窄带随机激励下三稳态压电俘能器的动力学特性与实验研究

Dynamical Behaviors and Experimental Analysis of Tri-stable Piezoelectric Energy Harvester Under Narrow-Band Random Excitations

本文研究了窄带随机激励下三稳态压电俘能器的动力学输出特性.首先,建立了非线性三稳态压电俘能器的分布参数型机电耦合运动方程,并基于多尺度法推导得到系统运动方程响应的解析解以及一阶、二阶稳态矩的表达式.其次,分析了磁铁间距、噪声强度和激励幅值等参数对系统稳态响应的影响.研究结果表明,在一定参数范围内,随着噪声强度的增加,压电振动俘能器会经历阱内振动、阱间振动甚至大轨道周期运动,以表现出单稳态、双稳态和三稳态特性;改变磁铁水平间距和竖直间距构造三稳态压电俘能器,其振动幅值和采集电压相较于双稳态明显提高.最后,通过实验比较了压电俘能器在不同位形时的采集性能,结果表明了三稳态压电俘能器的优越性,为窄带随机激励下的非线性振动俘能器的设计提供一定的理论依据.

In this paper,the dynamical behaviors of a tri-stable piezoelectric energy harvester under the narrow-band random excitation is studied.Firstly,the dynamical equation of a tri-stable nonlinear cantilever piezoelectric energy harvesting system is established.The analytical expressions of the dynamical response of the system together with the first and second steady moments are obtained by using the multiple scales method.Secondly,the effects of the distance between the tip magnet and the external magnets,the noise intensity and the excitation amplitude on the system response and harvesting performance are discussed.The obtained results show that as the noise intensity increases,the piezoelectric vibration energy harvester will experience mono-stable,bi-stable and tri-stable motion.Changing the horizontal and vertical spacing of the magnets makes the piezoelectric energy harvester perform tri-stable motion,and the displacement and acquisition voltage are significantly improved compared to the bi-stable case.Finally,the collection performance of the piezoelectric energy harvester in different configurations is compared through experiments.The results show the superiority of the tri-stable piezoelectric energy harvester,which provide the theoretical support for the design of the vibration energy harvester under the narrow-band random excitation.