Modeling and Analysis of a Moving Conductive String in a Magnetic Field

Abstract

A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled.