Uncertainty propagation in the dynamics of a nonlinear random bar

Abstract

This work studies the dynamics of a one-dimensional elastic bar with random elastic modulus and prescribed boundary conditions, fixed at one end, and attached to a lumped mass and two springs (one linear and another nonlinear) on the other extreme, subjected to a Gaussian white noise external force. The system analysis uses the maximum entropy principle to specify the elastic modulus (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.

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