Nonlinear vibration analysis of a spinning shaft with multi-disks

In this study the stability of a rotor system, which is comprised of a simply supported nonlinear spinning shaft with multi-rigid disk, near to the major critical speeds is investigated. The nonlinearity is due to the stretching and large amplitude. The influence of rotary inertia and gyroscopic effects are included, however, shear deformation is ignored. To analyze the nonlinear equations of motion, the method of multiple scales is applied to the ordinary differential equations of motion. The influences of different parameter such as number of disks, disk mass moment of inertia, rotational speed, external damping, and position of disks on the forward and backward linear frequencies, steady state response, stability and bifurcations of the rotor system are investigated. It is seen that in the higher rotational speeds, the backward frequency is increasing with an increase of number of disks, and in the lower rotational speeds, the backward frequency is decreasing with an increase of number of disks. By increasing number of disks, bifurcations occur in the lower speeds therefore, the instability occurrence for large number of disk is at speeds lower than that regarding to the low number of disks. By an increase of disk mass moment of inertia, the amplitude and the hardening effect decrease.