Non-linear problems of fractional calculus in modeling of mechanical systems

Wiesław Grzesikiewicz , Andrzej Wakulicz , Artur Zbiciak


The 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.
Author Wiesław Grzesikiewicz (FACME / IAE)
Wiesław Grzesikiewicz,,
- Institute of Automotive Engineering
, Andrzej Wakulicz - [Institute of Mathematics (IM PAN) [Polish Academy of Sciences (PAN)]]
Andrzej Wakulicz,,
- Instytut Matematyczny Polskiej Akademii Nauk
, Artur Zbiciak (FCE / IRB)
Artur Zbiciak,,
- The Institute of Roads and Bridges
Journal seriesInternational Journal of Mechanical Sciences, ISSN 0020-7403
Issue year2013
Publication size in sheets0.5
Keywords in EnglishFractional calculus, Non-linear mechanical systems, Asphalt–aggregate mixes, Rheology, Viscoelasticity, Plasticity
ASJC Classification2210 Mechanical Engineering; 2211 Mechanics of Materials; 3104 Condensed Matter Physics; 2500 General Materials Science; 2205 Civil and Structural Engineering
Languageen angielski
Score (nominal)40
Score sourcejournalList
ScoreMinisterial score = 35.0, 26-06-2020, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 26-06-2020, ArticleFromJournal
Publication indicators Scopus Citations = 46; WoS Citations = 37; GS Citations = 57.0; Scopus SNIP (Source Normalised Impact per Paper): 2013 = 2.331; WoS Impact Factor: 2013 = 2.061 (2) - 2013=2.168 (5)
Citation count*57 (2020-08-23)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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