A study of displacement-based fluid finite elements for calculating frequencies of fluid and fluid-structure systems

Abstract The widely-used displacement-based finite element formulation for inviscid, compressible, small displacement fluid motions is examined, with the specific objective of calculating fluid-structure frequencies. It is shown that the formulation can be employed with confidence to predict the static response of fluids. Also the resonant frequencies of fluids in rigid cavities and the frequencies of fluids in flexible boundaries are solved successfully if a penalty on rotations is included in the formulation. However, the reason for writing this paper is that problems involving structures moving through fluids that behave almost incompressibly - such as an ellipse vibrating on a spring in water - could not be solved satisfactorily, for which a general explanation is given.

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