### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 5pSA2. Average response of an infinite plate on a random elastic
foundation.

**Joseph A. Turner
**

**
Richard L. Weaver
**

**
**
*Dept. of Theor. and Appl. Mech., 104 S. Wright St., Univ. of Illinois,
Urbana, IL 61801
*

*
*
The average response of infinite thin plates with attached random
impedances is examined. The added impedance, which represents typical
heterogeneities that might occur on complex shells, provides light coupling
between the three propagation modes. The problem is formulated in terms of the
Dyson equation which governs the mean plate response. It is solved within the
assumptions of the Keller (smoothing) approximation which is valid when the
heterogeneities are weak. Scattering attenuations are derived for each
propagation mode. The specific case of delta-correlated springs provides a
simple intuitive result for a statistically homogeneous plate. The attenuation
of one wave type due to coupling to another is shown to be proportional to the
modal density of the other wave type. Thus the attenuation of extensional and
shear waves is predominantly due to mode conversion into flexural waves and is
proportional to the large modal density of flexural waves. The flexural degrees
of freedom serve as a sink for the energy of the membrane modes and constitute
for them an effective fuzzy structure. A similar result is expected for the
more complicated submerged shell case. A discussion of diffuse energy transport
on such a plate will also be presented. [Work supported by ONR.]