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| Free vibration characteristics of plates with complicated shapes based on an improved Rayleigh-Ritz method |
| ZHANG Jun1,2,3,LI Tianyun1,2,3,ZHU Xiang1,2,3,GUO Wenjie4 |
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 |
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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.
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Received: 24 January 2018
Published: 28 September 2019
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[1] 焦映厚,侯守武,陈照波,等. 采用波动法研究有限尺寸加肋L型板结构的振动特性[J]. 振动工程学报,2013,26(06):871-878.
JIAO Ying-hou, HOU Shou-wu, CHEN Zhao-bo. et al. Research on vibration properties of finite rib-stiffened L-shaped plate using wave method[J]. Journal of Vibration Engineering, 2013, 26(06): 871-878.
[2] 杨念，陈炉云，易宏，等. 含复杂结构应力的平板振动解析方法研究[J]. 振动与冲击, 2017, 36(20): 12-17.
YANG Nian, CHEN Lu-yun, YI Hong, et al. Analytical Method Study of the Complex Stressed Plate Vibration[J]. Journal of Vibration and Shock, 2017, 36(20): 12-17.
[3] 李正良, 胡浩, 于伟. 正交加筋圆柱壳-球壳组合结构自由振动分析[J]. 振动与冲击, 2015, 34(22): 129-137.
LI Zheng-liang，HU Hao，YU Wei. Free vibration analysis of joined and orthogonal stiffened cylindrical-spherical shells[J]. Journal of Vibration and Shock, 2015, 34(22): 129-137.
[4] 邱永康，李天匀，朱翔，等. 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-kang, LI Tian-yun, ZHU Xiang, et al. The free vibration characteristics analysis of rectangular plate with central opening using in arbitrary boundary conditions[J]. Journal of Vibration and Shock, 2017, 36(20): 112-117.
[5] 李凯, 何书韬, 吴国民, 等. 基于能量泛函的开口矩形板自由振动特性分析[J]. 振动与冲击, 2017, 36(11): 161-165.
LI Kai, HE Shu-tao, WU Guo-min, et al. The free vibration characteristics analysis of rectangular plate with central opening using energy functional method[J]. Journal of Vibration and Shock, 2017, 36(11): 161-165.
[6] D.J. Gorman. Free in-plane vibration analysis of rectangular plates with elastic support normal to the boundaries[J]. Journal of Sound and Vibration, 2005, 285: 941–966.
[7] Lorenzo Dozio. Free in-plane vibration analysis of rectangular plates with arbitrary elastic boundaries [J]. Mechanics Research Communications, 2010, 37: 627–635
[8] T.E. Carmichael. The vibration of a rectangular plate with edges elastically restrained against rotation[J]. Quarterly Journal of Mechanics and Applied Mathematics, 1959, 12: 29–42.
[9] G.B. Warburton, S.L. Edney. Vibrations of rectangular plates with elastically restrained edges[J], Journal of Sound and Vibration, 1984,95:537–552.
[10] W.L. Li. Vibration analysis of rectangular plates with general elastic boundary supports [J]. Journal of Sound and Vibration, 2004,273: 619–635.
[11] 王青山,史冬岩,罗祥程.任意边界条件下矩形板的面内自由振动特性[J]. 华南理工大学学报(自然科学版),2015,43(06):127-134.
WANG Qing-shan, SHI Dong-yan, LUO Xiang-cheng. In-Plane Free Vibration of Rectangular Plates in Arbitrary Boundary Conditions[J]. Journal of South China University of communications technology, 2015, 43(06):127-134.
[12] 吴绪权,杨国武. 切比雪夫多项式的通项表达式[J]. 武汉交通科技大学学报, 2000,24(05):573-576.
WU Xu-quan, YANG Guo-wu. The General Fomula of Chebyshev Polynomial[J]. Journal of Wuhan University of communications technology, 2000, 24(05): 573-576.
[13] W.L. Li, Xuefeng Zhang, Jingtao Du, Zhigang Liu. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports[J]. Journal of Sound and Vibration, 2009, 321(1-2): 254-269.
[14] X.F. Zhang, W.L. Li. Vibration of arbitrarily-shaped triangular plates with elastically restrained edges[J]. Journal of Sound and Vibration, 2015, 357:195-206.
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