Analytical investigation on nonlinear vibration behavior of an unbalanced asymmetric rotor using the method of multiple scales

Abstract

In this paper, the vibration behavior of a rotor with an asymmetric shaft subjected to unbalanced forces is analyzed theoretically. The model is a rotor composed of a rigid disk and a flexible shaft. The shaft is considered to be a beam with a rectangular cross section. The general equations of motion were first derived by considering the effect of high order large deformation in bending. In this process, a continuous shaft, gyroscopic effects, and rotor mass unbalance are taken into account to study the rotor’s nonlinear vibratory behavior near the main resonances. The equations are discretized using the Rayleigh–Ritz method. The obtained equations are nonlinear coupled differential equations which are solved using the multiple-scales method. It can be concluded from the results that nonlinearity due to an asymmetric shaft severely affects the resonance behavior of the rotor.