Dynamic stability of spinning beams of unsymmetrical cross-section with distinct end conditions

Abstract

The equations of motion of a spinning beam of uniform rectangular cross-section are formulated by using Euler beam theory and the assumed mode method. The equations of motion are then transformed to the standard form of an eigenvalue problem for determining the critical spinning speeds corresponding to the divergence behavior of the spinning beam. The effects of the aspect ratio of the rectangular cross-section of the beam on its stability are investigated for various combinations of end conditions for the transverse vibrations in the two principal directions of the cross-section. Emphasis is focused on the dynamic behavior of a spinning beam with distinct end conditions for the transverse vibrations in the two principal directions of the cross section. The spinning beams are found to have distinct stable and unstable spinning speed zones separated by critical spinning speeds. Moreover, for a beam having the same flexural rigidities in the two principal directions of the cross-section, the unstable speed zones shrink to isolated points corresponding to the critical behaviors but only when the end conditions for the transverse vibrations in the two principal directions of the cross-section are identical. © 1996 Academic Press Limited.