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

谐和与有界噪声联合参激作用下的Visco-Elastic系统

1.
西北工业大学应用数学系, 西安 710072;
2.
佛山科技学院数学系, 广东佛山 528000;
3.
西北工业大学振动工程研究所, 西安 710072

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
计量
- 文章访问数: 2569
- HTML全文浏览量: 75
- 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

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

1.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P.R.China;
2.
Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P.R.China;
3.
Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, P.R.China

摘要

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。
- 参数主共振 /
- visco-elastic项 /
- 多尺度法 /
- 最大Liapunov指数 /
- 分岔
Abstract: The principal resonance of a visco-elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analyses. The contributions from the visco-elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, band-width, and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses are verified by numerical results.
- principal resonance /
- visco-elastic system /
- multiple scale method /
- largest Liapunov exponent /
- bifurcation

HTML全文

参考文献(13)

[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.