Buckling of a thin annular plate under uniform compression

thin rods, is solved. The analysis yields a set of stability criteria involving the system parameters such as the body moments of inertia, the length and mass distribution of the elastic rods, the lowest natural frequencies of the rods, and the satellite spin velocity. The power of the method is illustrated by the relative ease with which closed-form stability criteria are derived and by the amount of information which can be extracted from their ready physical interpretation. In particular, the analysis shows that, for stability, the spinning motion is to be imparted about the axis of maximum moment of inertia. This is the well-known "greatest moment of inertia" requirement. Moreover, the initial spin velocity flc should not be merely lower than the first natural frequencies Aiu and Air associated with the transverse vibration of the rods (as the frequency of simple harmonic excitation of the rods should be if resonance is to be prevented), but the ratios Os/AiM and fi./Ai,, are dictated by the system parameters. Of course, for very stiff rods the natural frequencies AI« and AIV may be sufficiently high that the satisfaction of criteria (40) is ensured. References