## 3aSA4. Multiple scattering theory for a plate with randomly sprung masses.

### Session: Wednesday Morning, December 4

### Time: 8:50

**Author: Richard L. Weaver**

**Location: Dept. of Theoretical and Appl. Mech., 216 Talbot Lab., 104 S. Wright St., Univ. of Illinois, Urbana, IL 61801**

**Abstract:**

The flexural response of an infinite homogeneous plate attached to a random
uniform distribution of single degree of freedom undamped oscillators
constituting a ``fuzzy substructure'' is studied theoretically using methods
from diagrammatic multiple scattering theory. A Dyson equation is posed for the
ensemble average Green's function, and a Bethe--Salpeter equation is posed for
the average of the square of the Green's function. The Dyson equation is solved
within three different approximations: the ``first-order smoothing
approximation'' (equivalent to that of Pierce, Sparrow, and Russell) the
``average T-matrix (or Foldy) approximation,'' and the self-consistent
``coherent potential approximation.'' The mean Green's function is found to be
equal to the Greens' function proposed by Pierce, Sparrow, and Russell, if the
individual sprung masses are not large. The Bethe--Salpeter equation is solved
within the latter approximation and in the limit that the length and time scales
of the diffuse field are long compared to wavelengths and periods. In the
further limit that these length and time scales are also long compared to
mean-free paths and mean-free times, it is found that the Bethe-Salpeter
equation reduces to a diffusion equation. [Work supported by ONR.]

ASA 132nd meeting - Hawaii, December 1996