Approximation of the Vibration Modes of a Plate and Shells Coupled With a Fluid

Abstract

We consider a method to compute the vibration modes of an elastic thin structure (shell or plate) in contact with a compressible fluid. For the structure, the classical Naghdi equations, based on the Reissner–Mindlin hypothesis, are considered and its approximation using the mixed interpolation of tensorial component 4 finite element method. The fluid equations are discretized by using Raviart–Thomas elements, and a non-conforming coupling is used on the fluid-solid interface. Numerical experiments are reported, assessing the efficiency of this coupled scheme.