Attractors of a rotating viscoelastic beam

Abstract

We investigate the non-linear oscillations of a rotating viscoelastic beam with variable pitch angle. The governing equations of motion are two coupled partial differential equations for the longitudinal and transversal displacements. Using a perturbation technique and Galerkin's projection, we reduce the equations of motion to a non-autonomous ordinary differential equation. Our regular perturbation technique is based on the expansion of longitudinal displacement and the amplitude of first transversal mode in terms of a small parameter. We numerically generate the Poincaré maps of the reduced equations and reveal that the system exhibits regular and chaotic attractors. The regular attractors are stable limit-cycles that are relevant to stable, short-period oscillations of the beam. A bifurcation analysis has also been performed when the pitch angle is constant.