Development of a CMUT model for non-linear actuation and contact dynamics

We present a computationally-scalable model for Capacitive Micromachined Ultrasonic Transducer (CMUT) arrays capable of simulating CMUTs in all modes of operation. To solve the fluid-structure problem, a coupled finite element and boundary element method (FE-BEM) is employed. Scalable performance is achieved using data-sparse routines for Hierarchical Matrices. The fluid-structure problem is solved in the frequency domain and used to generate a set of reduced-order linear time-invariant system relating applied mean pressure to mean displacement for a set of lumped sub-domains. A simple non-linear contact model is added to simulate potential contact forces between membrane and substrate. This coupled dynamic system is evolved in time using an algorithm based on fixed-point iteration. The model is validated against finite element software for a representative CMUT geometry and various input voltage signals corresponding to the different regimes of operation.