Modeling of flexible blade rigid-disk flexible shaft rotor system supported by elastic bearings: Stability analyses

A Simple mathematical model describing the motion of a rotating flexible blade rigid-disk flexible shaft assembly is derived. The model provides a fast parametric study for the dynamic behavior of the proposed rotor system. The Lagrangian approach combined with the assumed mode method is used to derive the governing equations of motion for this system. The model consists of asymmetrical continuous shaft mounted on two isotropic supports; an end support, represented by two rotational and two translational springs, and an intermediate support, represented by two translational springs only. A rigid disk, with a number of flexible blades of uniformly distributed stiffness and mass, cantilevered. to the disk, is attached to the free end of the shaft. The effect of support flexibility on the stability of the system is studied. Instability regions are presented for different system parameters. The proposed mathematical model results are similar to that found in the literature.