A Spectral Description of Inertial Effects in Fluid-Loaded Plates

The wavenumber-based formulation of the surface variational principle (SVP) describes the surface pressure and displacement as a comparatively small set of interacting waves. It enables one to pose questions of parametric sensitivity from a global perspective. The present paper is the first application of such an approach to the question of the level of detail to which a model must be constructed. It considers a two-dimensional problem of an elastic plate in an infinite baffle, with pinned boundary conditions. A study by Feit and Johnson (1991) demonstrated that the signal scattered by the plate is significantly altered by the presence of an attached mass, and that the distribution of mass as well as the total mass, is important. In order to explore these issues, a line mass attached to the plate is replaced in the SVP formulation by a continuous spatial distribution. The functional form of this distribution is described in a spectral manner using Fourier series, whose ascending orders represent successive stages in refinement of the scale to which a model describes inertial effects. The excitation applied to the plate is taken as a concentrated line harmonic force. With the excitation held fixed, the influence of each spectral component of inertial distribution on the surface response and radiated power are assessed. Evaluations carried out for a range of frequencies shed light on how small scale inertial heterogeneities can influence macroscopic radiation features.