Distributed-order fractional constitutive stress–strain relation in wave propagation modeling

Distributed-order fractional model of viscoelastic body is used to describe wave propagation in an infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem is obtained explicitly. The wave propagation speed is found to be related to the material properties a...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2019-04, Vol.70 (2), p.1-21, Article 51
Main Authors: Konjik, Sanja, Oparnica, Ljubica, Zorica, Dušan
Format: Article
Language:English
Subjects:
Cauchy problems
Constitutive models
Electric power distribution
Engineering
Material properties
Mathematical Methods in Physics
Propagation
Stress concentration
Stress propagation
Theoretical and Applied Mechanics
Viscoelasticity
Wave propagation
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Summary:Distributed-order fractional model of viscoelastic body is used to describe wave propagation in an infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem is obtained explicitly. The wave propagation speed is found to be related to the material properties at initial time. The fundamental solutions corresponding to four thermodynamically acceptable classes of linear fractional constitutive models and power-type distributed-order models are also obtained.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-019-1097-z