考虑滞回效应的螺栓连接组合结构非线性随机振动分析

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摘要针对具有滞回效应的螺栓连接组合结构，结合虚拟激励法和多谐波平衡法实现了随机振动响应频域功率谱分析。首先，对于随机激励作用下的组合结构，以Jenkins模型进行本构建模。其次，将随机激励表达为复指数级数，将响应谱分析转化虚拟响应的向量运算，提出了扩展虚拟激励法（E–PEM）。最后，对虚拟响应求解中频域本构的计算困难，引入时频变换（AFT）处理；将非线性迭代转换为优化问题并利用信赖域方法求解，有效解决了传统牛顿法的收敛困难。以二自由度和组合梁模型为对象，研究了结构的随机振动响应谱特性，并同蒙特卡罗模拟法（MCS）对比验证E–PEM的正确性，同时对结构特有的非线性随机振动机制进行了讨论。结果表明：本文建立的E–PEM为一般非线性结构随机振动频域分析提供了一个可借鉴的求解思路。

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	吴鹏辉1
	王纪磊1
	毛晨洋1
	赵岩1
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关键词 ：滞回效应, 随机振动, 虚拟激励法, 多谐波平衡法

Abstract：For the bolted assembly structure with hysteresis effects, a frequency domain approach was developed for the power spectral density analysis of the random vibration response of a structure by combining the pseudo excitation method and the multi-harmonic balance method. First, for an assembly structure with random excitation, the constitutive was modeled using the Jenkins model. Second, the random excitation was expressed as a complex exponential series expansion form. Then, the extended pseudo excitation method (E–PEM) was proposed to transform the response spectral analysis into a vector operation of the pseudo response. Finally, for the constitutive computation in the frequency domain during the pseudo response solution, the time-frequency transform (AFT) was introduced to deal with it. Furthermore, convergence difficulties of the traditional Newton method were solved by converting the iterative solution problem into an optimization problem and solving it using the trust region method. The random vibration response spectral characteristics of the assembly structure were investigated by using the two-DOF model and the assembly beam model. The correctness of E–PEM was verified by comparison with Monte Carlo simulation (MCS), and some nonlinear random vibration mechanisms specific to the structure were discussed. The results show that the E–PEM in this paper provides a useful solution idea for the frequency domain analysis of random vibration of general nonlinear structures.

Key words： hysteresis effects random vibration pseudo excitation method multi-harmonic balance method

收稿日期: 2023-03-06 出版日期: 2024-03-15

引用本文:

吴鹏辉1,王纪磊1,毛晨洋1,赵岩1,2. 考虑滞回效应的螺栓连接组合结构非线性随机振动分析[J]. 振动与冲击, 2024, 43(5): 223-230.
WU Penghui1,WANG Jilei1,MAO Chenyang1,ZHAO Yan1,2. Nonlinear random vibration analysis of bolted composite structure considering hysteresis effect. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(5): 223-230.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I5/223

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