An Overview of Transverse Vibration of Axially Travelling String

The paper presents a comprehensive review of transverse vibration of axially travelling string. Axially travelling string includes many mechanical systems such as conveyor belt, aerial tramways, magnetic tapes, textile fibres, band-saw blades, thread lines and pipe conveying fluid. The analysis of transverse vibration of axially travelling string has theoretical as well as industrial significance because it is the simplest representation of the gyroscopic system. In the paper, the major emphasis is given on different types of modelling, the governing equations and the method of analysis of axially travelling string. In the discussion of linear model of axially travelling string, the paper describes about governing equation, modal analysis and response solution. In the discussion of non-linear model of axially travelling string, the paper discusses about governing equation, the method of analysis using direct perturbation method and the discretised perturbation method and numerical methods based on Galerkin discretization. A discussion is also made on the modelling of the dissipative mechanism by considering string as viscoelastic material based on Kelvin viscoelastic model. The paper also describes about linear and non-linear parametric excitation of axially travelling string which occurs due to tension and velocity fluctuation.