The free vibration characteristics analysis of rectangular plate with central opening using in arbitrary boundary conditions
QIU Yong-kang1 LI Tian-yun1,2,3 ZHU Xiang1,2 GUO Wen-jie1 MAO Yi-da1
1.School of Naval Architecture and Ocean Engineering，Huazhong University of Science and Technology，Wuhan 430074，China;
2.Hubei Provincial Key Laboratory of Ship and Marine Hydrodynamics, Wuhan 430074,China;
3.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240,China
Abstract：This paper based on the improved Fourier series method to establish a free vibration analysis model and calculate the natural frequency of rectangular plate with a central opening. When considering the opening, only a quarter of the plate is researched by using the symmetry of rectangular plate with central opening，which is divided into three regions. The admissible function displacement of each region is expressed by the improved Fourier series. By using the linear spring, which is uniform distribution along the border, simulate arbitrary boundary conditions. And through the continuous conditions of displacements determine the relationship of each regional plate. According to the Rayleigh-Ritz energy functional and variational method, we can get the overall energy functional. We can get the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. Solving the equation can obtain the natural frequencies and the corresponding vibration modes of rectangular plate with central opening. Finally, according to the calculation of numerical examples, comparing the calculated results with the finite element method to verify the accuracy and effectiveness of the method in this paper.
邱永康1,李天匀1，2，3,朱翔1，2，郭文杰1,毛艺达1. 任意边界条件下中心开口矩形板自由振动特性分析[J]. 振动与冲击, 2017, 36(20): 112-117.
QIU Yong-kang1 LI Tian-yun1,2,3 ZHU Xiang1,2 GUO Wen-jie1 MAO Yi-da1. The free vibration characteristics analysis of rectangular plate with central opening using in arbitrary boundary conditions. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(20): 112-117.
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