LINEAR AND NONLINEAR STABILITY ANALYSIS OF ROTTATING DYNAMICAL SYSTEMS WITH ELASTIC AND DAMPED SUPPORTS

Abstract

An inclusive historical background and literature review on the subject of rotor-bearing systems modeling and analysis are presented. The dynamics and stability of a uniform rigid spinning shaft with an appendage mounted on two dissimilar 8-coefficient end bearings possessing nonlinear anisotropic and cross coupling stiffuess and damping coefficients are analyzed. Lagrange's equations are used to derive the system governing equations of motion in the form of four coupled nonlinear second order differential equations.

A linear stability analysis via Routh-Hurwitz stability criterion is presented for investigating the effects of various end support parameters on the dynamic stability of the translational and rotational modes of whirling motion of the system. Stability boundaries presented graphically as functions of the various end support nondimensionalized parameters afford a comprehensive demonstration of the effects of these parameters on the whirling stability ofthe system.

A nonlinear stability analysis of the system via Liapunov's direct method is performed. Based on the developed stability criterion of the considered system, the effect of nonlinearity of bearing stiffuess and damping parameters on the asymptotic