Resonance analysis and time-delay feedback controllability for a fractional horizontal nonlinear roller system

Zhoujin Cui; Xiaorong Zhang; Tao Lu; Zhoujin Cui; Xiaorong Zhang; Tao Lu

doi:10.3934/math.20241209

AIMS Mathematics

2024, Volume 9, Issue 9: 24832-24853. doi: 10.3934/math.20241209

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Resonance analysis and time-delay feedback controllability for a fractional horizontal nonlinear roller system

1.
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing, 210013, China
2.
School of Economics and Management, Jiangsu Maritime Institute, Nanjing, 211170, China

Received: 28 June 2024 Revised: 19 August 2024 Accepted: 20 August 2024 Published: 23 August 2024
MSC : 34A08, 37N35

In this paper, we investigated the nonlinear vibration characteristics and time-delay feedback controllability of a fractional horizontal roll system, which is described by a fractional Duffing-van der Pol oscillator under an external harmonic excitation. We focused on the resonance of fractional roller systems and conducted corresponding vibration control. The amplitude-frequency equations of primary resonance and superharmonic resonance were obtained using the multiple scale method. The amplitude-frequency characteristic curves of the system with different parameters were presented, and the influence of system parameters on the curves was analyzed. In addition, the time-delay feedback controller was designed to control the parameter excitation vibration. The numerical simulation results have verified the effectiveness of the time-delay controller in eliminating the jumping and hysteresis phenomena of the rolling system. The comparisons of approximate analytical solution and numerical solution was fulfilled, and the result certifies the correctness and satisfactory precision of the approximately analytical solution. The analysis results provide certain theoretical guidance for the vibration reduction of the horizontal nonlinear roller system.
- fractional horizontal nonlinear roller system,
- primary resonance,
- superharmonic resonance,
- multiple scale method
Citation: Zhoujin Cui, Xiaorong Zhang, Tao Lu. Resonance analysis and time-delay feedback controllability for a fractional horizontal nonlinear roller system[J]. AIMS Mathematics, 2024, 9(9): 24832-24853. doi: 10.3934/math.20241209

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Abstract

In this paper, we investigated the nonlinear vibration characteristics and time-delay feedback controllability of a fractional horizontal roll system, which is described by a fractional Duffing-van der Pol oscillator under an external harmonic excitation. We focused on the resonance of fractional roller systems and conducted corresponding vibration control. The amplitude-frequency equations of primary resonance and superharmonic resonance were obtained using the multiple scale method. The amplitude-frequency characteristic curves of the system with different parameters were presented, and the influence of system parameters on the curves was analyzed. In addition, the time-delay feedback controller was designed to control the parameter excitation vibration. The numerical simulation results have verified the effectiveness of the time-delay controller in eliminating the jumping and hysteresis phenomena of the rolling system. The comparisons of approximate analytical solution and numerical solution was fulfilled, and the result certifies the correctness and satisfactory precision of the approximately analytical solution. The analysis results provide certain theoretical guidance for the vibration reduction of the horizontal nonlinear roller system.

References

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