分数阶时滞反馈下Rayleigh-Duffing系统的主共振

Primary Resonance of Rayleigh-Duffing Systems under Fractional-Order Delayed Feedback

利用平均法研究了在参数激励和外激励下,具分数阶时滞反馈的Rayleigh-Duffing系统的主共振.首先,通过平均法求得系统的近似解析解,并且通过数值方法验证了解析解的准确性.建立了稳态响应的幅频方程,并基于Lyapunov稳定性理论得到了稳态解的稳定性条件.最后通过数值仿真并结合幅频曲线分析了系统参数对系统动力学行为的影响.结果表明:参激幅值和外激励幅值造成的多解现象并不相同;时滞对系统幅频曲线的影响具有周期性.

The primary resonance of Rayleigh-Duffing system with fractional time-delay feedback under parametric excitation and external excitation is studied by the averaging method.Firstly,the approximate analytical solution of the system is obtained by the averaging method,and the accuracy of the analytical solution is verified by numerical method.The amplitude-frequency equation of steady-state response is established,and the stability condition of steady-state solution is obtained based on Lyapunov stability theory.Finally,the influence of system parameters on the dynamic behavior of the system is analyzed by numerical simulation and amplitude-frequency curve.The results show that the multiple solutions due to parametric excitation amplitude and external excitation amplitude are not the same.The effect of time-delay on the amplitude-frequency curve of the system is periodic.