Free vibration analysis of a string with vibration suppressor (When the position of vibration suppressor is opposite to the pulled position)

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. However, the vibration of the string that has a vibration suppressor has been studied for a few conditions because of its geometric nonlinearity. In this paper, an exact solution for the free vibration of a string when the position of the vibration suppressor is opposite to the pulled position is presented. In this analysis, a problem of free vibration with a vibration suppressor is transposed to a problem of forced vibration. Further, to verify the validity of this exact solution, a finite difference analysis of the string vibration with a vibration suppressor is performed. The calculated results obtained from the finite difference analysis are in good agreement with those of the exact solution.

Keywords

• string
• free vibration
• vibration suppressor
• exact solution
• elevator rope
• rope sway