Implementation of discrete fuzzy structure models in Mathematica
Article first published online: 29 JUN 2005
Copyright © 1994 John Wiley & Sons, Ltd
International Journal for Numerical Methods in Engineering
Special Issue: Selected Papers from the Symposium on Computational Structural Acoustics, Second U.S. National Congress on Computational Mechanics
Volume 37, Issue 17, pages 3005–3014, 15 September 1994
How to Cite
Sparrow, V. W., Russell, D. A. and Rochat, J. L. (1994), Implementation of discrete fuzzy structure models in Mathematica. Int. J. Numer. Meth. Engng., 37: 3005–3014. doi: 10.1002/nme.1620371710
- Issue published online: 29 JUN 2005
- Article first published online: 29 JUN 2005
- Manuscript Revised: 30 NOV 1993
- Manuscript Received: 15 MAY 1993
- Office of Naval Research. Grant Number: N00014-91-J-4000
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.