一类非线性相对转动系统的动力学行为及其机理分析

摘要

研究了一类具有非线性刚度的相对转动系统的动力学行为.应用Routh-Hurwitz稳定性理论判断了相对转动系统平衡点的稳定性.应用分岔理论研究了平衡点失稳时的分岔行为,推导了平衡点产生fold分岔的条件,进而通过仿真得到了平衡点在双参数平面上的分岔集及单参数分岔曲线,研究了不同参数区域内平衡点的个数以及稳定性问题.应用分岔图研究了相对转动系统随平方非线性刚度系数及激励角频率变化的全局动力学行为,获得了周期三以及混沌等动力学行为.通过调整平方非线性刚度系数得到了慢变外激励下相对转动系统中的对称式和不对称式fold/fold簇发行为.%The dynamic behaviors of a nonlinear relative rotation system with nonlinear stiffness were studied.The torque perturbation was treated as the control parameter,and the equilibrium's stability of the torsional vibration system was judged by the Routh-Hurwitz criterion.The bifurcation theory was used to analyze the bifurcation behaviors of the equilibrium,and the condition of Fold bifurcation of the equilibrium was derived.The bifurcation set of the equilibrium on the parameter plane was obtained by simulation,and the stability of equilibrium in different parameter regions was studied.The global dynamic behaviors of torsional vibration system were studied by the bifurcation map and period-three motion and chaotic motion were obtained.Symmetric and asymmetric fold/fold burstings were obtained by adjusting the quadratic nonlinear stiffness coefficient.