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

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (18) : 54-59.

论文

李海涛1,2，丁虎2,3，陈立群2,3,4

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

LI Haitao1,2，DING Hu2,3，CHEN Liqun2,3,4

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摘要

本文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。首先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。

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.

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

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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[J]. Journal of Vibration and Shock, 2020, 39(18): 54-59

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