The forced vibration of an elastic plate under significant fluid loading

This paper gives an asymptotic analysis of the sound and vibration produced when a metal plate, which could be part of the hull of a ship, is forced into motion by its contact with vibrating machinery on one side, and radiates sound into water on the other side. The frequency range is that for which the water significantly affects the vibration of the plate. The mathematical method used is scaling of the frequency with the square of the intrinsic fluid-loading parameter to maximise the number of terms in the dispersion relation which balance at leading order. This 'significant' scaling, which gives accurate results over a wide frequency range, is used to obtain scaling laws for all aspects of the acoustic field and plate vibration, including the sizes of the different parts of the near field, the amount of radiated acoustic energy, and the amount of energy propagating in the surface wave. The results extend a previous asymptotic theory of heavy fluid loading, valid only in a restricted part of the frequency range covered by significant loading. (C) 2005 Elsevier Ltd. All rights reserved.