Friction Induced Transverse Vibrations of an Axially Accelerating String

The purpose of this study is to investigate the dynamic response of axially translating continua undergoing both the effect of friction and axial acceleration. The axially moving continuum is initially modeled as a string, neglecting its flexural stiffness; the response, with particular interest given to transverse vibrations and dynamic stability, is studied through numerical methods. A finite element method is employed to discretize the space domain and an implicit α–method is employed to integrate the resulting matrix equation in the time domain. Results are given through time history diagrams and stability considerations.