A Hybrid Boundary Element Model for Simulation and Optimization of Large Piezoelectric Micromachined Ultrasonic Transducer Arrays

A hybrid boundary element model is proposed for the simulation of large piezoelectric micromachined ultrasonic transducer (PMUT) arrays in immersion. Multiphysics finite element method (FEM) simulation of a single-membrane structure is used to determine stiffness and piezoelectrically induced actuation loading of the membranes. To simulate the arrays of membranes in immersion, a boundary element method is employed, wherein membrane structures are modeled by a surface mesh that is coupled mechanically by mass, stiffness, and damping matrices, and acoustically by a mutual impedance matrix. A multilevel fast multipole algorithm speeds up computation time and reduces memory usage, enabling the simulation of thousands of membranes in a reasonable time. The model is validated with FEM for a small 3
$\times $
3 matrix array for both square and circular membrane geometries. Two practical optimization examples of large PMUT arrays are demonstrated: membrane spacing of a 7
$\times $
7 matrix array with circular membranes, and material choice and top electrode coverage of a 32-element linear array with 640 circular membranes. In addition, a simple analytical approach to electrode optimization based on normal mode theory is verified.