Abstract
A number of problems are solved for the resonant frequencies of oscillation of a fluid in rectangular or circular containers having internal bodies such as surface or bottom-mounted vertical blocks or circular apertures in the top surface. The variation of these frequencies with the dimensions of the bodies is obtained. The method uses matched eigenfunction expansions and Galerkin expansions to derive explicit forms for the elementsS ijof a 2×2 matrix required in the course of the solution. An approximate formula for an arbitrary-shaped body in a container which gives good agreement with the more accurate Galerkin approach is used to solve the resonant frequencies when the internal body is a submerged cylinder.
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Watson, E.B.B., Evans, D.V. Resonant frequencies of a fluid in containers with internal bodies. J Eng Math 25, 115–135 (1991). https://doi.org/10.1007/BF00042849
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DOI: https://doi.org/10.1007/BF00042849