Complex power, reciprocity, and radiation modes for submerged bodies

This study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface. A corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance, even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric. The reciprocity properties lead to two eigenvalue problems, whose solution yields velocity and pressure radiation modes, each of which decouples the complex surface acoustic power. The matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid-structure interaction. Further analysis reveals that the velocity and pressure modes occur in a one-to-one correspondence, with a relative phase angle that decreases monotonicaly as the radiated power increases relative to the reactive power. Using the radiation modes to form modal series for the surface pressure and normal velocity due to a specified excitation offers a new perspective for acoustic interaction phenomena. In an example, the acoustic equations for a slender spheroidal body are used to evaluate the radiation mode patterns in a range of frequencies. These modes are then used to decompose the surface velocity and pressure fields corresponding to a uniform breathing motion of the spheroidal surface. (C) 1995 Acoustical Society of America.