University of Illinois Urbana-Champaign

Average response of infinite plate on random foundation

Turner, Joseph A.; Weaver, Richard L.

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https://hdl.handle.net/2142/112483

Description

Title
Average response of infinite plate on random foundation
Author(s)
  • Turner, Joseph A.
  • Weaver, Richard L.
Issue Date
1995-03
Keyword(s)
  • Infinite Plate
  • Random Foundation
Abstract
The average response of an infinite thin plate with statistically homogeneous attached random impedances is examined. The added impedances, which represent typical heterogeneities that might occur on complex shells, provide light coupling between the extensional, shear, and flexural waves. The mean plate response is formulated in terms of the Dyson equation which is solved within the assumptions of the first-order smoothing approximation, or Keller approximation, valid when the heterogeneities are weak. Scattering attenuations are derived for each propagation mode. It is shown that the attenuation of one wave type due to coupling to another is 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. The specific case of delta-correlated springs is considered for purposes of illustration.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 787
  • 1995-6009
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112483
Copyright and License Information
Copyright 1995 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.