Air-Coupled Array of Pmuts at 100 kHz with PZT Active Layer: Multiphysics Model and Experiments

Abstract

This work is focused on the multi-physics modelling via the finite element method (FEM) of an air-coupled array of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) and its preliminary experimental validation in the time domain for the mechanical and acoustic behaviour.Two numerical models are used to simulate the complete performance of the system based on the response of the diaphragm.In the former, the electro-mechanical-acoustic (EMA) problem for the single PMUT is solved, exploiting the axial symmetry of the system, with the following features: the presence of the fabrication induced residual stresses, which determine a non-linear initial deformed configuration and a substantial linearized fundamental mode frequency shift of the piezo-plate; the multiple couplings between different physics, namely piezoelectric coupling in the active layer and acoustic-structural interaction for the waves propagation in the surrounding fluid. When the non-linearities are activated in the dynamic response, by the involved large displacements, the system shows an initial beating behaviour with small steady state amplitude increment as the voltage input increases.In the latter model, the full set of PMUTs belonging to the silicon die in a 4 × 4 array configuration is considered in which the vibrating plates are modelled as equivalent oscillating rigid plane circular pistons, with reduced imposed acceleration amplitude, on a rigid baffle represented by the remaining part of the surface die.The results of the numerical simulations are compared with the experimental ones in terms of the initial static pre-deflection and pressure at 15 cm from the centre of the diaphragm, on the vertical direction along its own acoustic axis, in the case of the TX test with a single actuated transducer for different voltage amplitudes.