Nano- and viscoelastic Beck’s column on elastic foundation

Abstract

Beck’s type column on a Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli–Euler model describing the rod, two generalized models will be adopted: Eringen’s nonlocal model corresponding to nano-rods and a viscoelastic model of fractional Kelvin–Voigt type. The analysis shows that for a nano-rod the Herrmann–Smith paradox holds whilst for a viscoelastic rod it does not.