Primary resonance of a fractional-order Rayleigh-Duffing system

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (16) : 111-117.

CHEN Jufeng1,2，WANG Yuanyuan2，SHEN Yongjun1,3，LI Xianghong2

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Abstract

In this paper, the primary resonance of a fractional-order Rayleigh-Duffing system under harmonic excitation is studied by multi-scale method. Firstly, the approximate analytical solution is obtained based on the multi-scale method. The numerical simulation shows that the analytical solution agrees well with the numerical solution, and the accuracy of the approximate analytical solution is verified. Then, the amplitude-frequency and phase-frequency equations for the steady-state solution are established, and its stability conditions are obtained based on the Lyapunov stability theory. Finally, through numerical simulation combined with amplitude-frequency curves, it is found that the parameters such as nonlinear stiffness coefficient, linear damping coefficient, and fractional order have important effects on the system dynamics characteristics, which is of great significance for the optimization and control of such systems.

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fractional-order derivative / multi-scale method / Rayleigh-Duffing system / primary resonance

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CHEN Jufeng1,2，WANG Yuanyuan2，SHEN Yongjun1,3，LI Xianghong2. Primary resonance of a fractional-order Rayleigh-Duffing system[J]. Journal of Vibration and Shock, 2024, 43(16): 111-117

References

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