多开口矩形板自由振动特性分析

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (14) : 142-147.

论文

多开口矩形板自由振动特性分析

张俊1,2,3，李天匀1,2,3，朱翔1,2,3

作者信息 +

Free vibration characteristics analysis on a rectangular plate with multiple cutouts

ZHANG Jun1,2,3,LI Tianyun1,2,3,ZHU Xiang1,2,3

Author information +

文章历史 +

摘要

基于Rayleigh-Ritz法，对带有多个开口的矩形板的自由振动性能进行研究。结构的各种边界条件采用刚度可变的弹簧来模拟。选取改进的傅里叶级数作为试函数，以配合弹簧模型模拟不同的边界条件。引入数值方法对应变能、动能及弹性势能进行计算，这样能够对较复杂形状的结构进行计算，且节省计算时间；根据能量泛函变分原理得到振动系统的特征方程，求解特征方程即得固有频率。通过对比该研究算例结果与有限元软件的结果验证了该方法的准确性，为实际工程问题提供参考。

Abstract

Based on the Rayleigh Ritz method, the free vibration characteristics of a rectangular plate with multiple cutouts were studied.Various boundary conditions of the structure were simulated by using springs with variable stiffness.The improved Fourier series was selected as an admissible function.A numerical method was introduced to calculate the strain energy, kinetic energy and elastic potential energy for the structures with more complex shapes and also for saving computing time.According to the energy functional variational principle, the characteristic equation of the vibration system was obtained, and the natural frequency was obtained by solving the characteristic equation.The accuracy of the proposed method was verified by comparing the results of numerical examples with the results of finite element method.The results provide a reference to practical engineering problems.

导出引用

张俊1,2,3，李天匀1,2,3，朱翔1,2,3. 多开口矩形板自由振动特性分析[J]. 振动与冲击, 2020, 39(14): 142-147

ZHANG Jun1,2,3,LI Tianyun1,2,3,ZHU Xiang1,2,3. Free vibration characteristics analysis on a rectangular plate with multiple cutouts[J]. Journal of Vibration and Shock, 2020, 39(14): 142-147

参考文献

[1] Logah P, Tso C P, Lim T L. Analysis of thin plates with holes by using exact geometrical representation within XFEM [J]. Journal of Advanced Research, 2016, 7(3): 445-452.
[2] Soni K, Uphadhyay A K, Shukla K K. Stress Analysis for an infinite plate with circular holes [J]. 5th International Conference on Materials Processing and Characterization, Proceedings, 2017, 4: 2323–2332.
[3] 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.
[4] 王旻昊, 李凯, 邱永康, 等. 基于傅里叶级数法的开孔板振动固有特性分析[J].中国舰船研究，2017,12(4): 102-109.
WANG Min-hao, LI Kai, Qiu Yong-kang, et al. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method [J]. Chinese Journal of Ship Research, 2017, 12(4): 102-109.
[5] 李天匀,张俊,朱翔,等.含任意形状内开口的矩形板振动特性分析[J].华中科技大学学报(自然科学版),2018,46(11):1-6.
LI Tian-yun, ZHANG Jun, ZHU Xiang, et al. Vibration characteristics analysis on rectangular plates with
arbitrarily-shaped cutout[J]. Journal of Huazhong University of Science and Technology(Nature Science Edition), 2018, 46(11): 1-6.
[6] Shi S, Xiao B, Jin G, et al. Modeling and Simulation of Transverse Free Vibration Analysis of a Rectangular Plate with Cutouts Using Energy Principles[J]. Shock and Vibration, 2018, 2018,1-16.
[7] 王龙侃,祝祥刚,陈舸,等.集成上层建筑开口群力学性能分析[J].计算机辅助工程,2013,22(S2):274-279.
WANG Long-kan, ZHU Xiang-gang, CHEN Ge, et al. Mechanical properties of opening group of integrated superstructure[J]. Computer Aided Engineering, 2013, 22(S2): 274-279.
[8] Hota S S , Padhi P. Vibration of plates with arbitrary shapes of cutouts[J]. Journal of Sound & Vibration, 2007, 302(4):1030-1036.
[9] Liu Y , Lin Z , Ding H , et al. A modified Fourier–Ritz formulation for vibration analysis of arbitrarily restrained rectangularplate with cutouts[J]. Shock and Vibration, 2018, 2018:1-22.
[10] Dae S C, Jin H K, Tae M C, et al. Free and forced vibration analysis of arbitrarily supported rectangular plate systems with attachments and openings, Engineering Structures, 2018, 171: 1036-1046,
[11] Avalos D R , Laura P A A . Transverse vibrations of simply supported rectangular plates with two rectangular cutouts[J]. Journal of Sound and Vibration, 2003, 267(4):967–977.
[12] Larrondo H A , Avalos D R , Laura P A A , et al. Vibrations of simply supported rectangular plates with varying thickness and same aspect ratio cutouts[J]. Journal of Sound and Vibration, 2001, 244(4):738-745.
[13] 李凯,何书韬,陈静,等. 一种基于区域分割的多开口板架振动特性计算方法[P]. 湖北：CN106202745A,2016-12-07.
LI kai, HE shutao, CHEN jing, et al. Calculation method of vibration characteristics on multi-opening plate frame based on regional segmentation method [P]. Hubei: CN106202745A,2016-12-07.
[14] W. L. Li. Free vibrations of beams with general boundary conditions[J]. Journal of Sound and Vibration, 2000, 237(4):709-725.
[15] 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 Technology (Natural Science Edition), 2015,43(06):127-134.