考虑频变阻尼的粘弹性阻尼层板结构模态分析方法

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摘要结构动力中的模态分析可归结为数学上矩阵特征值问题的求解。研究了一种求解有限元非线性特征值问题的数值方法，即RSRR，该方法通过对系统矩阵逆矩阵的采样，构造可靠的特征空间用于非线性特征值问题的求解，比现有基于围道积分的非线性特征值解法稳定性更好、精度更高。采用基于Layerwise离散层理论的Layerwise板单元建立粘弹性阻尼结构有限元模型比混合单元建模方法简单方便，结合Layerwise板单元建模方法，将RSRR拓展应用于粘弹性阻尼结构的模态分析，算例结果表明RSRR求解精度高、稳定性好，是粘弹性阻尼结构模态分析的有效数值方法。

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	周航1
	校金友2
	徐超2

关键词 ：粘弹性, 模态分析, Rayleigh-Ritz方法, Layerwise板单元

Abstract：

The modal analysis in structure dynamics can be summed up as solving the eigen problems of matrices in mathematics. A numerical method for solving the nonlinear eigen problems (NEPs) in finite element analysis was introduced, namely RSRR. In the method, by sampling the inverse matrix of the system matrix, a reliable eigenspace was constructed to solve the NEPs, which has better stability and higher precision than the existing eigenvalue solving method based on the contour integral. It is simple and convenient to establish the finite element model of viscoelastic damping structures by using the Layerwise plate element based on the Layerwise discrete plate theory. Combined with the Layerwise plate element modeling method, the RSRR was extended to solve the NEPs of viscoelastic damping structures. The results show that the RSRR has high accuracy and good stability, and is an efficient numerical method for the modal analysis of viscoelastic damping structures

Key words： viscoelastic modal analysis Rayleigh-Ritz method；Layerwise plate element

收稿日期: 2017-02-27 出版日期: 2018-07-15

引用本文:

周航1，校金友2，徐超2. 考虑频变阻尼的粘弹性阻尼层板结构模态分析方法[J]. 振动与冲击, 2018, 37(14): 208-213.
ZHOU Hang 1,XIAO Jinyou2,XU Chao2. Modal analysis method for viscoelastically damped laminated structures with frequency-dependent damping. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(14): 208-213.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I14/208

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