|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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