Free vibration analysis of a string with vibration suppressor located at 1/N of the string (When N is an even number)

Abstract

When an elevator rope for a high-rise building is forcibly excited by the displacements of the building induced by wind forces and/or by long-period ground motion, rope displacement becomes large even if the ground acceleration and the buildings acceleration is small. Vibration suppressor is used to change natural frequency of the elevator rope, and to avoid resonance. The advantage of using the vibration suppressors for reducing the rope lateral vibration is demonstrated through numerical calculation. Further, when arbitrary position of the rope is pulled, exact solution to the free vibration of the rope with vibration suppressor, which located at the center of the rope has been presented. However, in the case where the position of vibration suppressor is 1/N of the rope and the pulled position is center of the rope, no exact solution to the free vibration has yet been obtained. In this paper, an exact solution to the free vibration of this case is presented. In the analysis, the rope is modeled with string. Finite difference analyses of the rope vibration with vibration suppressor are also performed. The calculated results of the finite difference analyses are in fairly good agreement with those of the exact solution.