TY - JOUR
T1 - Nonlinear dynamics of a rotating shaft subject to periodic perturbations
AU - McDonald, Robert J.
AU - Sri Namachchivaya, N.
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:17544365285
SN - 1521-4613
VL - 91
SP - 179
EP - 184
JO - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
JF - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
ER -