Stability analysis of Beck's column over a fractional-order hereditary foundation

This paper considers the case of Beck's column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple (Cβ, β) that characterize the material of the element and is ruled by a Caputo's fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.