Analysis of a Beck's column over fractional-order restraints via extended Routh-Hurwitz theorem

The fascinating dynamic stability of a column with inherent paradoxes depending on the kind of external restraint has attracted several scientists to help represent the mechanics of rods and columns in different engineering fields. The presence of the Zener element represents a specific generalization of the Routh-Hurwitz theorem since, for fractional-order dynamical systems, the conventional condition involving the sign of the real part of the problem eigenvalues no longer holds. Linear hereditariness is certainly the field of the most extensive applications of fractional calculus, in view of its ability to model hereditary phenomena with long memory. This chapter outlines the evaluation of the critical instability load of Beck's column. The analysis of Beck's column resting on an external foundation is a challenging and unsolved problem in the field of mechanics. The presence of well-established paradoxes arising from stability analysis and involving the evaluation of critical loads yields unreliable solutions in terms of stability.