Analysis of whirl speeds of rotor-bearing systems with internal damping by C⁰ finite elements

A C⁰, three-node isoparametric finite element model is developed to study the whirl speeds of a rotor-bearing system with both internal viscous and hysteretic damping. The equations of motion for such a system are formulated based on the Timoshenko beam theory. In addition to the effects of translational and rotatory inertia, gyroscopic moments, the combined effects of transverse shear deformation and internal damping as well as the effect of the centrifugal force, which arises from the rotating shaft mass, are also incorporated into the mathematical model. Results of forward and backward whirl speed are presented and compared with other published works. It is shown that both the transverse shear derformation and the centrifugal force have the influence of lowering the whirl speeds. The good convergence of the present finite element model is also demonstrated with the numerical example given.