Analysis of a Rotating Shaft with a Thin-Walled Open Cross-Section Having One Symmetrical Axis

The purpose of this paper is to analyze structural statics and dynamics of a rotating shaft with a thin-walled open cross-section having one symmetrical axis. For the shaft, flexural-torsional coupling must be considered because the centroid axis and the shear-center axis do not always coincide. After deriving the governing equations of motion for a uniform shaft rotating at a constant angular velocity, we propose methods to estimate static deflection and dynamic stability. Numerical calculations for cantilever shafts with and without internal damping indicate that the distance between the centroid and the shear-center contributes to the dynamic instability. Moreover, an application of the methods to an elastically supported model indicates that a spin-axis antenna rod for future scientific satellites under consideration is dynamically stable in the operational spin-rate.