Computational methods for the interior structural acoustics of small spaces

Abstract

In some biomechanical systems and micro-electro-mechanical systems (MEMS), the interaction of a viscous compressible fluid confined in a space bounded in part by a flexible structure is of central importance. Two specific examples are MEMS microphones (condenser or piezoelectric) and the cochlea. In both the manmade and biological acoustical sensor, the interior space is typically smaller than an acoustic wavelength, and a successful design involves trade-offs between sensitivity, bandwidth, and noise (including thermal, mechanical, electrical, or channel generated noise); the latter two criteria depend critically on the viscous and thermal forces in the system. A direct numeric approach to modeling viscous and thermal effects is often prohibitively expensive, as boundary layers must be resolved in the mesh. In this talk, we will present approximate methods that enable the inclusion of viscothermal effects in a computational framework. In particular, a variational approach amenable to inclusion in a finite element based code will be presented. Results for this method, which retains the accuracy of a Navier-Stokes formulation with the computational cost of a standard scalar acoustic formulation, will be given along with the limitations of the method and a discussion of alternative numerical approaches.