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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振动与冲击 ›› 2024, Vol. 43 ›› Issue (5) : 223-230.

论文

吴鹏辉1,王纪磊1,毛晨洋1,赵岩1,2

作者信息 +

Nonlinear random vibration analysis of bolted composite structure considering hysteresis effect

WU Penghui1,WANG Jilei1,MAO Chenyang1,ZHAO Yan1,2

Author information +

文章历史 +

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。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2024, 43(5): 223-230

参考文献

[1] 陈学前, 沈展鹏, 刘信恩, 等. 典型螺栓连接界面轴向动态特性的不确定性研究 [J]. 振动与冲击, 2021, 40(10): 20-24+56. CHEN Xueqian, SHEN Zhanpeng, LIU Xinen, et al. Uncertainty analysis on the normal dynamic characteristics of bolted joint interfaces [J] Journal of Vibration and Shock, 2021, 40(10): 20-24+56. [2] Brake M R. The mechanics of jointed structures [M]. Switzerland: Springer Cham, 2016. [3] Witteveen W, Kuts M, Koller L. Can transient simulation efficiently reproduce well known nonlinear effects of jointed structures? [J]. Mechanical Systems and Signal Processing, 2023, 190: 110111. [4] Yuan J, Salles L, Nowell D, et al. Influence of mesoscale friction interface geometry on the nonlinear dynamic response of large assembled structures [J]. Mechanical Systems and Signal Processing, 2023, 187: 109952. [5] Mathis A T, Balaji N N, Kuether R J, et al. A review of damping models for structures with mechanical joints [J]. Applied Mechanics Reviews, 2020, 72(4): 040802. [6] Tamatam L R, Botto D, Zucca S. A coupled approach to model wear effect on shrouded bladed disk dynamics [J]. International Journal of Mechanical Sciences, 2023, 237: 107816. [7] 康佳豪, 徐超, 李东武, 等. 基于谐波平衡-时频转换法的摩擦振子稳态响应分析[J]. 振动与冲击, 2020, 39(12): 170-176. KANG Jiahao, XU Chao, LI Dongwu, et al. Steady state response analysis of friction vibrator based on harmonic balance time-frequency conversion method [J]. Journal of Vibration and Shock, 2020, 39 (12): 170-176. [8] 王东, 张周锁. 连接局部迟滞非线性的时频域动力学降阶方法[J]. 振动工程学报, 2021, 34(03): 559-566. WANG Dong, ZHANG Zhousuo. Time-frequency domain dynamic order reduction method connecting local hysteretic nonlinearity [J]. Journal of Vibration Engineering, 2021, 34 (03): 559-566. [9] Balaji N N, Chen W, Brake M R W. Traction-based multi-scale nonlinear dynamic modeling of bolted joints: Formulation, application, and trends in micro-scale interface evolution [J]. Mechanical Systems and Signal Processing, 2020, 139: 106615. [10] LI D W, Botto D, LI R Z, et al. Experimental and theoretical studies on friction contact of bolted joint interfaces [J]. International Journal of Mechanical Sciences, 2022, 236: 107773. [11] WANG D, ZHANG Z S. High-efficiency nonlinear dynamic analysis for joint interfaces with Newton–Raphson iteration process [J]. Nonlinear Dynamics, 2020, 100(1): 543-559. [12] Krack M, Gross J. Harmonic balance for nonlinear vibration problems [M]. Switzerland: Springer Cham, 2019. [13] LIN J H, ZHANG Y H, ZHAO Y. Pseudo Excitation Method and Some Recent Developments [J]. Procedia Engineering, 2011, 14: 2453-2458. [14] 叶文伟, 陈林聪, 孙建桥. 泊松白噪声激励下强非线性系统的半解析瞬态解[J]. 力学学报, 2022, 54(12): 3468-3476. YE Wenwei, CHEN Lincong, SUN Jianqiao. Semi-analytical transient solutions of strongly nonlinear systems excited by Poisson white noise [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54 (12): 3468-3476. [15] 孔凡, 晁盼盼, 徐军, 等. 随机与谐和联合激励下分数阶非线性系统的统计线性化方法[J]. 振动工程学报, 2021, 34(04): 756-764. KONG Fan, Chao Panpan, Xu Jun, et al. Statistical linearization method for fractional-order nonlinear systems under combined random and harmonic excitation [J]. Journal of Vibration Engineering, 2021, 34 (04): 756-764. [16] Malara G, Spanos P D. Nonlinear random vibrations of plates endowed with fractional derivative elements [J]. Probabilistic Engineering Mechanics, 2018, 54: 2-8. [17] Boussaa D, Bouc R. Elastic perfectly plastic oscillator under random loads: Linearization and response power spectral density [J]. Journal of Sound and Vibration, 2019, 440: 113-128. [18] Claeys M, Sinou J J, Lambelin J P, et al. Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints – Application on a test structure named “Harmony” [J]. Mechanical Systems and Signal Processing, 2016, 70-71: 1097-1116. [19] Shinozuka M, JAN C M. Digital simulation of random processes and its applications [J]. Journal of Sound and Vibration, 1972, 25(1): 111-128. [20] Roncen T, Sinou J J, Lambelin J P. Experiments and simulations of the structure Harmony-Gamma subjected to broadband random vibrations [J]. Mechanical Systems and Signal Processing, 2021, 159: 107849. [21] Cameron T M, Griffin J H. An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems [J]. Journal of Applied Mechanics-Transactions of The ASME, 1989, 56(1): 149-154. [22] Krack M, Salles L, Thouverez F. Vibration prediction of bladed disks coupled by friction joints [J]. Archives of Computational Methods in Engineering, 2017, 24(3): 589-636. [23] 贾硕, 李钢, 李宏男. 基于Woodbury非线性方法的迭代算法对比分析[J]. 工程力学, 2019, 36(08): 16-29+58. JIA Shuo, LI Gang, LI Hongnan. Comparative analysis of iterative algorithms based on Woodbury nonlinear method [J]. Engineering Mechanics, 2019, 36 (08): 16-29+58. [24] 柯艺芬. 非线性方程组迭代解法[M]. 北京: 电子工业出版社, 2021. KE Yifen. Iterative solution of nonlinear equations [M]. Beijing: Electronic Industry Press, 2021. [25] Nocedal J, Wright. S J. Numerical Optimization [M]. Switzerland: Springer Verlag, 2006. [26] Bograd S, Reuss P, Schmidt A, et al. Modeling the dynamics of mechanical joints [J]. Mechanical Systems and Signal Processing, 2011, 25(8): 2801-2826. [27] Wang J H, Chen W K. Investigation of the vibration of a blade with friction damper by HBM [J]. Journal of Engineering for Gas Turbines and Power, 1993, 115(2): 294-299. [28] Smith S A, Brake M R W, Schwingshackl C W. On the characterization of nonlinearities in assembled structures [J]. Journal of Vibration and Acoustics, 2020, 142(5): 051105. [29] Li D, Xu C, Li R, et al. Contact parameters evolution of bolted joint interface under transversal random vibrations [J]. Wear, 2022, 500-501: 204351. [30] Ibrahim R A, Pettit C L. Uncertainties and dynamic problems of bolted joints and other fasteners [J]. Journal of Sound and Vibration, 2005, 279(3-5): 857-936.