Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

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Original languageEnglish
Pages (from-to)47-55
Journal / PublicationComputers and Structures
Online published18 Feb 2014
Publication statusPublished - May 2014


We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification. © 2014 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Fractional Mathieu-Duffing oscillator, Parametric bifurcation, Time delay, Viscoelastic column