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.]