Free vibration of taut cable with a damper and a spring

Abstract

SUMMARY The damping and frequency of taut cable with a damper and a spring are investigated in this paper, which is motivated by cross-ties and damper that are both utilized in mitigation of oscillation of the stays in cable-stayed bridges or damper located near cable anchorage with rubber bushing. The dynamic characteristics of the cable-damper-spring system are analyzed on the basis of the taut string theory and considering the compatibility requirements on each constraint point. By using a transfer matrix method, the complex frequency equation of the cable-damper-spring system is derived. The complex frequency equation is further re-written in terms of real and imaginary parts. The special limiting solutions are presented. Asymptotic approximate solutions for damper and spring close to cable ends are developed with small frequency shifts between free cable and damped system mode. The effects of spring stiffness and location to maximum cable vibration damping, optimum damper constant, and frequency are also addressed when spring is not located near cable anchorage. The mode behaviors when damper and spring is parallel connected are given. The general solutions for arbitrary location of damper and spring along the cable are further discussed. The results of this study are helpful to understanding the damper parameter optimization of cable-damper-rubber-bushing system and the basic dynamics of the complex cable-cross-ties-damper system. Copyright © 2013 John Wiley & Sons, Ltd.