Effects of axial base excitations on the dynamic stability of spinning per-twisted cantilever beams

Abstract

The equations of motion of a pre-twisted cantilever beam with a spinning base subject to axial base excitations are formulated by using Euler beam theory and the assumed mode method. The effects of sinusoidal perturbations in terms of the axial accelerations of the beam are then examined by using Bolotin's 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. The instability diagrams are found to be strongly dependent on the spinning speed, the pre-twist angle and the aspect ratio of the cross-section of the beam. Moreover, the unstable regions are complicated by the coalescence and bifurcation of the perturbation frequencies defining the boundaries of unstable regions, a phenomenon not found for the stability of a non-spinning pre-twisted beam.