Analysis of the nonlinear stochastic dynamics of an elastic bar with an attached end mass

This work studies the nonlinear dynamics of a one-dimensional elastic bar, attached to discrete elements, with viscous damping, random elastic modulus, and subjected to a Gaussian white-noise distributed 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 discrete–continuous 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 a lumped mass in the overall behavior of this dynamical system. The simulation results show that the system response presents multimodal probability distribution, irregular distribution of energy throughout the spectrum of frequencies, and a limit behavior, for large values of the lumped mass, similar to a mass-spring system.

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