Dynamic Properties of a Moving Thread Line

Abstract

A mathematical model representing the transverse vibration of axially moving elastic strings is presented considering tension and mass variation. A suggested numerical scheme was successfully used to solve the nonlinear partial differential equations of motion. For axially nonmoving strings, the effect of initial amplitudes, and consequently the tension variation on the fundamental frequency is obtained. Also, the effect of the initial tension and the mass of the string per unit length on the fundamental frequency and their corresponding mathematical relations are presented. For axially moving strings, the effect of the axial velocity on the fundamental frequency as well as the tension distribution along the thread is given. Also the behavior of the string at velocities equal and greater than the wave speed is shown.