University of Illinois Urbana-Champaign

Multiple scattering theory for plate with sprung masses mean and mean- square responses

Weaver, Richard L.

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https://hdl.handle.net/2142/112529

Description

Title
Multiple scattering theory for plate with sprung masses mean and mean- square responses
Author(s)
Weaver, Richard L.
Issue Date
1996-07
Keyword(s)
  • Multiple Scattering Theory
  • Sprung Masses
  • Mean And Mean-square Responses
Abstract
Diagrammatic multiple scattering theory is applied to the case of an infinite homogeneous plate in flexure attached to a random distribution of sprung masses. This system is a prototypical example of a wave-bearing master structure with a locally reacting 'fuzzy' substructure. Results are obtained from the first order smoothing approximation, the Foldy average t-matrix approximation, and Soven's Coherent-potential approximation. It is found that the attenuation as calculated by Pierce et al differs from that of the multiple scattering theory by a fractional amount which is small if the individual sprung masses are weak. It is also found that fluctuations away from the mean are weak if the spectral and areal density of sprung masses is great. A radiative transfer equation is found to govern the flow of energy on time scales greater than the inverse of the frequency, and a diffusion equation is found to govern the flow of energy at times greater than the dwell time of energy in the substructure.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 828
  • 1996-6015
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112529
Sponsor(s)/Grant Number(s)
Multiple Scattering Theory; Sprung Masses; Mean and Mean-Square Responses
Copyright and License Information
Copyright 1996 Board of Trustees of the University of Illinois

Owning Collections

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.