Dynamic Response of an Overhead Crane Beam Due to a Moving Mass Using Moving Finite Element Approximation

Abstract

In this study, dynamic behaviour of a beam system of an overhead crane is investigated. A MATLAB code is developed for numerical analyses. The moving mass on the beam is modelled as a moving finite element to include inertial effects of mass. Dynamic response of the beam is obtained depending on the mass ratio between load and beam mass. Besides, a variety of mass velocities are considered. Analysis are carried out considering mass ratio (mass of the load/mass of the beam m/M) as 0.1, 0.2, 0.4, 0.6, 0.8 and 1 and mass velocities as 1, 2, 4, 8, and 12.5 m/s. Dynamic response of the beam depends on velocity and mass of moving load. As the position of the moving mass in the span changes, it alters the natural frequency of the beam system. Generally, if the mass velocity increases, maximum beam deflection occurs far from the beam midpoint. For some values of the velocity, the maximum response may occur before the beam midpoint. At very high speeds, the maximum beam deflection occurs near the beam endpoint. At very slow speeds, the maximum beam deflection occurs near the midpoint because the system reduces to a quasi-static solution. At the same mass ratio, load velocity increases, with the increment of the beam deflection. Both mass velocity and mass ratio affects the dynamic response of the beam but the effect of velocity is greater than the mass ratio.