The paper is focused on the multi-physics modeling, via the finite element method (FEM), of a 4 × 4 air-coupled array of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs), and on its mechanical and acoustic validation by means of the comparison, in the time domain, with experimental results. A two-stage numerical procedure is employed, in order to evaluate the complete performance of the device, by means of two FEM models. In the first stage, the electro-mechanical-acoustic (EMA) problem is solved for the stand-alone transducer, taking into account the fabrication induced residual stresses and the multiple couplings between different physics. The numerical results are compared with the experimental ones in terms of initial deflection and time histories of pressure, in the linear and non-linear regime: the proposed model correctly captures the reported phenomena and perfectly matches the experimental trends. The second stage is devoted to the simulation of the 4 × 4 PMUTs array performance, belonging to the silicon die. The vibrating plates are modeled as equivalent rigid pistons. The acceleration histories, computed in the first stage, are imposed on the pistons, while a rigid baffle condition is enforced on the remaining part of the die surface. The model is adopted to predict the pressure field for different patterns of the array’s activation.

本文着重于通过有限元方法（FEM）对4×4空气微阵列压电微机械超声换能器（PMUT）进行多物理场建模，并通过比较进行机械和声学验证，在时域中，具有实验结果。为了通过两个有限元模型评估设备的完整性能，采用了两阶段数值程序。在第一阶段，考虑到制造引起的残余应力和不同物理之间的多重耦合，解决了独立换能器的机电声（EMA）问题。在线性和非线性状态下，将数值结果与实验结果进行了初始挠度和压力时间历程的比较：所提出的模型正确地捕获了所报告的现象并与实验趋势完全匹配。第二阶段专门用于模拟4×4 PMUT阵列性能，属于硅芯片。振动板被建模为等效的刚性活塞。在第一阶段中计算出的加速度历史记录被施加到活塞上，同时在模具表面的其余部分施加了刚性的挡板状态。该模型用于预测阵列激活不同模式的压力场。施加在活塞上，而在模具表面的其余部分上施加刚性挡板条件。该模型用于预测阵列激活不同模式的压力场。施加在活塞上，而在模具表面的其余部分上施加刚性挡板条件。该模型用于预测阵列激活不同模式的压力场。