Abstract
G. Szego showed that the sum of the three translational virtual masses along any three mutually perpendicular directions is an invariant for a solid moving in an infinite, incompressible, frictionless and irrotational fluid medium. A similar hypothesis is presented here, which shows, through a finite approximate analysis, that this sum is also an invariant when the fluid medium is finite, irrotational and friction-less but compressible, provided that the exciting frequencies are lower than the fundamental natural frequency of the medium. As an example this invariant has been obtained in the case of a thin flat plate for different depths of submersion and different frequency parameters by using the well-known method of `finite elements'.
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