Parametric resonance and jump analysis of a beam subjected to periodic mass transition

Abstract

In this paper, the dynamic stability of a simply supported beam excited by the transition of circulating masses is investigated by preserving nonlinear terms in the analysis. The intermittent loading across the beam results in a time-varying periodic equation. The effects of convective mass acceleration besides large deformation beam theory are both considered in the derivation of governing equations which is performed through adopting a variable-mass-system approach. In order to deal with the coupling between longitudinal and transversal deflections, the inextensibility assumption is implicitly introduced into the Hamiltonian formulation to reduce the model order. An appropriate interpretation is presented in order to maintain this approximation reasonable. Different semi-analytical methods are implemented to find the domains of stability and instability of the problem in a parameter space. By accounting the non-autonomous form of the governing equations, a qualitative change in behavior due to nonlinear terms is demonstrated which has not been addressed in previous studies.