小曲率粘弹性索非线性随机稳定性分析

李映辉; 高庆

小曲率粘弹性索非线性随机稳定性分析

李映辉,
高庆

西南交通大学, 应用力学与工程系, 成都 610031

详细信息

作者简介:
李映辉(1964),男,四川南江人,副教授,博士(E-mail:li-yinghui@sina.com).

中图分类号: TU501;TU5113⁺2
计量
- 文章访问数: 2012
- HTML全文浏览量: 92
- PDF下载量: 464
- 被引次数: 0
出版历程
- 收稿日期: 2002-01-08
- 修回日期: 2003-04-21
- 刊出日期: 2003-08-15

Nonlinear Random Stability of Viscoelastic Cable With Small Curvature

Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R, China

摘要

摘要: 基于Kelvin粘弹性材料本构模型,研究小曲率粘弹性索在窄带随机激励作用下的非线性随机稳定性及均方响应。首先建立小曲率粘弹性索数学模型;然后提出一种确定粘弹性索均方响应及概率渐近稳定性方法;给出了系统均方稳定对激励带宽、幅值、中心频率等要求;给出系统的稳定区域;最后讨论了材料粘性、波速比及介质阻尼对系统不稳定区域的影响。
- 索 /
- 均方响应 /
- 随机稳定性 /
- Kelvin粘弹性模型 /
- 窄带随机激励
Abstract: The non-linear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied.The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material.Amathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first.And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted.Finally,the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.
- cable /
- mean square response /
- stochastic stability /
- Kelvin viscoelastic model /
- narrow band random excitation

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参考文献(12)

[1]	Triantafyllon M S,Grinfogel L.Natural frequencies and modes of inclined cables[J].Journal of Structure Engineering,1987,113(1):139-148.
[2]	Rega G,Benedettini F.Parametric analysis of large amplitude free vibrations of a suspended cable[J].International Journal of Non-Linear Mechanics,1984,20(1):95-105.
[3]	Rega G,Benedettini F.Non-linear dynamics of an elastic cable under planar excitation[J].International Journal of Non-Linear Mechanics,1987,23(3):497-509.
[4]	李映辉,殷学纲.粘弹性索非线性响应分析[J].非线性动力学学报,1999,6(3):242-248.
[5]	Li Y H,Peng R Q,Gao Q.The stochastic stability of a viscoelastic cable with small sag[J].Journal of Southwest Jiaotong University,2001,13(1):31-39.
[6]	Li Y H,Jian K L,Gao Q,et al.Wave propagation in viscoelastic cable with small sag[J].Acta Mechanica Solida Sinica,2001,14(2):147-154.
[7]	李映辉,殷学纲.小垂度粘弹性索非线性响应及动力稳定性[J].重庆大学学报,1999,26(3):342-348.
[8]	Alberti F P.Non-stationary random response of a finite cable[J].Journal of Sound and Vibration,1983,86(2):227-233.
[9]	Perkin N C,Mote D C.Three-dimensional vibration of traveling elastic cables[J].Journal of Sound and Vibration,1987,114(2):325-340.
[10]	Warnitchai P,Fujino Y,Susumpov T.A non-linear dynamic model for cables and its application to a cable structure system[J].Journal of Sound and Vibration,1995,187(4):695-712.
[11]	Richard K,Anand G V.Non-linear resonance in strings under narrow band random excitation[J].Journal of Sound and Vibration,1982,85(1):85-98.
[12]	龙运佳,梁以德.近代工程动力学--随机*混沌[M].北京:科学出版社,1998.