On the dynamics of a nonlinear continuous random system

International audienceThe dynamics of a mechanical system shows dependence on parameters such as physical and geometrical properties, initial and boundary conditions, etc. In a deterministic system all of these parameters are fixed and a single set of differential equations completely describes the system behavior. However, in a stochastic system one or more of these parameters are random and there is a set of differential equations associated with it (one for each realization of the system). Thus, to characterize the dynamics of a random system, it is necessary to employ methods for stochastic computations. This work studies the dynamics of one-dimensional elastic bar, with random elastic modulus and prescribed boundary conditions, say, fixed at one end and attached to two springs (one linear and another nonlinear) fixed at a rigid wall. The system analysis assumes that the elastic modulus has gamma probability distribution and uses Monte Carlo simulations to compute the propagation of uncertainties for the bar displacement. After describing the deterministic and stochastic modeling of the bar, two configurations of the stochastic model are analyzed to characterize the effect of nonlinearity on the overall behavior of this mechanical system. The results indicate that nonlinearity tends to affect more the spatial behavior of the elastic bar than its temporal behavior