单边碰撞分数阶Rayleigh振子的随机P-分岔

孙万奇1,王军1,2,申永军1,2,张建超2

振动与冲击 ›› 2022, Vol. 41 ›› Issue (23) : 160-167.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (23) : 160-167.
论文

单边碰撞分数阶Rayleigh振子的随机P-分岔

  • 孙万奇1,王军1,2,申永军1,2,张建超2
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Random P-bifurcation of fractional-order Rayleigh oscillator with unilateral collision

  • SUN Wanqi1, WANG Jun1,2, SHEN Yongjun1,2, ZHANG Jianchao2
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摘要

基于非光滑变换和随机平均法分析了随机激励下含有分数阶微分的Rayleigh振子碰撞振动系统的随机P-分岔问题。首先,基于Caputo定义计算了分数阶导数,将分数阶微分等效为相应的阻尼力与恢复力,并用非光滑变换将原系统等效为一个新的不含速度跳的系统;其次,基于随机平均法建立了随机伊藤方程,得到了随机响应的Markovian近似,进而计算出系统的概率密度函数及其稳态解;最后,引入突变理论推导出随机P-分岔的临界参数条件表达式,并分析了分数阶系数、分数阶阶次、恢复系数等主要参数对分数阶Rayleigh振子碰撞系统发生分岔的影响。
关键词:单边碰撞;分数阶;随机平均法;非光滑变换;随机P-分岔

Abstract

Based on non-smooth transformation and stochastic averaging method, the stochastic P-bifurcation problem of Vibro-impact Rayleigh oscillator with fractional-order derivative under stochastic excitation is analyzed. First, based on the Caputo definition, the fractional-order derivative is calculated, the fractional-order derivative is equated to the corresponding damping force and the recovery force, and the original system is equivalent to a new system without velocity jumps with a non-smooth transformation; Secondly, based on the stochastic averaging method, the stochastic Ito equation is established, and the Markovian approximation of the stochastic response is obtained, and then the probability density function of the system and its steady-state solution are calculated; Finally, the critical parameter condition expression of stochastic P-bifurcation is derived by introducing mutation theory, and the effects of major parameters such as fractional order coefficient, fractional order order, and recovery coefficient on the bifurcation of the fractional order Rayleigh oscillator collision system are analyzed.
Key words:unilateral vibro-impact; fractional-order; stochastic averaging method; Non-smooth transformation; stochastic P-bifurcations

关键词

单边碰撞 / 分数阶 / 随机平均法 / 非光滑变换 / 随机P-分岔

Key words

unilateral vibro-impact / fractional-order / stochastic averaging method / Non-smooth transformation / stochastic P-bifurcations

引用本文

导出引用
孙万奇1,王军1,2,申永军1,2,张建超2. 单边碰撞分数阶Rayleigh振子的随机P-分岔[J]. 振动与冲击, 2022, 41(23): 160-167
SUN Wanqi1, WANG Jun1,2, SHEN Yongjun1,2, ZHANG Jianchao2. Random P-bifurcation of fractional-order Rayleigh oscillator with unilateral collision[J]. Journal of Vibration and Shock, 2022, 41(23): 160-167

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