Nonlinear dynamics of a rotating shaft subject to periodic perturbations

In this paper, we study the global dynamics of a rotating shaft parametrically excited by a time-dependent rotation rate. The partial differential equations of motion for the shaft are first discretized using the Galerkin procedure. The equations are rewritten as Hamiltonian equations in order to study the global dynamics of the system using the methods of perturbed Hamiltonian systems. After performing unfoldings and determining the normal form, the equations are put into action-angle coordinates, the most suitable form for a study of the global dynamics. The unperturbed system is found to contain both homoclinic and heteroclinic orbits for different parameter values. By considering the perturbation of the unperturbed Hamiltonian system, we can determine whether chaotic behavior is present.