Dynamic stability of slender columns with semi-rigid connections under periodic axial load: verification and examples

The dynamic stability of an elastic prismatic slender column with semirigid connections at both ends of identical stiffness and with sidesway between the two ends totally inhibited, subject to parametric axial loads including the combined effects of rotary inertia and external damping was presented in a companion paper. Closed-form expressions that predict the dynamic instability regions of slender columns were developed by making use of Floquet’s theory. The proposed equations are straightforward and simple to apply. The proposed solution is capable of capturing the phenomena of stability of columns under periodic axial loads using a single column element. The proposed method and corresponding equations can be used to investigate the effects of damping, rotary inertia and semirigid connections on the stability analysis of slender columns under periodically varying axial loads. Sensitivity studies are presented herein that show the effects of rotary inertia, damping and semirigid connections on the dynamic stability of columns under parametric axial loads. Analytical studies indicate that the dynamic behavior of columns under periodic loading is strongly affected by the flexural stiffness of the end connections and the external damping, but not so much by the rotary inertia. Three examples are presented in detail and the calculated results are compared with those reported by other researchers.