一类相对转动时滞非线性动力系统的稳定性分析

建立了具有时变刚度、非线性阻尼和谐波激励的一类相对转动时滞非线性动力系统的动力学方程.采用多尺度法推导出时滞动力系统的分岔响应方程,运用奇异性理论研究系统结构稳定性,得到主共振稳态响应方程的转迁集以及不同参数下分岔曲线的拓扑结构.应用Hopf分岔理论讨论了时滞动力系统动态稳定性,给出了系统产生极限环的条件,最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响。

Stability analysis of a relative rotation time-delay nonlinear dynamic system

The dynamic equation of a relative rotation time-delay nonlinear dynamic system is established, which contains time-varying stiffness, nonlinear damping and harmonic excitation. The bifurcation equation of time-delay dynamic system is deduced by the method of multiple scales. The structure stability of the system is studied by singularity theory, the transfer concourse of primary resonance equation and topological structure of bifurcation function are obtained. The dynamic stability of the system is discussed by the Hopf bifurcation theory and the condition for the limit cycle occurrance is given. Moreover, it is indicated by numerical method that parameters of time delay affect the limit cycle amplitude.