In-Plane Vibration and Buckling of a Rotating Beam Clamped Off the Axis of Rotation

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Abstract
Some work on the in-plane vibrations and buckling of rotating beams, clamped off the axis of rotation, is unclear as to behavior in the limit of small stiffness and small off-clamping. In this paper, asymptotic expansion formulas are developed for both small and large values of stiffness and off-clamping parameters. A composite expansion formula is also introduced as an engineering approximation to the buckling curve for all values of parameters. The present results agree quite well with an exact numerical solution and indicate that buckling can occur for arbitrarily small stiffness and off-clamping.

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