双稳态压电能量获取系统的分岔混沌阈值  

Bifurcation and Chaos Thresholds of Bistable Piezoelectric Vibration Energy Harvesting Systems

作　　者：李海涛[1] 秦卫阳[1] 

机构地区：[1]西北工业大学工程力学系,西安710072

出　　处：《应用数学和力学》2014年第6期652-662,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172234)~~

摘　　要：建立了双稳态压电能量获取系统动力学模型并且分析了系统的同宿分岔和混沌等非线性动力学行为.根据受压梁的双稳态特性,提出了等效双稳态压电能量获取系统的数学模型.基于Melnikov理论,获得了谐波激励作用下的能量获取系统关于同宿分岔的定性研究方法.通过优化系统参数,得到了发生同宿分岔的阈值曲线.数值结果显示系统在临界阈值处由单阱运动演变为双阱运动,验证了理论分析的有效性.结果表明Melnikov方法可为能量获取系统的参数设计提供有效的理论依据.Nonlinear dynamic performances such as homoclinic bifurcation and chaos were modeled and analyzed for bistable nonlinear vibration energy harvesting systems. According to bistability of the beam under axial loading, a model of the bistable nonlinear vibration energy harvester was established. Based on the Melnikov theory, a qualitative method was proposed to address homoclinic bifurcation of the bistable energy harvester under harmonic excitation, and the criteria for homoclinic bifurcation and the high-energy solution were derived from the Melni- kov function through parameter optimization. Numerical simulation shows that the singlewell- to-doublewell transitions occur at the critical thresholds, which verifies the theoretical analysis. Research on the Melrdkov method for nonlinear energy harvesting systems promises effective tools for the parametric design of high-performance energy harvesters.

关 键 词：双稳态能量获取系统 MELNIKOV方法 同宿分岔 

分 类 号：O322[理学—一般力学与力学基础]