New Approach to Instability Threshold of a Simply Supported Rayleigh Shaft

The main goal of this research is to analyse the effect of angular velocity on stability and vibration of a simply supported Rayleigh rotating shaft. To this end, non-dimensional kinetic and potential energies are written while lateral vibration is considered. Finite element method is employed to discrete the formulations and Linear method is applied to analyse instability threshold of a rotating shaft. These results represent the significant effects of mass moment of inertia, centrifugal forces and rotational speed. Also, the differences between Rayleigh and Euler-Bernoulli modelling are delivered. Furthermore, the effect of slenderness ratio on instability threshold and the natural frequencies are illustrated. Increasing rotational speed leads to decreasing of instability threshold and forward and backward natural frequencies. These formulations can be used to choose the safe working conditions for a shaft.