### ASA 124th Meeting New Orleans 1992 October

## 4pSA8. Wigner function description of fluid-loaded plates.

**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.