Nonlinear Behaviour of Fixed-Fixed Beam with a Moving Mass

Abstract

This study addresses the coupled nonlinear behaviour of a fixed-fixed beam under the travelling mass. Because of the beam and mass interaction phenomenon, coupling terms are more likely to arise which results in kinematic nonlinearities in the system. The major focus of this paper is to develop a theoretical model by introducing nonlinearities in the system. Later analysis of modal amplitude, mass position and tip deflection are done. For the beam modelling, Euler–Bernoulli beam assumptions are taken for consideration. Initially, a coupled mathematical model of the mentioned system is derived by using Hamilton’s principle. Afterwards, the Galerkin discretization technique followed by the perturbation method is implemented in the mathematical system to analyse the dynamic characteristics of the desired system. Then, MATLAB ODE solver is used to plot various graphs for variation of amplitude and deflection with respect to time in case of both beam and mass. Under the internal resonance condition, the time-response curves are plotted to analyse the beating phenomenon for the beam and mass.