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

TL;DR

This paper investigates how an attached end mass influences the dynamics of a one-dimensional elastic system with uncertain properties, using stochastic modeling and Monte Carlo simulations to analyze uncertainty propagation.

Contribution

It introduces a stochastic model of an elastic system with an attached mass and nonlinear springs, analyzing the impact of the mass on system behavior under uncertainty.

Findings

The attached mass significantly affects the system's dynamic response.

Monte Carlo simulations effectively quantify uncertainty propagation.

The model highlights the role of the lumped mass in system stability.

Abstract

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 modulus 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.