University of Illinois Urbana-Champaign

Mean and mean-square responses of prototypical master/fuzzy structure

Weaver, Richard L.

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https://hdl.handle.net/2142/112523

Description

Title
Mean and mean-square responses of prototypical master/fuzzy structure
Author(s)
Weaver, Richard L.
Issue Date
1996-04
Keyword(s)
  • Master/fuzzy Structure
  • Mean-square Responses
Abstract
Analytical estimates are made for mean and mean square transient responses of a single degree of freedom master oscillator attached to an undamped N degree of freedom random substructure. The ensemble averaged response is found to be, asymptotically for a large number of substructural degrees of freedom, in accord with the predictions of the PierceSparrow- Russell theory. In particular the mean response of the master oscillator manifests an apparent damping. Corrections to this behavior are also predicted, but are found to lie well below the root mean square level of the fluctuations. The corrections are therefore, for practical purposes, unimportant. The ensemble average of the square of the response is also investigated and found to take a value at later times that is in accord with simple equipartition arguments advanced in an earlier paper. The power spectral density of the late time behavior is shown to be proportional to the square of the power spectrum of the early time response, and thus to be sharper than that of the early time behavior. Numerical simulations are presented which agree with the analytical predictions at moderate times, but also show an enhanced backscatter that develops over longer time scales.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 823
  • 1996-6010
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112523
Sponsor(s)/Grant Number(s)
National Science Foundation 96/04 PHY94 07194 96/04; Office of Naval Researchearch 96/04 N 00014 94 0855 96/04
Copyright and License Information
Copyright 1996 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.