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Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative

Department of Applied Mathematics, Moscow State University of Civil Engineering, 129337 Moscow, Russia
Mathematics 2020, 8(10), 1843; https://doi.org/10.3390/math8101843
Received: 4 August 2020 / Revised: 3 September 2020 / Accepted: 5 September 2020 / Published: 20 October 2020
(This article belongs to the Special Issue Dynamical Systems and Optimal Control)
The article presents a solution to a boundary value problem for a wave equation containing a fractional derivative with respect to a spatial variable. This model is used to describe oscillation processes in a viscoelastic medium, in particular changes in the deformation-strength characteristics of polymer concrete (dian and dichloroanhydride-1,1-dichloro-2,2-diethylene) under the influence of the gravity force. Based on the obtained solution to the boundary value problem, the article presents four numerical examples corresponding to homogeneous boundary conditions and various initial conditions. The graphs of the found solutions were constructed and the calculation accuracy in the considered examples was estimated. View Full-Text
Keywords: wave equation; fractional differentiation; eigenvalues and eigenfunctions of boundary value problem wave equation; fractional differentiation; eigenvalues and eigenfunctions of boundary value problem
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MDPI and ACS Style

Kirianova, L. Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative. Mathematics 2020, 8, 1843. https://doi.org/10.3390/math8101843

AMA Style

Kirianova L. Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative. Mathematics. 2020; 8(10):1843. https://doi.org/10.3390/math8101843

Chicago/Turabian Style

Kirianova, Ludmila. 2020. "Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative" Mathematics 8, no. 10: 1843. https://doi.org/10.3390/math8101843

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