Nonlinear vibration of in-extensional rotating shaft under electromagnetic load

In this paper, nonlinear vibration of a simply supported rotating shaft with nonlinear curvature and gyroscopic effect under transversely electromagnetic load is investigated. It is assumed that the shaft is inextensible and electromagnetic load depends on the shaft deformations. The non-linear partial equations of motion derived by Hamilton's principle are solved using the succession of Galerkin and the multiple-scales perturbation method. By properly tuning the primary resonance of the system, the modulation equations of the rotating shaft are obtained. Stability of fixed points and saddle-node bifurcation of steady-state solution are presented in frequency response diagrams. Results show that the magnetic load has noticeable effects on the steady state response of the rotating shaft. Also, the change in qualitative nature (hardening- type, and softening- type) of primary resonance curves is observed by considering the geometric nonlinearity effects.