Forced Vibration Analysis of an Elevator Rope With Both Ends Moving

An elevator rope for a high-rise building is forcibly excited by the displacement of the building caused by wind forces. Regarding the rope, there are two boundary conditions. In the first case, one end moves with time and the other end is fixed, while in the second case, both ends move with time. A theoretical solution to the forced vibration of a rope where one end is moving has been already obtained. In this paper, a theoretical solution to the forced vibration of a rope where both ends are moving is presented, based on the assumption that rope tension and movement velocity are constant, and that the damping coefficient of the rope is zero or small. The virtual sources of waves, which can be assigned to reflecting waves, are used to obtain the theoretical solution. Finite difference analyses of rope vibration are also performed to verify the validity of the theoretical solution. The calculated results of the finite difference analyses are in fairly good agreement with that of the theoretical solution. The effects of the changing rate of rope length and the damping factor on the maximum rope displacement are quantitatively clarified.