Exact solution for whirling analysis of axial-loaded Timoshenko rotor using basic functions

In this paper, an analytical solution for whirling analysis of axial-loaded Timoshenko rotor is presented and corresponding basic functions are derived. The set of governing equations for whirling analysis of the rotor consists of four coupled partial differential equations; using complex displacements, these equations can be reduced to two coupled partial differential equations. The versatility of the proposed solution is confirmed using published results and the effect of angular velocity of spin, axial load, slenderness and Poissonʹs ratio on the natural frequencies of the rotor are investigated.