The stability control of a coupled nonlinear torsional vibration dynamic system

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (9) : 140-144.

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LIU Hao-ran1; ZHU Zhan-Long2; SHI Pei-Ming2; HOU Dong-Xiao2

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Abstract

Considering the nonlinear stiffness of a torsional vibration system with three degree of freedom, the nonlinear equation of a torsional vibration which contains coupled terms is established. With time-delays control, the method of multiple scales is employed to obtain the analytical solutions of time-delays dynamic system when primary resonance and 1:1 internal resonance occur simultaneously. The necessary and sufficient condition of the stability of system is deduced by using the Routh-Hurwitz criterion. Moreover, the stability of the coupled system is well-controlled by choosing appropriate time-delays parameters, and the numerical results are presented that confirm the analytical predictions.

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cubic nonlinear / coupled system / time-delays feedback control / stability

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LIU Hao-ran;ZHU Zhan-Long;SHI Pei-Ming;HOU Dong-Xiao. The stability control of a coupled nonlinear torsional vibration dynamic system[J]. Journal of Vibration and Shock, 2011, 30(9): 140-144