摘要
双稳态俘能器可实现宽频和高效的俘能效果.目前的研究主要在双稳态结构中接入单一电阻电路进行俘能.本文将非线性RLC(电阻-电感-电容)谐振电路引入到三弹簧式双稳态结构中,构建两自由度非线性系统,以实现俘能特性的提升.设计永磁体与线圈的构型,获得了非线性机电耦合系数.推导并得到了两自由度非线性俘能器的控制方程.利用谐波平衡法推导得到了系统的电流与位移的频率响应关系.基于雅可比矩阵对解的稳定性进行了判别.将解析解与数值解进行了对比验证.结果表明,在双稳态俘能器中引入非线性二阶谐振电路不仅有利于低频俘能,还可进一步提升俘能响应,拓宽俘能带宽.相同的电路参数下,与线性电路相比非线性电路可通过电流的倍频现象实现结构更低频率的能量俘获.减小谐振电路与双稳态结构共振频率之比,增加基础激励幅值,减小静平衡点之间的距离均可提升俘能器的俘能效果.通过调控谐振电路与双稳态共振频率之比和基础激励幅值等参数,可实现系统单倍周期响应、多倍周期响应及混沌响应之间的切换.
The bistable harvester can achieve wide band and high-efficiency energy harvesting performance under low frequency and low excitation levels.Previous studies mainly use a simple resistor circuit to capture the energy in the bistable structures.This paper proposes a two-degree-of-freedom(DOF)nonlinear system formed by coupling a threespring bistable structure with a nonlinear RLC(resistance-inductance-capacitance)resonant circuit for energy harvesting enhancement.The nonlinear electromagnetic coupling coefficient between the circuit and structure is obtained by the special configuration between permanents and coils.The governing equation of the two DOF nonlinear systems is acquired.The analytical responses of the current and displacement are derived by the harmonic balance method,whose stability is judged by the Jacobin matrix.The analytical solution is compared with the numerical solution.Results demonstrate that introducing a nonlinear two-order resonant circuit into the bistable energy harvester can further improve the harvesting responses and broaden the energy bandwidth.With the same circuit parameters,the nonlinear resonant circuit can achieve lower frequency energy harvesting performance through frequency doubling of the current compared with the traditional linear circuit.One can enhance the energy harvester performance by decreasing the resonant ratio between the resonant circuit and bistable structure,increasing the excitation amplitude,and decreasing the distance between two static equilibrium points.The system can realize the switching of single-period response,multi-period response,and chaotic responses by adjusting the resonant ratio between circuit and bistable structure,and excitation amplitude.
作者
梁超
马洪业
王珂
严博
Liang Chao;Ma Hongye;Wang Ke;Yan Bo(College of Mechanical and Electronic Engineering,Jiaozuo University,Jiaozuo 454003,Henan,China;Key Laboratory of Space Utilization,Technology and Engineering Center for Space Utilization,Chinese Academy of Sciences,Beijing 100094,China;Faculty of Mechanical Engineering,Zhejiang Sci-Tech University,Hangzhou 310018,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2023年第5期1181-1194,共14页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金项目(52175125)资助。
关键词
电磁俘能
双稳态
谐波平衡
混沌运动
低频振动
electromagnetic energy harvesting
bistable
harmonic balance
chaotic motion
low-frequency vibration
