材料和结构参数对悬壁梁式压电振子机电耦合性能的影响

Effects of physical and geometrical parameters on electromechanical coupling characteristics of a cantilevered piezoelectric vibrator

对材料和结构参数对压电和基板不等长的矩形截面悬臂梁式双晶压电振子机电耦合性能影响进行研究。由Hamilton原理推导了压电振子振动方程模型,并试验验证了模型的准确性。理论分析显示,当电路阻抗匹配时,转换效率最大,且当粘性阻尼系数相同时,最优转换效率随着机电耦合系数增大而增大。压电振子机电耦合系数和压电材料机电耦合因子成正比;随着压电与基板模量比增大,机电耦合系数增大;压电与基板密度比对机电耦合系数影响微弱;机电耦合系数随压电与基板长度比和厚度比都呈先增后减趋势,存在最优长度比和厚度比使机电耦合系数达到最大值。结构优化后的机电耦合系数随模量比的增加而增大;不同模量比和密度比条件下,最佳长度比变化较小,总体变化范围为0.6~0.7;模量比对最佳厚度比影响显著,随着模量比增大最佳厚度比减小。研究成果可用以指导压电振子的设计。

Here, the effects of physical and geometrical parameters on the electromechanical coupling characteristics of a one-step cantilevered piezoelectric energy harvester were studied.The model equation governing vibration of a piezoelectric vibrator was derived based on Euler-Bernoulli beam assumption in the linear and elastic range, and validated through comparison of theoretical results with experimental ones.Results revealed that the impedance matching leads to the maximum mechanical to electrical energy transfer efficiency;the optimal energy transfer efficiency increases with increase in the electromechanical coupling coefficient under a constant air and structural damping;the coupling coefficient is proportional to the material electromechanical coupling factor;and the coupling coefficient increases with increase in the modulus ratio between piezoelectric structure and base plate;the effect of piezoelectrics structure to base plate density ratio on the coupling coefficient is relatively smaller;with increase in length and thickness ratios between them,the coupling coefficient increases initially then decreases;there are the optimal length ratio and the optimal thickness ratio,they make the coupling coefficient reach the maximum;the optimal length ratio has a variation range of 0.6~0.7;the modulus ratio has an obvious effect on the optimal thickness ratio,the latter decreases with increase in the former.The study results provided a guidance for design of piezoelectric vibrators.