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Mode analysis of structures using the Fourier p-element method

Wu Guorong (吴国荣) and Zhong Weifang(钟伟芳)

Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract: The Fourier p-element method is an improvement to the finite element method, and is particularly suitable for vibration analysis due to the well-behaved Fourier series. In this paper, an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem. Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration, the plate in-plane vibration and annular plate flexural vibration modes, respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation, especially for higher mode analysis.

Keywords: vibration mode analysis; eigenvalue problem; FEM; dynamic condensation; Fourier series; polynomial interpolation