Effect of an attached end mass in the dynamics of uncertainty nonlinear continuous random system

This work studies the dynamics of a one dimensional elastic bar with random elastic modulus and prescribed boundary conditions, say, fixed at one end, and attached to a lumped mass and two springs (one linear and another nonlinear) on the other extreme. The system analysis assumes that the elastic mod-ulus has gamma probability distribution and uses Monte Carlo simulations to compute the propagation of uncertainty in this continuous–discrete system. After describing the deterministic and the stochastic modeling of the system, some configurations of the model are analyzed in order to characterize the effect of the lumped mass in the overall behavior of this dynamical system.