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  

Chaotic dynamics of a bi-stable energy harvesting system with asymmetric potential well characteristics

作　　者：李海涛[1,2] 丁虎 陈立群[2,3,4] LI Haitao;DING Hu;CHEN Liqun(Department of Mechanics,School of Science,North University of China,Taiyuan 030051,China;Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China;Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University,Shanghai 200072,China;Department of Mechanics,Shanghai University,Shanghai 200444,China)

机构地区：[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]上海大学上海市力学在能源工程中的应用重点实验室,上海200072 [4]上海大学力学系,上海200444

出　　处：《振动与冲击》2020年第18期54-59,69,共7页Journal of Vibration and Shock

基　　金：中国博士后基金(2018M640373);山西省基础应用项目(201801D221037);中北大学科学研究基金(XJJ201810)。

摘　　要：针对带有非对称势能阱的双稳态能量采集系统开展混沌动力学研究。建立考虑重力因素影响的能量采集系统非线性动力学模型。针对动力学方程的非对称势能阱开展分析,得到同宿轨道的解析表达形式。通过Melnikov方法获得发生同宿分岔的阈值,并使用数值方法验证。结果表明当激励强度低于Melnikov理论预测的临界阈值时,响应限制在单个非对称的势能阱当中;当激励强度大于Melnikov理论预测的临界阈值时,同宿分岔将会引发双阱运动。重力参数和阻尼显著影响同宿分岔的阈值曲线,考虑重力参数影响所得到的阈值明显高于对称双阱能量采集系统的阈值。增加重力参数会抑制混沌响应的产生,导致系统从混沌-周期响应共存逐渐演化为周期-周期响应共存。此研究结果将拓展非线性动力学的研究范畴,为实现混沌响应的调控提供一种策略。The homoclinic bifurcation of a bi-stable energy harvesting system with asymmetric potential well characteristics was investigated.Firstly,the nonlinear dynamic model of a bi-stable energy harvesting system with gravitational parameters was established.Then an analytic expression for the homoclinic orbit was derived by analyzing the asymmetrical potential well of the governing equation.The Melnikov method was used to obtain the threshold of homoclinic bifurcation,and the criteria were verified by a numerical method.When the excitation intensity is lower than the critical threshold predicted by the Melnikov method,the response is restricted in the single asymmetric potential well;as the excitation intensity is higher 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 the bi-stable energy harvesting system with asymmetric potential well characteristics is higher than that with symmetric potential well characteristics.Increasing gravity parameters will suppress the generation of chaotic response,leading to the gradual evolution from the coexistence of chaotic-periodic responses to the coexistence of periodic-periodic responses.The results will expand the scope of nonlinear dynamics and provide a strategy for chaotic response control.

关 键 词：非对称势能阱 MELNIKOV方法 能量采集系统 同宿分岔 混沌动力学 

分 类 号：O322[理学—一般力学与力学基础]