Efficient Modeling and Simulation of Large PMUT Arrays for Biomedical Applications

This paper presents three innovative numerical modeling techniques tailored to meet the substantial computational demands of high-density Piezoelectric Micromachined Ultrasonic Transducer (PMUT) arrays, increasingly utilized in medical ultrasound imaging. The first strategy adopts first-order shear deformation theory (FSDT) to model the thin multilayered structure of PMUTs as equivalent 2D-shell elements, addressing the ultra-thin nature of these devices while maintaining the inherent 3D properties of the piezoelectric materials. The second, being an FE-based modeling technique, leverages Model Order Reduction (MOR) to condense the dynamic behavior of PMUTs into a limited set of piezo-mechanical eigenmodes, drastically reducing computational load during coupled acoustic analysis by minimizing the degrees of freedom (DOF) to those of the precomputed eigenmodes. The third approach likewise employs these modes while introducing the Discontinuous Galerkin Spectral Element Method to enhance accuracy and handle nonconforming grids effectively across extensive PMUT arrays. Validation of these models was conducted via simulation of a 1-D PMUT array, fabricated using sol-gel PZT thin-film-based MEMS technology, exhibiting a high correlation between the experimental hydrophone measurements and simulated acoustic pressures and spectra, thus confirming the efficacy of the proposed methods. These models substantially decrease computing demands while preserving excellent accuracy, offering a rapid and reliable framework that is particularly advantageous during the PMUT design process.