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 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.

The purpose of this work is to present recent advances in modeling and design of piezoelectric energy harvesters, in the framework of micro-electro-mechanical systems (MEMS). More specifically, the case of inertial energy harvesting is considered, in the sense that the kinetic energy due to environmental vibration is transformed into electrical energy by means of piezoelectric transduction. The execution of numerical analyses is greatly important in order to predict the actual behavior of MEMS devices and to carry out the optimization process. In the common practice, the results are obtained by means of burdensome 3D finite element analyses (FEA). The case of beams could be treated by applying 1D models, which can enormously reduce the computational burden with obvious benefits in the case of repeated analyses. Unfortunately, the presence of piezoelectric coupling may entail some serious issues in view of its intrinsically threedimensional behavior. In this paper, a refined, yet simple, model is proposed with the objective of retaining the Euler-Bernoulli beam model, with the inclusion of effects connected to the actual three-dimensional shape of the device. The proposed model is adopted to evaluate the performances of realistic harvesters, both in the case of harmonic excitation and for impulsive loads.

In this paper a complete Multiphysics modelling via the Finite Element Method (FEM) of an air-coupled Piezoelectric Micromachined Ultrasonic Transducer (PMUT) is described, with its experimental validation related to the mechanical and acoustic responses.The numerical model takes into account the presence of fabrication induced residual stresses, which determine a non-linear initial deformed configuration of the diaphragm and a substantial frequency shift associated with the fundamental eigenmode of the vibrating system.The complete simulation of the device's behaviour is obtained considering multiple coupling between different fields: electro-mechanical coupling for the piezoelectric model, thermo-acoustic-structural interaction and thermoacoustic-pressure interaction for the waves propagation in the surrounding fluid.The model gives a realistic estimation of the fundamental frequency and of the PMUT's quality factor through the adoption of large deformation analyses and by means of a proper modelling of the air, considering its thermo-viscous properties, that induce the power dissipation in the so-called boundary layer at the fluidstructure interface.The results of the numerical multi-physics model are compared with experimental ones in terms of the initial static pre-deflection, of the membrane center vertical displacement frequency spectrum and of the sound intensity at 3.5 cm on the vertical direction of the axisymmetric axis of the diaphragm.

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The application of piezoelectric materials in MEMS energy harvesters is continuously increasing, with the immediate corollary of a fundamental need for improved computational tools in order to optimize the performances at the design level. In this paper, a refined, yet simple model is proposed with the aim of providing fast and insightful solutions to the multi-physics problem of piezoelectric energy harvesting. The main objective is to retain a simple structural model (Euler-Bernoulli beam), with the inclusion of effects connected to the actual threedimensional shape of the device. A thorough presentation of the analytical model is presented, along with its validation by comparison with the results of full 3D computations