Affiliation:
1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 8, 1113 Sofia, Bulgaria
Abstract
The fractional Zener constitutive law is frequently used as a model of solid-like viscoelastic behavior. In this work, a class of linear viscoelastic models of Zener type, which generalize the fractional Zener model, is studied by the use of Bernstein functions technique. We prove that the corresponding relaxation moduli are completely monotone functions under appropriate thermodynamic restrictions on the parameters. Based on this property, we study the propagation function and establish the subordination principle for the corresponding Zener-type wave equation, which provides an integral representation of the solution in terms of the propagation function and the solution of a related classical wave equation. The analytical findings are supported by numerical examples.
Funder
Science and Education for Smart Growth Operational Program and co-financed by the European Union through the European structural and Investment funds
ulgarian National Science Fund
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
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