Dynamic stability of spinning pre-twisted beams

Abstract

The equations of motion of a spinning pre-twisted beam are formulated using Euler beam theory and the assumed mode method. The equations of motion are then transformed to the standard form of an eigen-value problem for determining the critical spinning speeds corresponding to the divergence behavior of the spinning beam. The effects of pre-twist angle and aspect ratio of the rectangular cross-section of the beam on its stability are investigated. Detailed numerical simulations show that the unstable spinning speed zones for a pre-twisted beam of a given aspect ratio of the cross-section do not become narrower with increased pre-twist angle. The main reason is that for a pre-twisted beam, the critical spinning speeds corresponding to divergence behaviors are no longer the dividing points for separating the speed zones into stable and unstable regions. This type of stability behavior of a pre-twisted beam is different from the stability behavior of a spinning beam without any pre-twisting. Such a spinning beam without pre-twisting is found to have distinct regions of stable and unstable spinning speed zones separated by critical spinning speeds. © 1994.