留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

谐和与有界噪声联合参激作用下的Visco-Elastic系统

徐伟 戎海武 方同

徐伟, 戎海武, 方同. 谐和与有界噪声联合参激作用下的Visco-Elastic系统[J]. 应用数学和力学, 2003, 24(9): 963-972.
引用本文: 徐伟, 戎海武, 方同. 谐和与有界噪声联合参激作用下的Visco-Elastic系统[J]. 应用数学和力学, 2003, 24(9): 963-972.
XU Wei, RONG Hai-wu, FANG Tong. Visco-Elastic Systems Under Both Deterministic and Bound Random Parametric Excitation[J]. Applied Mathematics and Mechanics, 2003, 24(9): 963-972.
Citation: XU Wei, RONG Hai-wu, FANG Tong. Visco-Elastic Systems Under Both Deterministic and Bound Random Parametric Excitation[J]. Applied Mathematics and Mechanics, 2003, 24(9): 963-972.

谐和与有界噪声联合参激作用下的Visco-Elastic系统

基金项目: 国家自然科学基金资助项目(10072049)
详细信息
    作者简介:

    徐伟(1957- ),男,浙江上虞人,教授,博士,博导(E-mail:weixu@nwpu.edu.cn).

  • 中图分类号: O324

Visco-Elastic Systems Under Both Deterministic and Bound Random Parametric Excitation

  • 摘要: 研究了带visco-elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题。用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,根据最大Liapunov指数可得系统解稳定的充分必要条件。讨论了系统的visco-elastic项对系统阻尼项和刚度项的贡献,给出了随机项和确定性参激强度等参数对系统响应影响的讨论。数值模拟表明该方法是有效的。
  • [1] Stratonovitch R L,Romanovskii Y M.Parametric effect of a random force on linear and nonlinear oscillatory systems[A].In:Kuznetsov P T,Stratonovitch R L,Tikhonov V I Eds.Nonlinear Translations of Stochastic Process[C].Oxford: Pergamon, 1965,16-26.
    [2] Dimentberg M F, Isikov N E, Model R.Vibration of a system with cubic-non-linear damping and simultaneous periodic and random parametric excitation[J].Mechanics of Solids,1981,16(1): 19-21.
    [3] Namachchivaya N S. Almost sure stability of dynamical systems under combined harmonic and stochastic excitations[J].Journal of Sound and Vibration,1991,151(1): 77-91.
    [4] Ariaratnam S T, Tam D S F. Parametric random excitation of a damped Mathieu oscillator[J].Z Aangew Math Mech,1976,56(3):449-452.
    [5] Dimentberg M F.Statistical Dynamics of Nonlinear and Time-Varying Systems[M].New York:Wiley, 1988.
    [6] RONG Hai-wu, XU Wei, FANG Tong.Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation[J].Journal of Sound and Vibration,1998,210(4):483-515.
    [7] Ariaratnam S T. Stochastic stability of linear viscoelastic systems[J]. Probabilistic Engineering Mechanics, 1993,8(1):153-155.
    [8] Cai G Q, Lin Y K, XU Wei.Strongly nonlinear system under non-white random excitations[A]. In: Spencer B F,Johnson E A Eds. Stochastic Structural Dynamic[C].Rotterdam: A A Balkema, 1999,11-16.
    [9] Wedig W V. Invariant measures and Lyapunov exponents for generalized parameter fluctuations[J].Structural Safety,1990,8(1):13-25.
    [10] Rajan S,Davies H G. Multiple time scaling of the response of a Duffing oscillator to narrow-band excitations[J].Journal of Sound and Vibration, 1988,123(3):497-506.
    [11] Nayfeh A H, Serhan S J. Response statistics of nonlinear systems to combined deterministic and random excitations[J].International Journal of Nonlinear Mechanics,1990,25(5):493-509.
    [12] Shinozuka M.Simulation of multivariate and multidimensional random processes[J].Journal of Sound and Vibration,1971,49(4):357-367.
    [13] Shinozuka M. Digital simulation of random processes and its applications[J].Journal of Sound and Vibration,1972,25(1):111-128.
  • 加载中
计量
  • 文章访问数:  2702
  • HTML全文浏览量:  108
  • PDF下载量:  495
  • 被引次数: 0
出版历程
  • 收稿日期:  2001-12-12
  • 修回日期:  2003-04-23
  • 刊出日期:  2003-09-15

目录

    /

    返回文章
    返回