Model Reduction of a Flexible Beam Rotating at High Speed Considering Dynamic Stiffening

Abstract

Linear model reduction methods have been successfully used to reduce the degreeof- freedom of elastic bodies undergoing low-speed rotational motion. The nonlinear geometric stiffness matrix should be taken into account if a flexible beam is rotating at high speed, otherwise, the errors get big. So linear model reduction methods can not be used directly in this situation. In this paper, arc coordinates are used to describe the deformations of the beam, and the dynamic coupling stiffness matrix is obtained. The dynamic coupling stiffness matrix is a nonlinear function of rotating speed, which is different from the nonlinear geometric stiffness matrix. When the beam rotates at a constant speed, the stiffness matrices are constant. Then, a modal method and a Krylov method are used to reduce the degree-of-freedom of the flexible beam, in which the dynamic stiffening is considered. Finally, the reduced models are adopted in the dynamic equations to compare with the full finite element model. The numerical simulations show that results using the reduced model based from the modal method and the Krylov method are in good agreement with the reference results. Using the Krylov method shows faster convergence than using the modal method. The method presented in this paper offers an efficient way to do model reductions of the flexible beam rotating at high speed considering dynamic stiffening