Authors: Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Hereditariness and non-locality in wave propagation modeling
Journal: Theoretical and Applied Mechanics
Volume: 47
Issue: 1
First page: 19
Last page: 31
Issue Date: 1-Jan-2020
Rank: M24
ISSN: 1450-5584
DOI: 10.2298/TAM200116005Z
Abstract: 
The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.
Keywords: Distributed-order fractional model | Fractional eringen model | Memory and non-local effects | Non-local hookean model | Wave equation
Publisher: Serbian Society of Mechanics
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Provincial Secretariat for Higher Education and Scientific Research under grant 142-451-2102/2019

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