Analysis of super-harmonic resonance and periodic motion transition laws of fractional order nonlinear vibration isolation system

QU Minghe, WU Shaopei, YU Liyang, DING Wangcai, LI Guofang, HUANG Ran

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (5) : 66-73.

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PDF(2864 KB)
Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (5) : 66-73.

Analysis of super-harmonic resonance and periodic motion transition laws of fractional order nonlinear vibration isolation system

  • QU Minghe, WU Shaopei, YU Liyang, DING Wangcai, LI Guofang, HUANG Ran
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Abstract

The fractional nonlinear Zener model is used to describe the nonlinear and viscoelastic constitutive relation of the vibration isolation system. The fractional-order derivative term was made equivalent to a term in the form of trigonometric function, the steady-state response of the system was solved by high-order harmonic balance method, and the results were compared with a variety of methods. The dynamic response of the system in the low frequency region was obtained by using numerically simulation. The bifurcation type of the system was determined by Floquet theory and the influence of fractional order term on dynamic response was revealed. The results show that there is a jump phenomenon in high-order super-harmonics, and periodic motion diversity in the process of adjacent-order super-harmonic transfer. Additionally, it is found that the periodic motion and chaos coexist in the system, and the transition laws of the polymorphic coexistence region and its adjacent regions was summarized explicitly.

Key words

Nonlinear Zener model / fractional-order derivative / super-harmonic resonance / transition law

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QU Minghe, WU Shaopei, YU Liyang, DING Wangcai, LI Guofang, HUANG Ran. Analysis of super-harmonic resonance and periodic motion transition laws of fractional order nonlinear vibration isolation system[J]. Journal of Vibration and Shock, 2023, 42(5): 66-73

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