三稳态能量收集系统的同宿分岔及混沌动力学分析

李海涛; 丁虎; 陈立群; 秦卫阳

doi:10.21656/1000-0887.410164

三稳态能量收集系统的同宿分岔及混沌动力学分析

doi: 10.21656/1000-0887.410164

¹中北大学理学院力学系, 太原 030051;²上海大学上海市应用数学和力学研究所, 上海 200072;³西北工业大学工程力学系, 西安 710072

基金项目: 国家自然科学基金青年科学基金(11902294)；中国博士后基金(2018M640373)；山西省应用研究基础计划(201801D221037)；山西省高等学校科技创新项目(2019L520)

详细信息

作者简介:
李海涛（1985—），男，副教授，博士(通讯作者. E-mail: lihaitao5884@163.com).

中图分类号: O322
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出版历程
- 收稿日期: 2020-06-08
- 刊出日期: 2020-12-01

Homoclinic Bifurcations and Chaos Thresholds of Tristable Piezoelectric Vibration Energy Harvesting Systems

¹Department of Engineering Mechanics, School of Science, North University of China, Taiyuan 030051, P.R.China;²Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;³Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Science Fund for Young Scholars of China(11902294)；China Postdoctoral Science Foundation(2018M640373)

摘要

摘要: 通过考虑动力系统平衡点的变化，构建了三稳态能量收集装置，分析了系统的同宿分岔和混沌等非线性动力学行为，全面研究了势能函数形状对压电能量收集系统响应的影响规律.建立了三稳态能量收集系统的集中参数模型，基于Padé逼近方法得到了同宿轨道解析形式的表达式.根据 Melnikov理论发展了能量收集系统同宿分岔以及混沌动力学的定性研究方法，得到了发生同宿分岔的阈值曲线.利用分岔图、最大Lyapunov指数和相平面图等数值方法验证解析结果，当激励幅值超过Melnikov临界阈值时，系统由阱内运动演变为大幅阱间振动.结果表明，调整对称的稳定平衡位置至非对称情形将导致三稳态能量收集系统非线性动力学行为的变化，不仅使系统在低激励强度下实现大幅阱间跳跃，还抑制了混沌响应产生，相关结果为实现优化能量输出效率提供了一定的理论参考.
- 三稳态 /
- 能量收集 /
- Melnikov函数 /
- 同宿分岔
Abstract: Nonlinear dynamic performances such as homoclinic bifurcation and chaos were investigated for tristable vibration energy harvesting systems. The analytical expression of the symmetric and asymmetric homoclinic solution was obtained through the Padé approximation, which was consistent with the numerical solution. According to the Melnikov theory, the qualitative method of studying the homoclinic bifurcation of the energy harvesting system with a triple well was developed, and the necessary condition for the occurrence of homoclinic bifurcation was obtained. Numerical simulations yielded bifurcation diagrams and maximum Lyapunov exponents that demonstrated the inter-well responses predicted with the Melnikov method. Compared with the system with symmetric potential energy, the system with asymmetric potential energy has a lower threshold of homoclinic bifurcation. For a low excitation level, the system with asymmetric potential energy witnesses inter-well chaos, while the response of the system with symmetric potential energy still keeps trapped in a single well. The change of symmetry of the system potential energy function improves the output voltage due to the increase in the probability of generating a large periodical inter-well oscillation response. The research on the homoclinic bifurcation of nonlinear energy harvesting systems with symmetric and asymmetric triple potential wells provides an effective tool for the parametric design of high-performance energy harvesters.
- tristability /
- energy harvesting /
- Melnikov function /
- homoclinic bifurcation

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