A two-point Pade approximation for the in-plane buckling of a rotating beam

A global approximation for the neutral stability curve describing the divergence buckling of a uniformly rotating beam clamped off the axis of rotation is proposed using two-point Padé approximants. The resulting formula is based on a local analysis of the bifurcation problem for two distinct values of a suitably chosen asymptotic parameter. Unlike previous ad hoc methods in the literature, our approach is versatile and applicable to similar scenarios. Furthermore, comparisons with direct numerical simulations confirm that the proposed strategy offers a straightforward way for accurately predicting the critical rotational speeds responsible for potential buckling instabilities.