1.School of Naval Architecture and Ocean Engineering,Huazhong University of Science & Technology, Wuhan 430074, China;
2.Hubei Provincial Key Lab of Naval Architecture & Ocean Ocean Engineering Hydrodynamics, Wuhan 430074, China;
3.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China;
4.Engineering Research Center of Railway Environment Vibration and Noise Ministry Education, East ChinaJiaotong University, Nanchang 330013, China
Abstract:An improved Rayleigh-Ritz method was proposed for solving vibration problems of plates with complicated shapes that were difficulty to be solved using the traditional Rayleigh-Ritz one.Aiming at plates with complicated shapes, through extending the function domain of their displacement trial function to rectangular domain outside curved edge domain and choosing appropriate displacement trial function, their displacement field could be easily described. Springs with different stiffness were used to simulate complicated boundary conditions at the curved boundary.Using the improved Fourier series, aplate’s strain energy, kinetic one and its boundary’s elastic potential one were obtained and natural frequencies of the plate were solved by searching the minimum value of the energy functional.Taking plates with straight edges and curved ones as calculation examples, the results obtained using the proposed method were compared with those using the finite element method or published in literature. Results showed that the proposed method is correct and reliable; it has good adaptability to solution of vibration problems of plates with complicated shapes.
张俊1,2,3,李天匀1,2,3,朱翔1,2,3,郭文杰4. 基于改进Rayleigh-Ritz法的复杂形状平面薄板自振特性分析[J]. 振动与冲击, 2019, 38(19): 45-51.
ZHANG Jun1,2,3,LI Tianyun1,2,3,ZHU Xiang1,2,3,GUO Wenjie4. Free vibration characteristics of plates with complicated shapes based on an improved Rayleigh-Ritz method. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(19): 45-51.
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