A large-signal model for CMUT arrays with arbitrary membrane geometry operating in non-collapsed mode

A large-signal, transient model has been developed to predict the output characteristics of a CMUT array operated in the non-collapse mode. The model is based on separation of the nonlinear electrostatic voltage-to-force relation and the linear acoustic array response. For modeling of linear acoustic radiation and crosstalk effects, the boundary element method is used. The stiffness matrix in the vibroacoustics calculations is obtained using static finite element analysis of a single membrane which can have arbitrary geometry and boundary conditions. A lumped modeling approach is used to reduce the order of the system for modeling the transient nonlinear electrostatic actuation. To accurately capture the dynamics of the non-uniform electrostatic force distribution over the CMUT electrode during large deflections, the membrane electrode is divided into patches shaped to match higher order membrane modes, each introducing a variable to the system model. This reduced order nonlinear lumped model is solved in the time domain using commercial software. The model has two linear blocks to calculate the displacement profile of the electrode patches and the output pressure for a given force distribution over the array. The force-to-array-displacement block uses the linear acoustic model, and the Rayleigh integral is evaluated to calculate the pressure at any field point. Using the model, the time-domain transmitted pressure can be simulated for different large drive signal configurations. The acoustic model is verified by comparison to harmonic FEA in vacuum and fluid for high- and low-aspect-ratio membranes as well as mass-loaded membranes. The overall software model is verified by comparison to transient 3-D finite element analysis and experimental results for different large drive signals, and an example for a phased array simulation is given.