Model order reduction for the analysis of large arrays of piezoelectric micromachined ultrasonic transducers in water

We present a new multiphysics Reduced Order Model (ROM) for the electro-mechanical-acoustic analysis of large arrays of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs). The solution strategy consists of two main stages. In the former one, the eigenvalue piezoelectric problem is solved on a representative PMUT and a few representative modes are identified. In the latter stage, the piezoelectric-acoustic problem is addressed by representing the mechanical response of each PMUT as a linear combination of the selected modes, each mode corresponding to a single Degree Of Freedom (DOF). The governing equations of the coupled problem are integrated by means of a time-marching staggered algorithm. The proposed formulation is benchmarked with the commercial software COMSOL Multiphysics 5.2, in the case of a single transducer in transmitting (TX) and receiving (RX) phases. The Finite Element Reduced Order Model (FE-ROM) provides a very good accuracy and largely reduced CPU time with respect to the standard coupled piezoelectric-acoustic full-order approach. Since the novel approach has been conceived to address beamforming, focusing and RX problems, the model is next applied to the simulation of pressure waves propagation, involving an array of several vibrating PMUTs. Two case studies are reported. In the former, acoustic energy has been focused at a preselected point along the transversal acoustic axis of the device by means of an array of 11 × 11 PMUTs; in the latter, a RX phase has been simulated with a 7 × 7 cluster of PMUTs, considering an incoming plane pressure wave.