Implementation of discrete fuzzy structure models in Mathematica

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Abstract

Since Soize introduced the concept of fuzzy structures in structural acoustics there has been little activity clarifying the basic elements which underlie his theory. Soize's papers are not easy reading due to the high level of mathematical formalism. In addition Soize simultaneously bases this fuzzy structure theory on two components: (1) a model for one Degree Of Freedom (DOF) fuzzy oscillators, and (2) a medium frequency solution method developed previously. It is unclear as to the role of the two components, although others have already undertaken a study of the medium frequency method by itself. In the present paper a fundamental analysis of the first component, the one‐DOF fuzzy oscillators, is undertaken. The symbolic manipulation program Mathematica is utilized to gain insight into this component of Soize's fuzzy theory. The resulting Mathematica simulations are easy to use and interpret, and they provide valuable insight into the parameters composing Soize's fuzzy oscillators. It is determined that in many cases of structural acoustics, where there is small damping and a medium to high modal density, the fuzzy mass primarily determines what effect a discrete fuzzy oscillator will have as an attachment.

Original languageEnglish (US)
Pages (from-to)3005-3014
Number of pages10
JournalInternational Journal for Numerical Methods in Engineering
Volume37
Issue number17
DOIs
StatePublished - Sep 15 1994

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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