Chaotic dynamics of a bi-stable energy harvesting system with asymmetric potential well characteristics
LI Haitao1,2，DING Hu2,3，CHEN Liqun2,3,4
1.Department of Mechanics, School of Science, North University of China, Taiyuan 030051, China;
2.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
3.Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
4.Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract：In this paper, the homoclinic bifurcation for bi-stable energy harvesting system with asymmetric potential well is investigated. Firstly, the nonlinear dynamic model of the bi-stable energy harvesting system with gravitational parameters is established. Then an analytic expression of the homoclinic orbit is obtained by analyzing the asymmetrical potential well of the governing equation. Melnikov method is used to obtain the threshold of homoclinic bifurcation, and the criteria are verified by numerical method. When the excitation intensity is lower than the critical threshold predicted by Melnikov method, the response is restricted the single asymmetric potential well; as the excitation intensity is larger than the critical threshold, the bifurcation will trigger the double well response. The results show that the gravity parameter and the damping effect have an influence on the bifurcation threshold curve. The threshold value of bi-stable energy harvesting system with asymmetric potential well is higher than that of the energy harvesting system with symmetric potential well. Increasing gravity parameters will suppress the generation of chaotic response, leading to the gradual evolution from the coexistence of chaotic and periodic response to the coexistence of periodic response. The results of this study will expand the scope of nonlinear dynamics and provide a strategy for chaos response control.
收稿日期: 2019-04-01
出版日期: 2020-09-15
引用本文:
李海涛1,2，丁虎2,3，陈立群2,3,4. 带有非对称势能阱特性的双稳态能量采集系统混沌动力学分析[J]. 振动与冲击, 2020, 39(18): 54-59.
LI Haitao1,2，DING Hu2,3，CHEN Liqun2,3,4. Chaotic dynamics of a bi-stable energy harvesting system with asymmetric potential well characteristics. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(18): 54-59.
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