Nano and viscoelastic Beck's column on elastic foundation

TL;DR

This paper analyzes Beck's column on an elastic foundation using advanced models: Eringen non-local for nano-rods and fractional Kelvin-Voigt for viscoelastic rods, revealing different stability paradoxes.

Contribution

It introduces generalized models for Beck's column, extending classical analysis to nano-scale and viscoelastic materials, and compares their stability behaviors.

Findings

Herrmann-Smith paradox persists in nano-rod model

Paradox does not hold in viscoelastic model

Different stability characteristics for nano and viscoelastic columns

Abstract

Beck's type column on 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 non-local model corresponding to nano-rods and viscoelastic model of fractional Kelvin-Voigt type. The analysis shows that for nano-rod, the Herrmann-Smith paradox holds while for viscoelastic rod it does not.