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Electrical analogous in viscoelasticity. (English) Zbl 1455.74022

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

MSC:

74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74F15 Electromagnetic effects in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics

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