Vibrations of a plate in fluid and associated damping due to energy transmission by dilatational waves

The paper presents a solution to the problem of harmonic vibrations of a plate submerged in an unbounded medium of inviscid compressible fluid. The solution is obtained, as a limiting case, by means of a solution to the problem of an infinite elliptic cylinder vibrating in the fluid. The latter problem is solved with the help of the Fourier method of separation of variables in the elliptic coordinate system. For comparison purposes, a similar problem of circular cylinder vibrating in the fluid is also investigated. From the discussion presented it follows, that the fluid compressibility is essential in estimating hydrodynamical forces, especially in calculating damping of plate vibrations for higher frequencies.