## 留言板

 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.

• 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.
##### 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

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈