A.B. Hasanov
Modeling the dynamics of fractal viscoelastic media under nonstationary influences

A general mathematical model is developed for solving problems of dynamic thermoviscoelasticity taking into account the dependence of material properties on temperature in the case of arbitrary hereditary functions describing the mechanical properties of the studied viscoelastic bodies. In the case when the hereditary functions are of the type of Mittag-Lefler functions, solutions of similar problems for viscoelastic bodies of fractal structure are obtained. The dependence of material properties on temperature is described by a temperature-time analogy for thermorheologically simple and complex media.

Keywords: Mathematical model, Dynamic problems, Viscoelastic bodies, Thermoviscoelasticity, Temperature-time analogy