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Analytic solution for N-electrode actuated piezoelectric disk with application to piezoelectric micromachined ultrasonic transducers

机译:N电极驱动压电盘的解析解及其在压电微机械超声换能器中的应用

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摘要

In this work, the deflection equation of a piezoelectrically-driven micromachined ultrasonic transducer (PMUT) is analytically determined using a Green's function approach. With the Green's function solution technique, the deflection of a circular plate with an arbitrary circular/ring electrode geometry is explicitly solved for axisymmetric vibration modes. For a PMUT with one center electrode covering ≈60% of the plate radius, the Green's function solution compares well with existing piece-wise and energy-based solutions with errors of less than 1%. The Green¿s function solution is also simpler than them requiring no numerical integration, and applies to any number of axisymmetric electrode geometries. Experimentally measured static deflection data collected from a fabricated piezoelectric micro ultrasonic transducer (PMUT) is further used to validate the Green's function model analysis. The center deflection and deflection profile data agree well with the Green's function solution over a range of applied bias voltages (5 to 21 V) with the average error between the experimental and Green's function data less than 9%.
机译:在这项工作中,使用格林函数方法解析地确定了压电驱动的微机械超声换能器(PMUT)的挠度方程。利用格林函数解技术,对于轴对称振动模式,可以明确解决具有任意圆形/环形电极几何形状的圆形板的挠曲问题。对于一个中心电极覆盖板半径约60%的PMUT,格林函数解决方案与现有的分段和基于能量的解决方案具有很好的比较,误差小于1%。 Green函数解比不需要数值积分的函数解还简单,并且适用于任意数量的轴对称电极几何形状。从制造的压电微超声换能器(PMUT)收集的实验测量的静态挠度数据可进一步用于验证Green的功能模型分析。在施加的偏置电压(5至21 V)范围内,中心偏转和偏转曲线数据与格林函数解决方案非常吻合,实验和格林函数数据之间的平均误差小于9%。

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