Nonlinear Random Stability of Viscoelastic Cable With Small Curvature

LI Ying-hui; GAO Qing

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LI Ying-hui, GAO Qing. Nonlinear Random Stability of Viscoelastic Cable With Small Curvature[J]. Applied Mathematics and Mechanics, 2003, 24(8): 857-864.

Citation:

LI Ying-hui, GAO Qing. Nonlinear Random Stability of Viscoelastic Cable With Small Curvature[J]. Applied Mathematics and Mechanics, 2003, 24(8): 857-864.

Citation:

LI Ying-hui, GAO Qing. Nonlinear Random Stability of Viscoelastic Cable With Small Curvature[J]. Applied Mathematics and Mechanics, 2003, 24(8): 857-864.

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Nonlinear Random Stability of Viscoelastic Cable With Small Curvature

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

Received Date: 2002-01-08
Rev Recd Date: 2003-04-21
Publish Date: 2003-08-15

Abstract

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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References(12)

References

[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.