Free vibration analysis of a string with vibration suppressors located at 1/N from both ends of the string(When N is an even 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. To gain an understanding of rope sway, the free vibration analysis of the string with vibration suppressors have been studied. In previous paper, an exact solution to the free vibration of the string with vibration suppressors located at 1/N from both ends of the string has been studied in the case where gap between string and vibration suppressor is zero. However, in the case where N is an even number and gap between string 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 is presented, when 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.