IEEE Trans Ultrason Ferroelectr Freq Control. 2018 Jan;65(1):50-59. doi: 10.1109/TUFFC.2017.2772331.
A hybrid boundary element model is proposed for the simulation of large piezoelectric micromachined ultrasonic transducer (PMUT) arrays in immersion. Multiphysics finite element method (FEM) simulation of a single-membrane structure is used to determine stiffness and piezoelectrically induced actuation loading of the membranes. To simulate the arrays of membranes in immersion, a boundary element method is employed, wherein membrane structures are modeled by a surface mesh that is coupled mechanically by mass, stiffness, and damping matrices, and acoustically by a mutual impedance matrix. A multilevel fast multipole algorithm speeds up computation time and reduces memory usage, enabling the simulation of thousands of membranes in a reasonable time. The model is validated with FEM for a small 3 3 matrix array for both square and circular membrane geometries. Two practical optimization examples of large PMUT arrays are demonstrated: membrane spacing of a 7 7 matrix array with circular membranes, and material choice and top electrode coverage of a 32-element linear array with 640 circular membranes. In addition, a simple analytical approach to electrode optimization based on normal mode theory is verified.
提出了一种混合边界元模型，用于模拟浸液中的大型压电微机械超声换能器（PMUT）阵列。采用多物理场有限元方法（FEM）对单个膜结构进行模拟，以确定膜的刚度和压电致动载荷。为了模拟浸液中的膜阵列，采用边界元法，其中膜结构通过表面网格建模，通过质量、刚度和阻尼矩阵以及互阻抗矩阵在力学上耦合，在声学上耦合。多级快速多极算法加速了计算时间并减少了内存使用，使在合理的时间内模拟数千个膜成为可能。该模型通过 FEM 对正方形和圆形膜几何形状的小 3 3 矩阵阵列进行了验证。演示了两个大型 PMUT 阵列的实际优化示例：圆形膜的 7 7 矩阵阵列的膜间距，以及具有 640 个圆形膜的 32 个元件线性阵列的材料选择和顶电极覆盖。此外，还验证了基于模态理论的简单电极优化分析方法。
