On the transversal vibrations of a conveyor belt with a low and time-varying velocity: Part II: the beam-like case

Electrical Engineering, Mathematics and Computer Scienc

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

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

On the transversal vibrations of a conveyor belt with a low and time-varying velocity: Part I: the string-like case

In this paper initial-boundary value problems for a linear wave (string) equation are considered. These problems can be used as simple models to describe the vertical vibrations of a conveyor belt, for which the velocity is small with respect to the wave speed. In this paper the belt is assumed to move with a time-varying speed. Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt. It also will be shown that the truncation method can not be applied to this problem in order to obtain approximations valid on long time scales.Electrical Engineering, Mathematics and Computer Scienc