This paper deals with a multiphysics numerical modelling via finite element method (FEM) of an air-coupled array piezoelectric micromachined ultrasonic transducers (PMUTs). The proposed numerical model is fully 3D with the following features: the presence of the fabrication induced residual stresses, which determine a geometrically non-linear initial deformed configuration of the diaphragms and a remarkable shift of the fundamental frequency; the multiple coupling between different physics, namely electro-mechanical-coupling for the piezo-electric model, acoustic-structure interaction at the acoustic-structure interface and pressure acoustics in the surrounding air. The model takes into account the complete set of PMUTs belonging to the silicon die in a 4 x 4 array configuration and the protective package, as well. The results have been validated by experimental data, in terms of initial static pre-deflected configuration of the diaphragms and frequency response function of the PMUT. The numerical procedure was applied, to analyze different package configurations of the device, to study the influence of the holes on the acoustic transmission in terms of SPL and propagation pattern and consequently extract a set of design guidelines.

中文翻译：

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封装对PMUT性能的影响—多物理场模型和频率分析

本文通过有限元方法（FEM）对空气耦合阵列压电微机械超声换能器（PMUT）进行多物理场数值建模。所提出的数值模型是完全3D的，具有以下特征：制造引起的残余应力的存在，该残余应力确定了膜片的几何非线性初始变形构型和基频的显着偏移；不同物理之间的多重耦合，即压电模型的机电耦合，声结构界面处的声结构相互作用以及周围空气中的压力声。该模型考虑了4×4阵列配置中属于硅芯片的PMUT的完整集合以及保护性封装。根据膜片的初始静态预挠曲配置和PMUT的频率响应函数，实验数据验证了结果。应用了数值程序，分析了设备的不同封装配置，从SPL和传播模式的角度研究了孔对声传输的影响，从而提取了一套设计准则。