Buckling and dynamic stability of spinning pre-twisted beams under compressive axial loads

Abstract The equations of motion of a spinning pre-twisted beam under compressive axial loads are formulated using Euler beam theory and the assumed mode method. The equations of motion are first transformed to the standard form of an eigenvalue problem for determining the critical buckling loads for various combinations of prescribed spinning speeds, aspect ratio of the cross-section and pre-twist angle of the beam. The equations of motion are then transformed to the form of another eigenvalue problem for determining the critical spinning speeds. Both the critical spinning speeds and critical buckling loads are found to exhibit similar trends of variation and curve veering phenomenon with respect to changes in the aspect ratio of the cross-section. For a spinning pre-twisted beam under axial compressive loads, the critical spinning speeds corresponding to divergent behaviours are found to be no longer the dividing points for separating the speed zones into stable and unstable regions, contrary to the stability behaviour of a nonpre-twisted beam which have distinct regions of stable and unstable spinning speed zones separated by critical spinning speeds.