Vibration Control of a Beam Under a Moving Mass Through Adjusting Trapezoidal Velocity Profile

Abstract

In this article, the residual vibration of a simply supported beam with a moving mass is studied. The mass moves from a starting point to an end point on the beam with a trapezoidal velocity profile having accelerating, constant velocity and decelerating time intervals. The residual vibration of the mid-point of the beam after the mass stops is analyzed. The mathematical model of the system is developed using the finite element (FE) theory. Newmark method is used for the solution of FE model having time dependent matrices because of the moving mass. The model is verified by comparing the solution results with the results given in the previous studies in the literature. It is seen that the relationship between the natural frequency of the system and the velocity profile of the moving mass has an effect on the residual vibration of the structure. If the natural frequency of the system and the inverse of the deceleration time interval of the moving mass are equal while the moving mass is at the stopping position, residual vibrations occur at a minimum level. It seen that with the right speed profile selection, the decrease in vibration levels approaches 70% during the movement and 80% after stopping.