Non-linear problems of fractional calculus in modeling of mechanical systems
Wiesław Grzesikiewicz , Andrzej Wakulicz , Artur Zbiciak
AbstractThe paper presents mathematical formulation and numerical algorithm for solving non-linear fractional-order differential equations (FDEs) modeling mechanical systems. The method presented in the paper involves the notion of variational inequalities. It is applied to one-term FDEs which are linear with respect to the fractional derivative. The examples of rheological models containing, in addition to fractional elements, the non-linear elastic, viscous and plastic elements are presented. The difference time-discretization schemes of Euler and Runge–Kutta types for solving initial-value problems are proposed. A special attention is paid to analysis of an original elastic-visco-plastic fractional model of asphalt–aggregate mixes being a modification of the classical Huet–Sayegh model. The results of numerical simulations of mechanical systems subjected to harmonic kinematic excitations are presented.
|Journal series||International Journal of Mechanical Sciences, ISSN 0020-7403|
|Publication size in sheets||0.5|
|Keywords in English||Fractional calculus, Non-linear mechanical systems, Asphalt–aggregate mixes, Rheology, Viscoelasticity, Plasticity|
|ASJC Classification||; ; ; ;|
|Score|| = 35.0, 26-06-2020, ArticleFromJournal|
= 40.0, 26-06-2020, ArticleFromJournal
|Publication indicators||= 46; = 37; = 57.0; : 2013 = 2.331; : 2013 = 2.061 (2) - 2013=2.168 (5)|
|Citation count*||57 (2020-08-23)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.