Multiphysics modelling and experimental validation of an air-coupled array of PMUTs with residual stresses

In this paper a complete multiphysics modelling via the finite element method (FEM) of an air-coupled array of piezoelectric micromachined ultrasonic transducers (PMUT) and its experimental validation are presented. Two numerical models are described for the single transducer, axisymmetric and 3D, with the following features: the presence of fabrication induced residual stresses, which determine a non-linear initial deformed configuration of the diaphragm and a substantial fundamental mode frequency shift; the multiple coupling between different physics, namely electro-mechanical coupling for the piezo-electric model, thermo-acoustic-structural interaction and thermo-acoustic-pressure interaction for the waves propagation in the surrounding fluid. The model for the single transducer is enhanced considering the full set of PMUTs belonging to the silicon dye in a 4 x 4 array configuration. The results of the numerical multiphysics models are compared with experimental ones in terms of the initial static pre-deflection, of the diaphragm central point spectrum and of the sound intensity at 3.5 cm on the vertical direction along the axis of the diaphragm.