Nonlinear Characteristics of Primary Resonances in Horizontally Supported Jeffcott Rotor

Abstract

This study deals with nonlinear dynamics of a horizontally supported Jeffcott rotor. The equations of motion are derived by considering the effects of gravity and the cubic nonlinearity of restoring force by the support condition. These effects produce the difference between the linear natural frequencies in the vertical and horizontal directions and make the stiffness in the vertical direction unsymmetric. It is also theoretically clarified that as the mass increases, the hardening spring characteristic becomes stronger in the horizontal direction and the spring characteristic in the vertical direction changes from the hardening-type to the softening-type. Therefore, in a relatively heavey rotor, the frequency response curve of the primary resonance in the horizontal direction exhibits hardening-type response and in the vertical direction, the frequency response curve has the softening-type nonlinearity. The experimental results by a simple apparatus qualitatively confirm the theoretically predicted nonlinear dynamics of the horizontally supported rotor.