compared with those of the existing approximate analytical method or finite element method (ABAQUS). Besides, the effect of eccentricity of the hole on the natural frequencies and modes is also considered. Moreover, the problem of spurious eigenvalue is investigated and the SVD updating technique is adopted to suppress the occurrence of spurious eigenvalues. Excellent accuracy, fast rate of convergence and high computational efficiency are the main features of the present method due to the semi-analytical procedure.