New approach to instability threshold of a simply supported rayleigh rotating shaft

The main goal of this research is to analyze the effect of angular velocity on stability and vi-bration of a simply supported 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 analyze instability threshold of a rotating shaft. These results represent the significant effects of centrifugal terms and rotational speed. Also, the effect of slenderness ratio on instability threshold and the natural frequencies are illustrated. Increasing rotational speed leads to decreasing of instability threshold and for-ward and backward natural frequencies. These formulations can be used to choose the safe working conditions for a shaft.

Keywords:

rotating shaft , stability , vibration , forward and backward natural frequencies