一类分数阶分段光滑系统的非线性振动特性

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摘要分析了一类含分数阶的单自由度分段光滑系统的振动特性。首先，建立了单自由度分数阶分段光滑系统的数学模型，采用平均法得到了系统的周期解，并与数值解进行了对比，二者吻合效果较好。其次分析了周期解幅频响应的跳跃现象及可能出现的鞍结分岔与擦边分岔，并利用数值仿真着重研究了分段刚度与阻尼、分数阶系数与阶次、分段间隙等参数对幅频响应及其稳定性的影响。最后基于奇异性理论对分岔方程进行了分析，得到了转迁集和系统分岔图，从而反映出该系统在不同参数区间的振动特性。

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	王军1
	申永军1
	杨绍普1
	温少芳2
	王美琪1

关键词 ：分数阶, 分段光滑, 周期解, 稳定性, 振动特性

Abstract：The nonlinear vibration performance of a single-degree-of-freedom piecewise smooth system with fractional-order derivative was considered. A mathematic model of the piecewise smooth system was built. The periodic solution of the system was obtained by the averaging method, which was in good agreement with the numerical solution. The jump phenomenon of amplitude-frequency responses of the periodic solution and the possible saddle-node bifurcation and grazing bifurcation were analyzed. The effects of the piecewise stiffness and damping, fractional-order coefficient, order, and clearance on the amplitude-frequency curve and its stability region were studied. By using the singularity theory, the bifurcation equation was established, and the transition sets and bifurcation behaviors were obtained, which could reflect the vibration characteristics of the system in different parameter ranges.

Key words： fractional-order piecewise smooth periodic solution stability vibration characteristics

收稿日期: 2019-02-25 出版日期: 2019-11-15

引用本文:

王军1，申永军1，杨绍普1，温少芳2，王美琪1. 一类分数阶分段光滑系统的非线性振动特性[J]. 振动与冲击, 2019, 38(22): 216-223.
WANG Jun1, SHEN Yongjun1, YANG Shaopu1, WEN Shaofang2, WANG Meiqi1. Nonlinear vibration performance of a piecewise smooth system with fractional-order derivative. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(22): 216-223.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I22/216

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