Vibration and stability of a composite thin-walled spinning tapered shaft

This paper deals with the vibration and stability of a circular cylindrical shaft modeled as a tapered thin-walled composite beam, spinning with constant angular speed about its longitudinal axis, and subjected to an axial compressive force. Hamilton's principle is used to derive the equations of motion and the associated boundary conditions. The resulting eigenvalue problem is analyzed, and the types of instability experienced by these structural systems are determined for selected taper ratios, spinning speeds and compressive force. It is also found that via the structural tailoring and beam tapering, the natural frequencies, stiffness and the stability regions can significantly be increased as compared to those of uniform shafts made of the same material. In addition, the structural damping effect in Bernoulli-Euler spinning beams is also considered and its implications on stability are discussed.