Authors: Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Hereditariness and non-locality in wave propagation modelling
Conference: 7th Congress of the Serbian Society of Mechanics
Issue Date: 2019
Rank: M30
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: wave equation | memory and non-local effects | distributed-order fractional model | non-local Hookean model | fractional Eringen model
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 

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