Dynamic stability of spinning pre-twisted beams subject to axial pulsating loads Original Research Article

The equations of motion of a spinning pre-twisted beam subject to axial loads are formulated using Euler beam theory and the assumed mode method. The effects of sinusoidal perturbations in respect of the axial loads are then examined using Bolotinʹs method. The equations of motion are transformed to the standard form of an eigenvalue problem for determining the perturbation frequencies defining the boundaries of the regions of instability of the spinning beam. Detailed numerical simulations show that the unstable regions are strongly affected by the spinning speed, the pre-twist angle and the aspect ratio of the cross-section of the beam. For a non-spinning pre-twisted beam, the regions of instability in terms of the magnitude of the axial load perturbation are in the familiar ‘V’ shape. However, for a spinning pre-twisting beam, the unstable regions are complicated by the coalescence and bifurcation of the perturbation frequencies defining the boundaries of unstable regions.