Comparison of Fractional Kelvin-Voigt and Fractional Zener Models for Large Deflection of Viscoelastic Beams

The large deflection response of viscoelastic beams has attracted the attention of many researchers in the last few decades. This paper deals with comparison of fractional derivative models for large deflection of viscoelastic beams. For this purpose, a finite element formulation for Kelvin-Voigt and Zener models of viscoelastic beams using fractional derivative constitutive equations has been developed. The geometrically non-linear implementation of fractional constitutive equations based on the Grünwaldian formulation into an elastic finite element code is demonstrated. The novelty of this work is that fractional viscoelastic models are compared for large deflection of viscoelastic beams. This comparison shown that the large deflection response of the viscoelastic beam in the fractional Kelvin-Voigt model at long times is near the response of the fractional Zener model. Since the Zener fractional derivative model is adaptive with the properties of viscoelastic materials, it is an effective tool to describe the behavior of the viscoelastic materials.

Keywords:

Viscoelastic beam , Fractional Zener model , Fractional Kelvin-Voigt model , Large deflection , Finite element