磁振子压电能量采集器的多尺度分析  

Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

作　　者：赵健[1] 张国策[2] 陈立群[1,2,3] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海大学理学院力学系,上海200444 [3]上海市力学在能源工程中的应用重点实验室(上海大学),上海200072

出　　处：《应用数学和力学》2015年第8期805-813,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重点项目)(11232009);上海市重点学科项目(S30106)~~

摘　　要：根据磁振子压电能量采集器实验系统的数学模型,基于系统静平衡位形,引入坐标变换,建立相对位移的标准控制方程.利用Taylor级数展开法处理磁力非线性项,运用多尺度法近似解析分析,通过消除长期项获得可解性条件,并由此推导出稳态响应时的幅频关系.四阶Runge-Kutta方法用于数值计算受迫振动时间历程,数值算例给出了系统前两阶主共振下的稳态幅频响应关系及其失稳区域.结果表明,多尺度方法所得到的一致有效解具有较高精度,可以为优化设计磁振子压电能量采集器提供理论依据.A piezoelectric energy harvester with a magnetic oscillator was studied. The dynamic equation was derived via introduction of coordinate transform based on the equih＇brium configu- ration. The Taylor series expansion method was employed to deal with the nonlinear function of the magnetic force. The multi-scale method was applied to obtain the steady-state periodic solu- tions of the system. The solvability condition and the amplitude-frequency relationship were de- rived through elimination of the secular terms. Then the Runge-Kutta method was used to nu- mericaUy calculate the system＇ s forced vibration time history and give the amplitude-frequency response characteristics and instability boundary of the 1st 2 primary resonance cases. The re- sults show that the multi-scale analysis yields uniformly valid solutions of high accuracy, and provides a theoretic base for the optimal design of piezoelectric energy harvesters with magnetic oscillators.

关 键 词：受迫振动 非线性 多尺度方法 能量采集 

分 类 号：O322[理学—一般力学与力学基础]