Fluid-Loading Interaction with Vibrating Surfaces

Abstract

When an elastic structure in contact with a fluid vibrates, unsteady pressures are generated in the fluid and exert a surface loading on the structure additional to that which may be exerted by mechanical excitation or by the surface pressures of a boundary layer formed over a perfectly rigid structure. The additional loading is referred to as “fluid loading”; it is a highly nonlocal loading, not necessarily connected with fluid compressibility or bulk fluid motion, which is crucial in determining many aspects of most structural acoustics problems in one part of parameter space or another. When the fluid loading is important (which, as we shall see, it is for some aspects of the acoustic or vibration fields even when the fluid density is small compared with that of the structure material) one is faced with a fully-cowpltd problem, involving transverse waves (and occasionally longitudinal waves) on the structure and their nonlocal coupling to either incompressible pressure fluctuations or compression waves in the fluid. Recently there has been considerable success in analytical studies of these problems, leading to simple and explicit descriptions of the structural and acoustic fields and the identification of resonance and other significant conditions, even under conditions of “heavy” fluid loading. The basic point of these notes is to illustrate in the simplest problem the rôles played by the five essential competing mechanisms for plane elastic plates under static fluid loading, to illustrate how the balances between them are different for different aspects of the system response and in different parameter ranges, and to give a general asymptotic method which provides a powerful approach to fluid-loaded structure problems.