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多自由度非线性随机系统的响应与稳定性

金肖玲 王永 黄志龙

金肖玲, 王永, 黄志龙. 多自由度非线性随机系统的响应与稳定性[J]. 力学进展, 2013, 43(1): 56-62. doi: 10.6052/1000-0992-12-026
引用本文: 金肖玲, 王永, 黄志龙. 多自由度非线性随机系统的响应与稳定性[J]. 力学进展, 2013, 43(1): 56-62. doi: 10.6052/1000-0992-12-026
JIN Xiaoling, WANG Yong, HUANG Zhilong. Response and stability of multi-degree-of-freedom nonlinear stochastic systems[J]. Advances in Mechanics, 2013, 43(1): 56-62. doi: 10.6052/1000-0992-12-026
Citation: JIN Xiaoling, WANG Yong, HUANG Zhilong. Response and stability of multi-degree-of-freedom nonlinear stochastic systems[J]. Advances in Mechanics, 2013, 43(1): 56-62. doi: 10.6052/1000-0992-12-026

多自由度非线性随机系统的响应与稳定性

doi: 10.6052/1000-0992-12-026
基金项目: 国家自然科学基金(11025211,11002077,11202181),浙江省自然科学基金(Z6090125,LQ12A02001)和高校博士点基金(20110101110050)资助项目
详细信息
    作者简介:

    黄志龙, 1965 年3 月生, 浙江大学航空航天学院工程力学系教授, 现任浙江大学航空航天学院副院长, 力学系主任. 长期从事随机动力学与控制研究, 特别是随机激励的耗散的Hamilton 系统理论方面的研究, 对随机动力学系统的精确平稳解、等效非线性系统法、随机平均法、随机稳定性、随机分岔、混沌、动态可靠性及随机最优控制各个方面都有研究, 已发表论文90 余篇, 其中SCI 收录50 余篇, 以第二完成人完成的项目“随机激励的耗散的Hamilton 系统理论”获2002 年度国家自然科学奖二等奖及教育部2001 年科技进步一等奖, 2005 年入选教育部新世纪优秀人才支持计划, 2008 年获全国优秀百篇博士论文, 2010 年获国家杰出青年基金.

    通讯作者:

    黄志龙

  • 中图分类号: O322,O324

Response and stability of multi-degree-of-freedom nonlinear stochastic systems

Funds: The project was supported by the National Natural Science Foundation of China (1025211, 11002077, 11202181), the Natural Science Foundation of Zhejiang Province (Z6090125, LQ12A02001) and the Research Fund for the Doctoral Program of Higher Education of China (20110101110050).
More Information
    Corresponding author: HUANG Zhilong
  • 摘要:

    响应与稳定性分析一直是随机动力学研究的热点, 发展预测随机响应及判定系统响应性态的方法具有重要的科学意义与广阔的应用前景. 本文综述了有关多自由度非线性随机系统的响应与稳定性的研究. 首先简介用于随机系统响应预测的Fokker-Planck-Kolmogorov方程法、随机平均法、等效线性化法、等效非线性系统法和Monte Carlo模拟法, 评述其优缺点, 进而讨论了多自由度非线性随机系统响应的精确平稳解、近似瞬态解的研究现状. 然后介绍了随机系统稳定性分析的两类方法, 即Lyapunov函数法及Lyapunov指数法,并综述了多自由度非线性随机系统稳定性分析的研究现状. 最后给出几点发展建议.

     

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出版历程
  • 收稿日期:  2012-03-01
  • 修回日期:  2012-07-16
  • 刊出日期:  2013-01-24

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