单自由度NES在高斯白噪声随机激励下的响应分析

薛继仁1,陈立群1,张业伟2,丁虎1

振动与冲击 ›› 2020, Vol. 39 ›› Issue (12) : 235-241.

PDF(1659 KB)
PDF(1659 KB)
振动与冲击 ›› 2020, Vol. 39 ›› Issue (12) : 235-241.
论文

单自由度NES在高斯白噪声随机激励下的响应分析

  • 薛继仁1,陈立群1,张业伟2,丁虎1
作者信息 +

Response analysis of single degree of freedom NES under random excitation of gaussian white oise

  • XUE Jiren1, CHEN Liqun1, ZHANG Yewei2, DING Hu1
Author information +
文章历史 +

摘要

对带有非线性能量汇的单自由度系统进行建模,采用有限差分法进行数值求解,再利用蒙特卡洛法进行数值模拟,比较了两种不同方法下得到的系统稳态统计响应;然后进行参数讨论和分析,讨论了不同参数对系统稳态统计响应的影响,为随机激励下的非线性能量汇动力学参数设计提供参考依据。

Abstract

The single-degree-of-freedom system with nonlinear energy sink is modeled, and the finite difference method is used to solve the numerical solution. Then the Monte Carlo method is used to simulate the system. The steady-state statistical response of the system obtained by two different methods is compared. The parameters discussion and analysis are carried out, and the influence of different parameters on the steady-state statistical response of the system is discussed, which provides a reference for the design of nonlinear energy sink dynamic parameters under random excitation.

关键词

非线性能量汇 / 有限差分法 / 蒙特卡洛法 / 随机响应

Key words

nonlinear energy sink / finite difference method / Monte Carlo method / random response

引用本文

导出引用
薛继仁1,陈立群1,张业伟2,丁虎1. 单自由度NES在高斯白噪声随机激励下的响应分析[J]. 振动与冲击, 2020, 39(12): 235-241
XUE Jiren1, CHEN Liqun1, ZHANG Yewei2, DING Hu1. Response analysis of single degree of freedom NES under random excitation of gaussian white oise[J]. Journal of Vibration and Shock, 2020, 39(12): 235-241

参考文献

[1] Al-Shudeifat MA, Wierschem N, Quinn DD, Vakakis AF, Bergman LA, Spencer BF. Numerical and experimental investigation of a highly effective single-sided vibro-impact non-linear energy sink for shock mitigation [J]. International Journal of Non-linear Mechanics, 2013, 52: 96-106.
[2] Vaurigaud B, Manevitch LI, Lamarque CH. Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer [J]. Journal of Sound and Vibration. 2011, 330(11): 2580-2595.
[3] Ahmadabadi ZN, Khadem SE. Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device [J]. Journal of Sound and Vibration. 2014, 333(19): 4444-4457.
[4] Starosvetsky Y, Gendelman OV. Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning [J]. Journal of Sound and Vibration. 2008, 315(3): 746-765.
[5] 熊怀,孔宪仁,刘源. 阻尼对耦合非线性阱系统影响研究[J]. 振动与冲击,2015,34(11):116-121
   Xiong Huai, Kong Xianren, Liu Yuan. Study on the Influence of Damping on Coupled Nonlinear Well Systems. [J]. Vibration and shock, 2015, 34(11): 116-121
[6] 刘中坡,吕西林,王栋,乌建中. 非线性能量阱优化计算与振动台实验[J]. 振动与冲击,2017,36(7)
    Liu Zhongpo, Lu Xilin, Wang Dong, Wu Jianzhong. Nonlinear energy trap optimization calculation and shaking table experiment [J]. Vibration and shock, 2017, 36(7)
[7] Zheng Lu, Zixin Wang, Ying Zhou, Xilin Lu. Nonlinear dissipative devices in structural vibration control: A review[J]. Journal sound and vibration, 2018, 423(2018): 18-49.
[8] Xinlin Lu, Zhongpo Liu, Zheng Lu. Optimization design and experimental verification of track nonlinear energy sink for vibration control under seismic excitation[J]. Structural Control and Health Monitoring, 2017.24(24):e2033.
[9] J.S. Yu, Y.K. Lin. Numerical path integration of a non-homogenous Markov process [J]. International Journal of Non-Linear Mechanics, 2004, 39(2004): 1493-1500.
[10] J.S. Yu, G.Q. Cai, Y.K. Lin. A NEW PATH INTEGRATION PROCEDURE BASED ON GAUSS-LEGENDRE SCHEME [J]. International Journal of Non-Linear Mechanics, 1997, 32(4): 759-768.
[11] Bergman LA, Spencer BF Jr. Solution of the first passage problem for simple linear and nonlinear oscillators by the finite element method [J]. Department of Theoretical and Applied Mechanics, T&AM Report No. 461; 1983.
[12] W.Y, B.F. Spencer Jr, L.A. Begman. Solution of Fokker-planck equations in high dimension [J]. Application of the concurrent finite element method, Structural Safety and Reliability. ShiraShi, Shinozuki and Wen(eds), 1998, 859-865.
[13] 朱位秋,非线性随机动力学与控制—Hamilton理论体系框架,科学出版社,2003.
    Zhu Weiqiu, Nonlinear Stochastic Dynamics and Control-Hamilton Theory System Framework. Science Press, 2003.
[14] Zhu WQ. Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation. ASME Applied Mechanics Reviews, July 2006, 59(4): 230-248.
[15] Xiong Huai, Kong. Xianren. Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink [J]. Chinese Journal of Aeronautics. 2015, 28(2): 457-468.
[16] D.Michael McFarland, Lawrence A. Bergman, Alexander F. Vakakis. Experiment study of non-linear energy pumping occurring at a single fast frequency [J]. International Journal of Non-linear Mechanics, 40(2005):891-899.
[17] Z Xu, Y K. CHEUNG. Averaging method using generalized harmonic functions for strongly non-linear oscillators [J]. Journal of Sound and Vibration, 1994, 174(4): 563-576.
[18] 张文生,科学计算中的偏微分方程有限差分法
[M],高等教育出版社,北京,2006.6,40-185.
Zhang Wensheng, Finite Difference Method for Partial Differential Equations in Scientific Computing. [M], Higher education press, Beijing, 2006.6, 40-185.
[19] Huang ZL, Zhu WQ, Suzuki Y. Stochastic averaging of strongly nonlinear oscillators under
combined harmonic and white noise excitations. Journal of Sound and Vibration, 2000, 238(2): 233-256.

PDF(1659 KB)

Accesses

Citation

Detail

段落导航
相关文章

/