Effect of disk flexibility on nonlinear vibration characteristics of shaft-disk rotors

Accurately predicting the nonlinear dynamic response of shaft-disk rotors is crucial in the design of rotary machines. In available studies, the disk is commonly treated as rigid body to simplify the analysis of the nonlinear problem. This paper aims to clarify the effect of disk flexibility on the nonlinear dynamic response of shaft-disk rotors. Both gyroscopic and centrifugal effects are considered. The shaft is considered as a Euler-Bernoulli beam with the von Kármán nonlinearity, and the disk is considered as a Kirchhoff plate. The differential equations of motion are derived utilizing the Lagrange equation. The pseudoarclength continuation method is employed to numerically analyze the nonlinear forced vibration response of the rotor under the unbalanced force. By comparing with the existing reference, the accuracy of the present model is verified. The effects of the flexibility, position, radius, and thickness of the disk, as well as the wall thickness and length of the shaft on the nonlinear vibration of the rotor are explored. Results show that ignoring the disk flexibility is acceptable only in very limited cases, in most cases, however, this simplification will overestimate the nonlinear vibration amplitude of the rotors, which makes the design of the shaft-disk rotors conservative.