John J. McCoy
Emilios K. Dimitriadis
School of Eng., Catholic Univ. of America, Washington, DC 20064
At a previous ASA meeting, a Wigner function description was presented of the spatially limited, narrow-band (in time) forcing of a fluid-loaded elastic plate and the radiation of sound therefrom. The formulation demonstrated that the complete experiment consists of a sequence of independent propagation/scattering events, each described by an operator that can be termed a propagator (in position coordinate)/filter (in Fourier coordinate). The intended application envisioned a stochastic forcing; e.g., at a turbulent boundary layer; but the framework is not so limited. In this presentation, a number of theoretical and numerical results are shown from a detailed study of this formulation. Several issues are addressed. Thus the propagator/filter for describing the process that transforms the Wigner function defined on the forcing to that defined on the plate deflection, is seen to be highly structured, difficult to interpret or numerically capture. This high degree of structure can be eliminated and an intuitive result obtained under two conditions: The propagator/filter is applied to a ``typical'' stochastic forcing to give the plate deflection Wigner function for the intended application. Or, a second operator that describes the effects of a linear phased array on the level of the Wigner function is applied to the propagator/filter. A number (3) of associated propagator/filters is then developed such that when viewed through the output of phased arrays tuned to respond to a particular Fourier component, approximate the output of the exact propagator/filter. These associated operators are given simple analytic expression; are intuitive; and, describe the contributions due to poles with small imaginary components, branch points, and what is left. Finally, expressions are derived for estimating the outputs of linear arrays of hydrophones located in planes at any distance from the plate.