On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity

Abstract

In this paper the weakly nonlinear, transversal vibrations of a conveyor belt will be considered. The belt is assumed to move with a low and time-varying speed. Using Kirchhoff's approach a single equation of motion will be derived from a coupled system of partial differential equations describing the longitudinal and transversal vibrations of the belt. A two time-scales perturbation method is then applied to approximate the solutions of the problem. It will turn out that the frequencies of the belt speed fluctuations play an important role in the dynamic behaviour of the belt. It is well-known in linear systems that instabilities can occur if the frequency of the belt speed uctuations is the sum of two natural frequencies. However, in the weakly nonlinear case as considered in this paper this is no longer true. It turns out that the weak nonlinearity stabilizes the system.Electrical Engineering, Mathematics and Computer Scienc