Vibration Analysis of Elevator Rope

(Forced Vibration of Rope with Time-Varying Length)

Abstract

Elevator rope for high-rise buildings is forcibly excited by the displacement of the building induced by wind force. An exact solution to the forced vibration of a rope with time-varying length is presented, on the assumption that the rope tension and the moving velocity are constant, and that the damping coefficient of the rope is zero. Virtual sources of waves that can be assigned to reflecting waves are used for obtaining the exact solution. Finite difference analyses of rope vibration are also performed to verify the validity of this exact solution. The calculated results of the finite difference analyses are in fairly good agreement with the calculated results of the exact solution.