Viscoelasticity: An electrical point of view

Abstract

Abstract-Time dependent hereditary properties of complex materials are well described by power-laws with real order exponent. This experimental observation and analogous electrical experiments, yield a description of these properties by using fractional-order operators. In this paper, elasto-viscous and viscoelastic behaviors of fractional order hereditary materials are firstly described by using fractional mathematical operators, based on recent work of some of the authors. Then, electrical analogous models are introduced. Viscoelastic models have elastic and viscous components which can be obtained by combining springs and dashpots: these models can be equivalently viewed 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. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.

Development of an electrical analogue for modeling natural vibrations of a viscoelastic structure with piezoelectric element

“…Since we proceed from the assumption that the materials of the piezoelectric element and structure are elastic, it seems reasonable to take into account energy losses due to the internal loss mechanisms both in the piezoelectric material and in the material of the main structure. The mechanisms of losses in piezoelectric materials have been studied for a rather long time, and in the literature there have been many relevant studies (Ala et al, 2014a, 2014b; Chen et al, 2006; Dong et al, 2017; Holland, 1967; Sherrit (1999); Uchino et al, 2011; Yuan et al, 2018). Holland (1967) and Uchino et al (2011) described in detail the losses in piezoelectric, which could be of three types: dielectric, elastic, and piezoelectric.…”