Maximum entropy approach for modeling random uncertainties in transient elastodynamics

A new approach is presented for analyzing random uncertainties in dynamical systems. This approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics. The information used does not require the description of the local parameters of the mechanical model. The probability model is deduced from the use of the entropy optimization principle, whose available information is constituted of the algebraic properties related to the generalized mass, damping, and stiffness matrices which have to be positive-definite symmetric matrices, and the knowledge of these matrices for the mean reduced matrix model. An explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to Monte Carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads. The fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed. Finally, an example is presented.