基于多尺度法的预载压电梁俘能特性

Energy Harvesting Characteristics of Preloaded Piezoelectric Beams Based on Multi-Scale Approach

低频、宽带和可调频一直是衡量压电能量采集器性能的重要指标,施加轴向预载是改善这些重要指标的有效措施。为了更好地揭示预载对俘能特性的影响,基于欧拉-伯努利梁理论和高斯定理,推导了预载压电梁的力电耦合方程,使用伽辽金离散和多尺度法,得到了位移、电压和平均输出功率的渐进解析解;同时通过理论分析,给出了短路开路谐振频率、开路电压幅值、最优输出功率和最优电阻的具体表达式。然后,针对悬臂梁模型,结合数值模拟验证了文中理论的有效性,之后进一步分析探究了预载对开路电压和最优输出功率的影响。结果表明:施加轴向预载可以提高压电悬臂梁的俘能效率,相较于无预载情况,预载20 N时,谐振频率降低31.6%,开路电压幅值增加120.8%,最优输出功率增加40.0%。

Low frequency,broad bandwidth and adjustable frequency have always been adopted as crucial indexes to measure the performance of piezoelectric energy harvesters(PEHs).The axial preload is deemed as one of the effective ways to improve these indexes.To explore the effect of preload on the energy harvesting characteristics,the electromechanical coupling governing equations were derived based on the Euler-Bernoulli beam theory and Gauss Theorem.The asymptotically analytic solutions of the displacement,the voltage and the average output po-wer were obtained with Galerkin discretization and the multi-scale approach.Then,through theoretical analysis,this paper obtained the expressions of the short-circuit and open-circuit resonance frequencies,the open-circuit voltage amplitude,the optimal output power and the optimal load resistance.For the cantilever beam model,the validity of the theory was verified by numerical simulation.Finally,the influence of preload on open-circuit voltage and optimal output power was analyzed.The results reveal that the axial preload can improve the energy harvesting efficiency of piezoelectric cantilever beam.Compared with the case without preload,the resonant frequency decreases by 31.6%,the amplitude of open-circuit voltage increases by 120.8%,and the optimal output power increases by 40.0%,when the preload is 20 N.