本文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。
Abstract
In this paper, the effect of physical and geometrical parameters on the electromechanical coupling characteristics of a one-step cantilevered piezoelectric energy harvester is studied. The model equation governing the vibration of a piezoelectric vibrator is derived based on the Euler-Bernoulli beam assumption in the linear and elastic regime, and validated through comparison of theoretical results with experimental ones. Results reveal that impedance matching leads to the maximum mechanical to electrical energy transfer efficiency. And the impedance-matching efficiency increases with the electromechanical coupling coefficient given a constant air and structural damping. The coupling coefficient increases linearly with the squared material electromechanical coupling factor, and is affected significantly by the piezoelectrics-to-substructure modulus, length and thickness ratios, while the effect of piezoelectrics-to-substructure density ratio is relatively small. It is shown that the coupling coefficient increases with the modulus ratio increasing. And with the length and thickness ratios increasing, the coupling coefficient increases initially then decreases after it reaches the maxima. The optimal length ratio, at which the maxima is reached, varies between 0.6~0.7 among a wide span of materials. And the optimal thickness ratio greatly varies depending on the modulus and density ratios. It monotonically increases with the modulus ratio.
关键词
压电俘能 /
优化 /
材料特性 /
结构尺寸
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Key words
piezoelectric energy harvesting /
optimization /
material properties /
geometrical parameters
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参考文献
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