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)

Abstract

A vibration suppressor is used to change the natural frequency of an elevator rope, and to prevent resonance. The elevator rope is modeled using a string. Linear string vibration is well known. However, the vibration of the string that has a vibration suppressor has been studied for a few conditions because of its geometric nonlinearity. An exact solution of the free vibration of a string with a vibration suppressor located at 1/N from one end of the string has been obtained. However, in the case when vibration suppressors are installed at 1/N from both ends of the string, no exact solution of the free vibration has yet been obtained. In this paper, an exact solution of the free vibration of this case is presented. Further, to verify the validity of this exact solution, a finite difference analysis of the string vibration with vibration suppressors is performed. The calculated results obtained from the finite difference analysis are in good agreement with those of the exact solution.