To the question on the correctness of fractional derivative models in dynamic problems of viscoelastic bodies

Abstract

The question is discussed on the possibility of utilization of such simplest fractional derivative viscoelastic models as Kelvin-Voigt and standard linear solid models for the description of the dynamic response of viscoelastic bodies, namely: beams and plates. It has been shown that the adoption of the Kelvin-Voigt model with the fractional derivative in conjunction with the time-independent Poisson’s ratio for the description of the dynamic behavior of a viscoelastic Kirchhoff-Love plate results in the fact that the given problem is reduced to the equivalent problem on dynamic response of an elastic Kirchhoff-Love plate in a viscoelastic medium with fractional damping. If Young’s operator is preassigned via the fractional derivative Kelvin-Voigt model in conjunction with the time-independent coefficient of volume extension-compression for solving the same problem, what seems to be more logical from the point of view of experimental data, then such a model tunes out to be inapplicable at all, while if the shear operator is governed by the fractional derivative Kelvin-Voigt model, then such a model could describe the behavior of so-called auxetic materials with negative Poisson’s ratios. As for the fractional derivative standard linear solid model, then it remains to be correct both with and without considering the volume relaxation.