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 s urface. A corollary of these principles is proof of the symmetry of th e matrix representing the acoustic contribution to the structural impe dance, even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric. The reciprocity propert ies lead to two eigenvalue problems, whose solution yields velocity an d pressure radiation modes, each of which decouples the complex surfac e acoustic power. The matrices required to obtain the eigensolutions a re shown to arise in the ordinary course of modeling fluid-structure i nteraction. Further analysis reveals that the velocity and pressure mo des occur in a one-to-one correspondence, with a relative phase angle that decreases monotonicaly as the radiated power increases relative t o the reactive power. Using the radiation modes to form modal series f or the surface pressure and normal velocity due to a specified excitat ion offers a new perspective for acoustic interaction phenomena. In an example, the acoustic equations for a slender spheroidal body are use d to evaluate the radiation mode patterns in a range of frequencies. T hese modes are then used to decompose the surface velocity and pressur e fields corresponding to a uniform breathing motion of the spheroidal surface. (C) 1995 Acoustical Society of America.