一类耦合非线性扭振动力系统的稳定性控制

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (9) : 140-144.

论文

一类耦合非线性扭振动力系统的稳定性控制

刘浩然1; 朱占龙2; 时培明2; 侯东晓2

作者信息 +

The stability control of a coupled nonlinear torsional vibration dynamic system

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

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文章历史 +

摘要

考虑一类三质量扭振系统的非线性阻尼力作用，建立含三次非线性耦合项的扭振系统的非线性动力学方程。采用时滞状态反馈对系统加以控制，运用多尺度法对加入时滞反馈的系统进行求解，得到系统在主共振和1：1内共振情形下的平衡解。应用Routh-Hurwitz稳定判据分析系统平衡解在原点处Jacobian行列式的特征方程得到系统稳定的充分必要条件，并通过选取合适时滞参数实现了对耦合系统稳定的良好控制，数值模拟证明了所给条件的正确性。

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.

导出引用

刘浩然; 朱占龙; 时培明; 侯东晓. 一类耦合非线性扭振动力系统的稳定性控制[J]. 振动与冲击, 2011, 30(9): 140-144

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