Analytical-Finite Element hybrid model for CMUT arrays with arbitrary membrane geometry

Finite Element Analysis (FEA) of CMUT arrays offers flexibility with membrane geometry, but it can become computationally expensive as the transducer array and fluidic space increases in size. The objective is to combine the modeling flexibility of 3D FEA with the computational effectiveness of 2D numerical methods to analyze and design CMUT arrays with arbitrary membrane shapes. Effective numerical methods for CMUT arrays combine finite difference (FD) approximations of thin plate equations with fluid coupling through the use of the Boundary Element Method. As such, the array can be modeled with a 2D surface mesh, but the thin plate approximations limit the analysis to CMUTs with high aspect ratios and uniform surfaces. A hybrid method using static FEA (COMSOL 4.2a) of an individual CMUT membrane was used to generate an equivalent stiffness matrix associated with the mesh density of the 2D surface, eliminating the dependence on the thin plate approximation. This FEA need only be performed once for a given geometry and mesh density as it is reused for an entire array. The resonant frequency of square CMUTs with 2 μm thickness in vacuum was evaluated using FD and hybrid methods. The hybrid method shows good agreement with full FEA, while the FD method deviated for low aspect ratios. Hybrid analysis of mass-loaded CMUTs with an aluminum electrode for operation at ~40 MHz shows good agreement FEA analysis while reducing the computation time by a factor of 20 for a simple array simulation.