Vibration Analysis of Elevator Rope (2nd Report, Forced Vibration of Rope with Damping)

Abstract

Elevator ropes in high-rise buildings are forcibly excited by the displacement of the building induced by wind force. An approximate solution to the forced vibration of a rope with time-varying length and having linear damping is presented here. It is assumed that the rope tension and the moving velocity are constant, and that the damping coefficient of the rope is small. Virtual sources of waves which can be assigned to reflecting waves are used for obtaining the approximate solution. Finite difference analyses of rope vibration are also performed to verify the validity of this approximate solution. The calculated results of the finite difference analyses are in fairly good agreement with the calculated results of the approximate solution. The effects of moving velocity and damping factor on the maximum rope deflection are quantitatively made clear.

Vibration Analysis of Elevator Rope (Comparison between Experimental Results and Calculated Results)

“…(3) and (4). It is confirmed that the calculated results from the finite difference analyses are in fairly good agreement with those of the exact solution (4), (5) , in the case where the rope tension and the moving velocity are constant.…”

“…Numerical analysis is performed by using the following difference equations (4), (5) , derived from Eq. (2).…”

“…The increased rope sway due to the displacement of buildings caused by earthquakes and strong winds becomes a problem in elevators installed in high-rise buildings. Some studies (1)(2)(3)(4)(5)(6)(7)(8)(9) have been conducted on the lateral vibration of an elevator rope whose length varies with time due to the up-and-down movement of the cage. These studies include those on exact solutions (1)(2)(3)(4)(5) to the free/forced vibration of a rope whose tension and movement velocity are constant, finite element analysis (6) , resonance problems (2), (5) , coupled vibration of the rope and cage (8) , and vibration control (9) .…”

“…In addition, for forced vibration of a rope whose tension and movement velocity are constant, the authors (4), (5) have compared an exact solution to a finite difference analysis. The calculated results of the finite difference analyses are in fairly good agreement with those of the theoretical solutions.…”

Free vibration analysis of a string with vibration suppressor (When the position of vibration suppressor is opposite to the pulled position)

“…This study investigates a string with one vibration suppressor. A numerical analysis is performed using the following difference equation (Kimura et al, 2007b(Kimura et al, , 2008, derived from Eq. (21).…”