Three-dimensional viscous finite element formulation for acoustic fluid–structure interaction

A three-dimensional viscous finite element model is presented in this paper for the analysis of the acoustic fluid–structure interaction systems including, but not limited to, the cochlear-based transducers. The model consists of a three-dimensional viscous acoustic fluid medium interacting with a two-dimensional flat structure domain. The fluid field is governed by the linearized Navier–Stokes equation with the fluid displacements and the pressure chosen as independent variables. The mixed displacement/pressure based formulation is used in the fluid field in order to alleviate the locking in the nearly incompressible fluid. The structure is modeled as a Mindlin plate with or without residual stress. The Hinton–Huang’s 9-noded Lagrangian plate element is chosen in order to be compatible with 27/4 u/p fluid elements. The results from the full 3D FEM model are in good agreement with experimental results and other FEM results including Beltman’s thin film viscoacoustic element [W.M. Beltman, P.J.M. Van der Hoogt, R.M.E.J. Spiering, H. Tijdeman, Implementation and experimental validation of a new viscothermal acoustic finite element for acousto-elastic problems, J. Sound Vib. 216 (1) (1998) 159–185] and two and half dimensional inviscid elements [A.A. Parthasarathi, K. Grosh, A.L. Nuttall, Three-dimensional numerical modeling for global cochlear dynamics, J. Acoust. Soc. Am. 107 (2000) 474–485]. Although it is computationally expensive, it provides a benchmark solution for other numerical models or approximations to compare to besides experiments and it is capable of modeling any irregular geometries and material properties while other numerical models may not be applicable.