Electrical analogous in viscoelasticity

In this paper, electrical analogous models of fractional hereditary materials are introduced.Based on recent works by the authors, mechanical models of materials viscoelasticitybehavior are firstly approached by using fractional mathematical operators. Viscoelasticmodels have elastic and viscous components which are obtained by combining springsand dashpots. Various arrangements of these elements can be used, and all of these viscoelasticmodels can be equivalently modeled as electrical circuits, where the spring anddashpot are analogous to the capacitance and resistance, respectively. The proposed modelsare validated by using modal analysis. Moreover, a comparison with numerical experimentsbased on finite difference time domain method shows that, for long timesimulations, the correct time behavior can be obtained only with modal analysis. Theuse of electrical analogous in viscoelasticity can better reveal the real behavior of fractionalhereditary materials.