Journal of Sound and Vibration (2000) , 000{000 Analysis of Mechanical Systems using Interval Computations applied to Finite Elements Methods.

This paper addresses the problem of mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to nd an envelope of transfer functions for mechanical systems modeled with Finite Elements. Within this con-text, a new formulation has been developed for Finite Elements problems involving bounded parameters, to avoid the problems of overestimation. An iterative algo-rithm is introduced, which leads to a conservative solution for linear mechanical problems. A method to ensure the convergence of this algorithm is also proposed. This new algorithm has been tested on simple mechanical systems, and leads to a conservative envelope of the transfer functions. c © 1999 Academic Press Nomenclature x scalar fxg vector [A] matrix x interval x interval lower bound x interval upper bound rad(x) interval radius m(x) = xc = x+x 2 interval center w(x) = x − x interval width fxg interval vector [A] interval matrix [M] mass matrix [K] stiness matrix hysteretic damping coecient E Young’s modulu