随机激励下双稳态压电俘能系统的相干共振及实验验证

Broadband energy harvesting from coherence resonance of a piezoelectric bistable system and its experimental validation

随着压电晶体材料的迅速发展,基于压电效应的能量采集系统是俘获环境中的宽带随机振动能量的一种有效途径.研究了有限宽带随机激励作用下,磁斥力双稳态压电俘能系统的相干共振俘能机理,并进行了实验验证.运用Euler-Maruyama方法求解了随机非线性压电振动耦合方程,比较分析了相干共振发生前后系统的动力学特性和俘能效率,然后基于Kramers逃逸速率解释了相干共振.最后的随机振动实验结果验证了双稳态压电俘能系统的相干共振俘能机理.并且观察到:当相干共振发生时,系统会在两个势能阱之间剧烈运动,此时宽带随机振动能量会被转化为大幅值窄带低频振动响应,从而极大地提高了宽带随机振动能量的俘获效率.

Piezoelectric effect is an effective way of harvesting energy from the environmental broadband vibration. In this paper, we investigate the coherence resonance of a piezoelectric bistable vibration energy harvester theoretically and experimentally. The device is comprised of a cantilever beam with magnetic repulsive force. Firstly, the electromechanical coupled equation is derived based on the Euler-Bernoulli beam theory. Then, analyzing the potential shapes, we learn that when the system oscillates between the two potential wells, it will produce a large voltage generally. And the beam dynamic response under the random excitation is simulated by Euler-Maruyama method. The results of simulations and experiments show that there is a coherence resonance threshold in the Duffing type piezoelectric bistable energy harvester. When the standard deviation of the random excitation is less than the threshold, the motion state of the system will be trapped in a single potential well, which results in a low average output power. And when the excitation standard deviation is larger than the threshold, the system stochastic stability will change. The dynamic displacement and strain clearly show that the system can exhibit large oscillation between the two potential wells. Then, Kramers rate is used to explain the coherence resonance threshold of the bistable system under the broadband random excitation. The experimental results show that when the coherence resonance takes place, the beam will oscillate between the two potential wells more frequently, and the broadband vibration energy can be transformed into large amplitude narrow band low-frequency oscillation response, which can greatly improve the harvesting effectiveness of broadband vibration energy.