Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Implementation of Discrete Fuzzy Structure Models in Mathematica

V. Sparrow
D. Russell
J. Rochat
Journal / Anthology

International Journal for Numerical Methods in Engineering
Year: 1994
Volume: 37
Page range: 3005-3014

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.

*Engineering > Mechanical and Structural Engineering