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 approxi-mate analytical solution of the system is obtained by the averaging method,and the accuracy of the ana-lytical solution is verified by numerical method.The amplitude-frequency equation of steady-state re-sponse 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 so-lutions 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.
关键词
分数阶导数/时滞/平均法/参数激励/Rayleigh-Duffing系统
Key words
fractional derivative/time-delay/averaging method/parametric excitation/Rayleigh-Duffing system
维普
万方数据