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Purpose <p>This paper investigates the primary and superharmonic simultaneous resonance of fractional-order Rayleigh-Duffing oscillator. The research question focuses on exploring how different system parameters affect the dynamic characteristics of this oscillator.</p> Methods <p>Firstly, the approximately analytical solution of the system is derived by using the multiple scale method. Then, the amplitude-frequency and phase-frequency equations for the steady-state solution are established, and the stability conditions are obtained with the help of Lyapunov stability theory. Finally, numerical simulation combined with amplitude-frequency curves is carried out.</p> Conclusion <p>Numerical simulations confirm the accuracy of the approximately analytical solution. It is found that system parameters including nonlinear stiffness coefficient, external excitation amplitudes, and fractional order have important impacts on the dynamic characteristics of the fractional-order Rayleigh-Duffing oscillator, which is significant for the optimization and control of such systems.</p>

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Primary and Superharmonic Simultaneous Resonance of Fractional-Order Rayleigh-Duffing Oscillator

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Jufeng Chen,
  • Yuanyuan Wang,
  • Yongjun Shen,
  • Jing Zhang

摘要

Purpose

This paper investigates the primary and superharmonic simultaneous resonance of fractional-order Rayleigh-Duffing oscillator. The research question focuses on exploring how different system parameters affect the dynamic characteristics of this oscillator.

Methods

Firstly, the approximately analytical solution of the system is derived by using the multiple scale method. Then, the amplitude-frequency and phase-frequency equations for the steady-state solution are established, and the stability conditions are obtained with the help of Lyapunov stability theory. Finally, numerical simulation combined with amplitude-frequency curves is carried out.

Conclusion

Numerical simulations confirm the accuracy of the approximately analytical solution. It is found that system parameters including nonlinear stiffness coefficient, external excitation amplitudes, and fractional order have important impacts on the dynamic characteristics of the fractional-order Rayleigh-Duffing oscillator, which is significant for the optimization and control of such systems.