09-09-2017, 11:32 AM
A new method is developed for the dynamic analysis of the response spectrum of a structural system with interval uncertainty. This method based on finite interval elements is able to obtain the limits on the dynamic response of a structure with interval uncertainty. The present method is performed using a theoretical formulation (range) to quantify the uncertainty present in the parameters of the structure, such as material properties and cross-sectional geometry. Independent and / or dependent variations are considered for each element of the structure. At each stage of the analysis, the existence of variation is considered as the presence of perturbation in a pseudo-deterministic system. Given this consideration, first, a problem of linear range eigenvalues is performed using the concept of monotonous behavior of eigenvalues for symmetric matrices subjected to non-negative defined perturbations. Then, using the procedures for the perturbation of invariant matrices sub-spaces, the limits of the directional (tilt) deviation of each mode shape are obtained. Next, the interval response spectrum analysis is performed considering the effects of the input variation in terms of the total response of the structure, which includes modal maximum coordinates, modal participation factors and mode shapes.