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.

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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.

Transverse vibrations of ropes spanning a high-speed elevator are induced by resonance when a building sways because of an earthquake or wind force. Hence, an effective solution is demanded. In this study, we undertake to suppress the vibration of an elevator rope by using an input device placed in the vicinity of the upper boundary of the rope. This input device has gaps between an actuator and the rope to prevent the progression of their abrasion. A nonstationary control method is effective for the control of a time-varying system with which an elevator rope and a crane wire are categorized. In addition, a sliding mode controller is robust toward nonlinearity at the position where input is introduced. Thus, in this paper, we present a method of vibration control for the elevator rope, which is based on the nonstationary sliding mode control method using the input device with gaps. The effectiveness and robustness of the proposed controller are examined by numerical calculation that simulates input saturation, stroke limitation, gap-width expansion, and varying parameters, in the presence of model errors of the elevator rope. The results indicate effective vibration suppression and high robustness in the above cases except for the case of varying parameters.