Nonlinear Dynamics of the Rotational Slender Axially Moving String with Simply Supported Conditions

Abstract

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are changed to non-dimensional form and discretized via Galerkin’ method. The bifurcation diagrams and Poincare' portraits are represented in the case that the mean axial speed, the speed fluctuation and the mass eccentricity are respectively varied. The dynamical behaviors are numerically identified based on the Poincare' portraits. Numerical simulations indicate that quasi-periodic motion occurs in the transverse vibrations of the string by variation of axial speed and mass eccentricity.