Free vibration analysis of a string with vibration suppressors located at 1/N from both ends of the string (When N is an odd number and gap between string and vibration suppressor is not zero)

Abstract

In high-rise buildings, the elevator rope may resonate with the building's sway induced by wind forces and/or by long period ground motion. Therefore, suppression of elevator rope vibration is desired. In previous paper, an exact solution to the free vibration of the rope with vibration suppressors located at 1/N from both ends of the rope was presented in the case where the gap between rope and vibration suppressor was zero. However, in the case where N is an odd number and the gap between rope and vibration suppressor is not zero, no exact solution of the free vibration has yet been obtained. In this paper, an exact solution to the free vibration of this case (N is an odd number and gap between string and vibration suppressor is not zero) is presented, when the center position of the rope is pulled. 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 good agreement with those of the exact solution.