On Vibrations Of An Axially Moving Beam Under Material Damping

Abstract

In this paper a materially damped linear homogeneous beam-like equation has been considered. The viscoelastic beam is simply supported at both ends, whereas general initial conditions are considered. From mechanical and physical point of view the problem describes a mathematical model of internally damped transversal vibrations of a moving conveyor belt or a viscoelastic chain drive. From Hamilton's principle, a fifth order partial differential equation (PDE) for axially moving continuum has been formulated. The axial speed of the beam is considered to be positive, constant and small compared to wave velocity, and it is also assumed that the introduced material damping is relatively small. The solutions of equation of motion are based upon a two timescales perturbation method. By application of this perturbation method, it has been shown that the material damping does in fact affect the solution responses, and it reduces the vibration and noise in the system. It has also been shown that the material damping generated in the system depends on the mode number n, which is obviously expected from mechanical point of view.