单晶压电悬臂梁等效粘性阻尼建模与实验分析

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单晶压电悬臂梁等效粘性阻尼建模与实验分析

房立清，张磊，郭德卿，马子龙，陈永超

（军械工程学院火炮工程系，河北石家庄050003）

摘要：为了完善压电悬臂梁非耦合集总参数模型，进而为压电振子的优化设计提供更为可靠的理论依据，对单晶压电振子等效粘性阻尼系数进行了理论建模研究。首先，根据机械振动理论以及阻尼理论，从能量的角度出发建立了单晶压电振子等效阻尼系数的理论模型。接着，针对基板材料性能，结构尺寸以及截面形状等不同因素对等效机械阻尼及电阻尼的影响规律进行了分析。最后，制备了三组不同形状尺寸的压电振子样品，并进行了冲击振动试验，验证了理论分析结果。研究表明，压电材料层对整体阻尼的影响主要取决于基板与压电材料的弹性模量比；压电材料每个振动周期的电能损耗与悬臂梁长度的三次方成正比，与宽度成反比；而决定振幅放大因子的阻尼比并非随结构尺寸单调变化。实验结果与理论模型误差在2.5%到14.7%之间，证明了理论模型的可靠性。分析表明，在可承受极限载荷相同的情况下，静态特性最优的变曲面悬臂梁，动态特性并非最佳。对于压电振子的优化设计具有一定现实意义。

关键词：等效粘性阻尼；单晶压电悬臂梁；建模；实验

中图分类号：TJ35；TK89；TB34 文献标识码：A

Modeling and experimental analysis of piezoelectric unimorph cantilever equivalent viscous damping

FANG Li-Qing, ZHANG Lei

（Dept. of Artillery Engineering ,Ordnance Engineering College, Shijiazhuang 050003, China）

Abstract: In order to perfect the simulation model of piezoelectric unimorph cantilever, thus to provide more reliable theoretical basisfor the optimal design of piezoelectric vibrator , the vibrator equivalent viscous damping coefficient were analysed . First of all, the analysis model of vibrator equivalent viscous damping coefficient were established established from the perspective of energy according to the theory of mechanical vibration and damping theory. Then, the influences of the material properties, structural dimensions as well as the cross-section shape on the machinery and electricity damping coefficient are analyzed. Finally, prepared three groups piezoelectric vibrator samples with different shape, size, and the impact vibration test were proceeded to verify the theoretical analysis. The results show that the impact of piezoelectric material layer on the overall damping depends on the elastic modulus ratio of the substrate and the piezoelectric material; in each vibration cycle, the piezoelectric material power loss is proportional to the cube of the cantilever length, and inversely proportional to the width; the damping ratio which is conclusive to amplitude amplification factor is not varies with the structure size monotonically. There was difference of 2.5% and 14.7% between the experimental results and theoretical model which proved the reliability of the theoretical model. While the extreme load is same which could withstand, the same case, piezoelectric unimorph cantilever with variable surface with optimal static characteristics may not with the best dynamic characteristics. For the optimal design of piezoelectric vibrator has a certain practical significance.

Key words: Equivalent viscous damping; Piezoelectric unimorph cantilever; Modeling; Experiment

收稿日期：2013-7-3；修订日期：2013-9-3