The Equilibrium States of a Heavy Rotating Column
Watson, Layne T.
Wang, Chang Y.
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A heavy, rotating vertical column is clamped at one end and free at the other end. The stability boundaries are found by both analytical approximations and numerical integration. The problem depends on two non-dimensional parameters: beta representing the importance of gravity to rigidity and alpha representing the importance of rotation to rigidity. Buckled shapes for the different modes are also obtained.