Free vibration analysis of string with vibration suppressors located in center part of string

Abstract

Vibration suppressors are used to change the natural frequency of an elevator rope and prevent resonance. The displacement of the parts of the elevator rope at both the ends is small compared to that of the center part of the rope; therefore, it is not necessary to position the vibration suppressors in the parts on either ends. The elevator rope is generally modeled using a string, and linear string vibration is well researched. However, the vibration of the string equipped with vibration suppressors encounters geometric nonlinearity, and hence, its characteristics have been studied under a few conditions. Furthermore, in the case in which the vibration suppressor is located in the center part of the string, no exact solution has yet been obtained for the free vibration of the string. In this paper, an exact solution is presented for the free vibration of a string when the vibration suppressors are located in the center part of the string. In the analysis for determining the exact solution, the problem of free vibration with vibration suppressors is transposed to a problem of forced vibration. Further, to verify the validity of the 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 the results of the exact solution.