Analysis of bilateral symmetrical vibro-impact of a fractional-order linear single-degree-of-freedom oscillator

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (16) : 20-28.

LIU Ruyu1，NIU Jiangchuan1,2，SHEN Yongjun1,2，YANG Shaopu1,2

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Abstract

Based on the two-sided rigid vibro-impact model of a single-degree-of-freedom oscillator with fractional-order derivative, the stability and bifurcation behavior of the bilateral symmetrical vibro-impact system under harmonic excitation were studied.The average method was used to obtain the equivalent stiffness and damping of the fractional order linear system, and then the steady-state solution of the vibro-impact system was obtained.And the iterative method was used to obtain more accurate transient natural frequency, so as to obtain the transient solution of the vibro-impact system.On this basis, the approximate analytical solution of the bilateral symmetrical vibro-impact system was acquired.According to the approximate analytical solution, the existence conditions of symmetric n-1-1 periodic motion were analyzed, and the stability of n-1-1 periodic motion was studied by Poincaré mapping.The bifurcation behaviors of the system were further analyzed with the change of the external excitation frequency, fractional order, and gap.The results show that there are grazing bifurcation, pitchfork bifurcation, period doubling bifurcation, and chaotic motion in the system.

Key words

vibro-impact / fractional-order derivative / stability / bifurcation

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LIU Ruyu，NIU Jiangchuan，SHEN Yongjun，YANG Shaopu. Analysis of bilateral symmetrical vibro-impact of a fractional-order linear single-degree-of-freedom oscillator[J]. Journal of Vibration and Shock, 2021, 40(16): 20-28

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