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 [2] and two and half dimensional inviscid elements [21]. 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.

中文翻译：

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用于声学流固耦合的三维粘性有限元公式

本文提出了一个三维粘性有限元模型，用于分析声流体结构相互作用系统，包括但不限于基于耳蜗的换能器。该模型由与二维平面结构域相互作用的三维粘性声学流体介质组成。流体场由线性化的 Navier-Stokes 方程控制，流体位移和压力被选为自变量。基于混合位移/压力的公式用于流体领域，以减轻几乎不可压缩流体中的锁定。该结构被建模为带有或不带有残余应力的 Mindlin 板。选择 Hinton-Huang 的 9 节点拉格朗日板单元是为了与 27/4 u/p 流体单元兼容。全 3d FEM 模型的结果与实验结果和其他 FEM 结果非常一致，包括 Beltman 的薄膜粘声单元 [2] 和二维半无粘性单元 [21]。尽管它在计算上很昂贵，但它为其他数值模型或近似值提供了基准解决方案，以便与实验之外的其他数值模型进行比较，并且它能够对任何不规则的几何形状和材料特性进行建模，而其他数值模型可能不适用。