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

In this research, dynamic analysis of the rotational slender axially moving string is investigated. Stringis assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and masseccentricity 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 tonon-dimensional form and are discretized via Galerkin’ method. The bifurcation diagrams andPoincare' portraits are represented in the case that the mean axial speed, the fluctuating speed and themass eccentricity are respectively varied. The dynamical behaviors are numerically identified based onthe Poincare' portraits. Numerical simulations indicate that quasi-periodic motion occurs in thetransverse vibrations of the string by variation of axial speed and mass eccentricity.