Open AccessMODELING OF HEREDITARY MATERIALS RELAXATION BY ABEL KERNEL
Author(s) -
M. Zh. Zhurinov,
Alibai Iskakbayev,
Bagdat Teltayev,
K. S. Kutimov
Publication year - 2020
Publication title -
izvestiâ nacionalʹnoj akademii respubliki kazahstan. seriâ geologii i tehničeskih nauk
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.323
H-Index - 9
eISSN - 2518-170X
pISSN - 2224-5278
DOI - 10.32014/2020.2518-170x.154
Subject(s) - kernel (algebra) , relaxation (psychology) , mathematics , nonlinear system , mathematical analysis , calculus (dental) , physics , pure mathematics , medicine , psychology , social psychology , dentistry , quantum mechanics
The present work is devoted to mathematical modeling of the process of the hereditary materials relaxation. Nonlinear integral equation of a hereditary type is proposed. The Abel kernel with two unknown parameters is adopted as the kernel of the integral equation: α∈(0,1),δ>0. Two new characteristics were introduced: 1) experimental rheological parameter of relaxation; 2) calculated (model) rheological parameter of relaxation. Using the least squares method, expressions are obtained to determine unknown parameters of the Abel kernel. A mathematical expression is given to approximate the process of the hereditary materials relaxation. Using examples of rheonomic materials different in structure (polyurethane matrix, propellant, polyoxymethylene, fiberglass), it is shown that the proposed methods allow to determine Abel kernel parameters with a high accuracy and to model the process of relaxation of rheonomic materials different in structure during a long period of time: from 102 to 1.8·106 seconds (500 hours).