Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System

Gan Chunbiao; Lu Qishao; Huang Kelei

Volume 24 Issue 5

May 1998

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Abstract

References

Journal of Beijing University of Aeronautics and Astronautics > 1998 > 24(5): 592-595.

Zhang Zhimin, Li Jinqiu, Guo Yanyanget al. Computational Model of Progressive Failure in Composite Sandwich Structures[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(5): 565-568. (in Chinese)

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Gan Chunbiao, Lu Qishao, Huang Keleiet al. Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(5): 592-595. (in Chinese)

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Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System

Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics

Received Date: 07 Oct 1997
Publish Date: 31 May 1998

Abstract

Abstract

This paper deals with a coupled nonlinear Van der Pol oscillator system with linear coupled elastic term,the dissimilar modes and their bifurcations have been discussed by modal analysis.Moreover,the stabilities and the superposition of the dissimilar modes have also been analyzed theoretically and numerically.It is shown that the modal superposition can effectively simulate the system's attenuation effects,the theoretical results are compared with the numerical ones,it is found that there exit very small errors between each other.However,when the parameter of the system passes through some value,the Hopf bifurcation takes place and a stable limit cycle arises in the modal equation of the system,and as a result,the modal superposition lose its efficacy,especially in their phase positions.
- nonlinear,
- stability,
- synthesis,
- nonconservative,
- modal bifurcation

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References(1)

References

1. Rosenberg R M.Normal modes of nonlinear dual-mode systems.J Appl Mech,1960,27:263~271 2. Mishra A K,Singh M C.The normal modes of nonlinear symmetric systems by group representation theory.Int J Non-Linear Mech,1974,9:364~480 3. 刘炼生,黄克累一种用于非线性振动系统的模态分析方法力学学报,1988,20(1):41~48 4. Vakakis A F,Rand R H.Normal modes and global dynamics of a two-degree-of-freedom nonlinear system-I(Low energies).Int J Non-Linear Mech,1992,27:861~874 5. Vakakis A F,Rand R H.Normal modes and global dynamics of a two-degree-of-freedom nonlinear system-I(Low energies).Int J Non-Linear Mech,1992,27:875~888 6. Shaw S W,Pierre C.Nonlinear normal modes and invariant manifolds.Journal of Sound and Vibration,1991,155(1):170~173 7. Shaw S W,Pierre C.Normal modes of vibration for nonlinear continuous systems.Journal of Sound and Vibration,1993,164(1):85~124 8. 甘春标,陆启韶,黄克累一类非线性耦合振子的模态分析非线性动力学学报,1996,3(2):163~167

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Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System