A Nonlinear Vibration Control of a String Using the Method Based on Its Time-Varying Length

Abstract

Strings are common components in various mechanical engineering applications, such as transmission lines, infusion pipes, stay cables in bridges, and wire rope of elevators. The string vibrations can affect the stability and accuracy of systems. In this paper, a time-varying string length method is studied for string vibration suppression. A dynamic model of a string with the time-varying length is formulated. The dimensionless variables are introduced into the nonlinear dynamic model to realize the separation of time and space variables. The finite difference method is used to solve the differential equations of time functions. The vibration characteristics of time-varying length string are analyzed, such as the free vibrations, forced vibrations and damping effect. The influences of the length time-varying frequency and length time-varying range on the suppression performances are discussed. The results show that the time-varying string length method can effectively disperse the resonance peak energy and suppress multimodal resonance at the same time. The suppression performance is better for the time-varying length string with a higher time-varying frequency and a higher time-varying range.