Development of a dynamic stiffness matrix for free vibration analysis of spinning beams

Following the derivation of the governing differential equations in free vibration by using Hamilton’s principle, the dynamic stiffness matrix of a spinning beam is developed. The Wittrick–Williams algorithm is then applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes for some illustrative examples. These results are discussed and compared with published ones. The paper concludes with some remarks.