Formulation numérique de la sensibilité de la réponse vibratoire aux incertitudes physiques d'un modèle structural

Abstract

This work presents a new method named PMO ("Points Modaux Optimaux" in French) that predicts the maximum and minimum dynamic response of any vibrating structure given uncertainties in the physical properties (Young's modulus, dimensions, etc...). The new method is based on the modal decomposition of the response and the linear or quadratic approximation of the eigenproperties versus the uncertain properties. The maximization or minimization of the response is achieved by linear programming or quadratic programming (SLP or SQP methods). The PMO method is compared with Monte Carlo simulations (MC) and first order perturbations (P1) to predict the maximum specific kinetic energy of 2D frames with up to 5 uncertain variables. It proves to be several orders of magnitude faster than MC and much more accurate than P1 for uncertainties as high as 120% of total variation about the mean of each uncertain variable.