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Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

Shi Pei-Ming Jiang Jin-Shui Liu Bin

Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

Shi Pei-Ming, Jiang Jin-Shui, Liu Bin
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  • Abstract views:  3183
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  • Received Date:  02 August 2008
  • Accepted Date:  03 September 2008
  • Published Online:  20 April 2009

Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

  • 1. 燕山大学测试计量技术及仪器河北省重点实验室,秦皇岛 066004

Abstract: The dynamic behaviors of a relative-rotation nonlinear dynamic system with cubic coupled terms are studied. First, the dynamic equation of coupled system with nonlinear elastic force and generalized friction and harmonic excitation is deduced. The approximate solution of coupled unautonomous equation under harmonic excitation is obtained by the method of multiple scales. The effect of coupled terms on system resonance is analyzed in respect of principal resonance and internal resonance. The singularity stability of bifurcation function of principal resonance is studied by singularity theory, and the transfer concourse and topological structure of bifurcation function are obtained.

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