多开口矩形板自由振动特性分析

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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。

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	张俊1
	2
	3
	李天匀1
	2
	3
	朱翔1
	2
	3

关键词 ：开口群, 复杂边界条件, Rayleigh-Ritz法, 改进的傅里叶级数, 矩形板

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.

Key words： multiple cutouts complex boundary conditions Rayleigh-Ritz method improved Fourier series rectangular plate

收稿日期: 2019-01-08 出版日期: 2020-07-15

引用本文:

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. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(14): 142-147.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I14/142

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