Primary Resonance of Rayleigh-Duffing Systems under Fractional-Order Delayed Feedback
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.
fractional derivativetime-delayaveraging methodparametric excitationRayleigh-Duffing system
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