基于等效线性化方法的非线性振动能量采集器功率分析  

Power analysis of nonlinear vibration energy harvester based on equivalent linearization method

作　　者：李佳诚 王志霞 王炜[1,2] 王辰 LI Jiacheng;WANG Zhixia;WANG Wei;WANG Chen(School of Mechanical Engineering,Tianjin University,Tianjin 300350,China;Tianjin Municipal Key Lab of Nonlinear Dynamics and Control,Tianjin 300350,China;Department of Civil and Environmental Engineering,Hong Kong Polytechnic University,Hong Kong 999077,China)

机构地区：[1]天津大学机械工程学院,天津300350 [2]天津市非线性动力学与控制重点实验室,天津300350 [3]香港理工大学土木与环境工程系,中国香港999077

出　　处：《振动与冲击》2022年第1期196-205,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(11772218,1187244,12021002);天津市应用基础与先进技术研究计划(17JCYBJC18900);中英NSFC-RS联合项目(11911530177,181496)。

摘　　要：输出功率分析是振动能量采集器结构设计、参数选择的重要依据。有鉴于传统功率分析方法比较复杂,以一类电磁式振动能量采集器为对象,提出了一种新的非线性振动能量采集器功率分析方法,其核心是将非线性振动方程进行等效线性化处理,并借助传递函数开展功率优化分析。首先,考虑非线性磁力以及基尔霍夫电流定律,建立了通用化的采集器1.5自由度七次非线性机电耦合模型;其次,将动态频率法用于求解该系统控制方程,采用高阶谐波成分替代方程中的非线性项,实现了原有系统控制方程的等效线性化;最后,利用传递函数推导了输出功率表达式,分析等效线性化系统负载,机电耦合系数等因素对于输出功率的影响。研究结果表明:以等效线性化为基础的功率分析,可以有效地克服传统非线性能量采集器系统功率分析方法复杂的问题,具有良好的适用性。Output power analysis is an important basis for structural design and parametric selection of vibration energy harvester.Here,aiming at the complexity of traditional power analysis methods,taking a type of electromagnetic vibration energy harvester as the study object,a new power analysis method of nonlinear vibration energy harvester was proposed.Its key was to do equivalent linearization treatment for nonlinear vibration equation and perform power optimization analysis with the transfer function method.Firstly,based on the nonlinear magnetic force and Kirchhoff current law,a generalized 1.5-DOF seventh order nonlinear electromechanical coupled model for harvester was established.Secondly,the dynamic frequency method was used to solve the control equation of the system,and high-order harmonic components were used to replace nonlinear terms in the equation,and realize the equivalent linearization of the original system control equation.Finally,the output power expression was derived by using the transfer function method,and effects of equivalent linearization system load,electromechanical coupled coefficient and other factors on output power were analyzed.The results showed that the proposed power analysis based on equivalent linearization can effectively solve complex problems brought by traditional nonlinear energy harvester system power analysis methods,and have good applicability.

关 键 词：非线性 动态频率法 能量采集 等效线性化 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3