Resonance in a Rigid Rotor with Elastic Support

Abstract

Abstract A model is formulated for a rotor with elastic support in axial and lateral directions which leads to the problem of stability of small vertical oscillations in the upright position. This is an autoparametric excitation problem which can be formulated as two coupled Mathieu‐like equations. The analysis of the cases without and with (linear) damping and the case of nonlinear damping is carried out using averaging and numerical bifurcation techniques leading in the nonlinear case to hysteresis and phase‐locking.