Analysis of the Nonlinear Stochastic Dynamics of an Elastic Bar With an Attached End Mass

Abstract

Abstract. 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. 682

On the nonlinear stochastic dynamics of a continuous system with discrete attached elements

“…The theoretical study developed aims to illustrate a consistent methodology to analyze the influence of coupled discrete elements into the stochastic dynamics of nonlinear mechanical systems. The results of this study complement a series of preliminary studies made on the same subject [8,9,10,11].…”

Uncertainty quantification through the Monte Carlo method in a cloud computing setting

“…The system of interest in this study case is an elastic bar fixed at a rigid wall, on the left side, and attached to a lumped mass and two springs (one linear and one nonlinear), on the right side, such as illustrated in Figure 4. The stochastic nonlinear dynamics of this system was investigated in [31,32,33,34], where the reader can see more details about the modeling procedure presented below. For simplicity, from now on, this system will be called the fixed-mass-spring bar or simply the bar.…”