双边约束下形状记忆合金梁的混沌运动

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (3): 653-658.

双边约束下形状记忆合金梁的混沌运动

刘亚妮, 冯进钤, 沈晓娜, 李玉婷, 王迎宵

西安工程大学理学院, 西安 710048

收稿日期:2019-04-28 出版日期:2021-05-26 发布日期:2021-05-23
通讯作者: 冯进钤 E-mail:jqfeng15@126.com

Chaotic Motion of Shape Memory Alloy Beam with Bilateral Constraints

LIU Yani, FENG Jinqian, SHEN Xiaona, LI Yuting, WANG Yingxiao

School of Science, Xi’an Polytechnic University, Xi’an 710048, China

Received:2019-04-28 Online:2021-05-26 Published:2021-05-23

摘要/Abstract

摘要： 基于非光滑系统的Melnikov方法, 研究谐和激励下双边约束形状记忆合金梁的混沌运动, 得到了系统出现Smale马蹄混沌的必要条件, 并通过数值仿真研究系统的相图、 Poincaré截面图以及最大Lyapunov指数. 结果表明: 数值仿真结果与Melnikov准则下的解析结果相符；当参数取特定值时, 较大的碰撞恢复系数可抑制混沌, 较大的谐和激励幅值可促进混沌产生.

关键词: 双边约束, 形状记忆合金梁, Melnikov方法, Smale马蹄混沌

Abstract: Based on the Melnikov method for non-smooth systems, we studied the chaotic motion of a shape memory alloy beam with bilateral constraints under harmonic excitation, and obtained the necessary conditions for the occurrence of Smale horseshoe chaos. The phase diagram, Poincaré section diagram and maximum Lyapunov exponent of the system were studied by numerical simulation. The results show that the numerical simulation results are consistent with the analytical results under Melnikov criterion. When parameters take specific values, the larger impact recovery coefficient can suppress chaos, and the larger harmonic excitation amplitude can promote the generation of chaos.

Key words: bilateral constraints, shape memory alloy beam, Melnikov method, Smale horseshoe chaos

中图分类号:

O415.1

刘亚妮, 冯进钤, 沈晓娜, 李玉婷, 王迎宵. 双边约束下形状记忆合金梁的混沌运动[J]. 吉林大学学报(理学版), 2021, 59(3): 653-658.

LIU Yani, FENG Jinqian, SHEN Xiaona, LI Yuting, WANG Yingxiao. Chaotic Motion of Shape Memory Alloy Beam with Bilateral Constraints[J]. Journal of Jilin University Science Edition, 2021, 59(3): 653-658.