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1:1内共振对随机振动系统可靠性的影响

王浩宇 吴勇军

王浩宇, 吴勇军. 1:1内共振对随机振动系统可靠性的影响[J]. 力学学报, 2015, 47(5): 807-813. doi: 10.6052/0459-1879-15-058
引用本文: 王浩宇, 吴勇军. 1:1内共振对随机振动系统可靠性的影响[J]. 力学学报, 2015, 47(5): 807-813. doi: 10.6052/0459-1879-15-058
Wang Haoyu, Wu Yongjun. THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 807-813. doi: 10.6052/0459-1879-15-058
Citation: Wang Haoyu, Wu Yongjun. THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 807-813. doi: 10.6052/0459-1879-15-058

1:1内共振对随机振动系统可靠性的影响

doi: 10.6052/0459-1879-15-058
基金项目: 国家自然科学基金资助项目(11272201,11372271,11132007).
详细信息
    通讯作者:

    吴勇军,副研究员,主要研究方向:非线性随机动力学.E-mail:yj.wu@sjtu.edu.cn

  • 中图分类号: O322;O324

THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM

Funds: The project was supported by the National Natural Science Foundation of China (11272201, 11372271, 11132007).
  • 摘要: 研究了二自由度耦合非线性随机振动系统在高斯白噪声激励下基于首次穿越模型的可靠性问题. 在1:1内共振情形,原始系统的运动方程经平均后化为一组关于慢变量的伊藤随机微分方程. 建立了后向柯尔莫哥洛夫方程以及庞德辽金方程,在一定的边界条件和(或) 初始条件下求解这两个偏微分方程,分别得到系统的条件可靠性函数以及平均首次穿越时间. 进而建立了无内共振情形系统的后向柯尔莫哥洛夫方程与庞德辽金方程.将无内共振情形的结果与1:1 内共振情形的结果做比较,发现1:1 内共振能显著降低系统可靠性. 用蒙特卡罗数值模拟验证了理论结果的有效性.

     

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出版历程
  • 收稿日期:  2015-02-11
  • 修回日期:  2015-07-08
  • 刊出日期:  2015-09-18

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