Stability and bifurcations analysis of rotating shafts with base excitations

Base excitation in a rotating machinery such as turbo generators, aircraft engines, etc could occur when these systems are subjected to the base movements. This paper investigates the nonlinear behavior of a symmetrical rotating shaft under base excitation when the system is in the vicinity of the main resonance. Dynamic imbalances and harmonic base excitations are the sources of excitation in this system. The equations of motion are derived using the extended Hamilton principle and are mapped into the complex plane. The complex partial differential equation of motion is transformed to the ordinary one utilizing mode shape of the linear system. The method of multiple scales is used to solve the equation of motion. The steady state solutions and their stability are determined, and the effects of damping coefficient, base excitations, and eccentricities of shaft on the stability and bifurcations of the system are investigated. The numerical integration is performed to validate the perturbation results. It is shown that the achieved results from two over-mentioned methods are in accordance with each other.