Forced Vibration Analysis of an Elevator Rope With Both Ends Moving

Abstract

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.

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

“…Moreover, Yamamoto et al (5) have obtained an approximate solution, based on the assumption that the moving velocity is very low compared with the propagation velocity of the transverse wave. However, in the case where the moving velocity is not very low, no theoretical solution has yet been obtained except for an elevator rope with both ends moving (11) .…”

“…Some studies (1)- (11) , including those on free vibration (1)- (4) , resonance problems (5) , coupled vibration of the rope and cage (6) , and vibration control (10) , 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. For the free vibration of a rope whose tension and movement velocity are constant and whose damping coefficient is zero, Hashimoto (1) and Kotera (2) have obtained an exact solution to the free vibration induced by an initial displacement.…”

Dynamic Modeling and Analysis of a Mine Hoisting System with Constant Length and Variable Length

“…ere are few literatures on nonlinear vibration behavior of the coal mine hoist. e kinematic and dynamic model of the mine hoisting system is similar to the elevator system or the axially moving system [9][10][11][12][13][14][15][16][17][18][19][20][21]. e stability problem of a nonlinear system is considered [22].…”

Lateral and torsional vibrations of cable-guided hoisting system with eccentric load

“…Zhu and Chen [12] conducted innovative experiments on a scaled elevator to validate the theoretical predictions for the uncontrolled and controlled lateral responses of a moving cable. Kimura et al [13] performed a theoretical solution to the forced vibration of an elevator cable where both ends are excited and clarified the effect of the rate of change of cable length and the damping factor on the maximum lateral displacement. Bao et al [14] theoretically and experimentally studied the nonlinear lateral vibration of a moving elevator cable and analyzed the passage through resonances by calculating the natural frequencies of the system.…”