Smyth Katherine, Bathurst Stephen, Sammoura Firas, Kim Sang-Gook
IEEE Trans Ultrason Ferroelectr Freq Control. 2013 Aug;60(8):1756-67. doi: 10.1109/TUFFC.2013.2756.
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%.
在这项工作中，使用格林函数方法解析确定了压电驱动微机械超声换能器（PMUT）的挠度方程。借助格林函数求解技术，针对轴对称振动模式明确求解了具有任意圆形/环形电极几何形状的圆形板的挠度。对于一个中心电极覆盖约60%板半径的PMUT，格林函数解与现有的分段解和基于能量的解相比，误差小于1%，吻合良好。格林函数解也比它们更简单，无需数值积分，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）收集的实验测量静态挠度数据进一步用于验证格林函数模型分析。在一系列施加的偏置电压（5至21 V）范围内，中心挠度和挠度分布数据与格林函数解吻合良好，实验数据与格林函数数据之间的平均误差小于9%。
