Pollack Periodica
Volume/Issue:
Volume 13: Issue 3
Numerical examination of nonlinear oscillators
Author:
Flóra Hajdu Széchenyi István University, Egyetem tér 1. H-9026 Győr, Hungary

Search for other papers by Flóra Hajdu in
Current site
Google Scholar
PubMed Close
Pages:
95–106
Online Publication Date:
Dec 2018
Publication Date:
01 Dec 2018
Article Category:
Research Article
DOI:
https://doi.org/10.1556/606.2018.13.3.10
Keywords:
Nonlinear oscillator; Numerical simulation; System modeling
Restricted access

The numerical examination of nonlinear oscillators is presented in this paper. First some methods of nonlinear system modeling are described then the numerical creation of phaseplane, bifurcation diagrams and Poincaré sections are expounded in detail. The next part of the paper is the numerical examination of nonlinear oscillators, like the Duffing-Holmes oscillator and a mechatronic semi-active suspension system. The paper concludes with further development tasks.

  • [1]

    Fülep D. , Zsoldos I., Lászó I. Self-organised formation of nanotubes from graphene ribbons: A molecular dynamics study, Materials Research Express, Vol. 3, No. 10, 2016, paper 5044.

    • Search Google Scholar
    • Export Citation
  • [2]

    Zhang K. , Wu Y. S., Bodvarsson G.S. Parallel computing simulation of fluid flow in the unsaturated zone of Yucca Mountain, Nevada, Journal of Contaminant Hydrology, Vol. 62–63, 2003, pp. 381–399.

    • Search Google Scholar
    • Export Citation
  • [3]

    Krejci T. , Kruis J., Koudelka T. Sejnoha M. Processor farming in two-level analysis of historical bridge, Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Pécs, Hungary, 30-31 May 2017, Civil-Comp Press, Stirlingshire, UK, 2017, Paper 12.

    • Search Google Scholar
    • Export Citation
  • [4]

    Strofylas G. A. , Porfyri K. N., Nikolos I. K., Delis A. I., Papageorgiou M. Calibrating a traffic flow model with parallel differential evolution, Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Pécs, Hungary, 30-31 May 2017, Civil-Comp Press, Stirlingshire, UK, Paper 26.

    • Search Google Scholar
    • Export Citation
  • [5]

    Takács D. , Stépán G. Contact patch memory of tyres leading to lateral vibrations of fourwheeled vehicles, Philosophical Transactions of the Royal Society A, Mathematical Physical and Engineering Sciences, Vol. 371, No. 1993, 2013, Paper 20120427, p. 12.

    • Search Google Scholar
    • Export Citation
  • [6]

    Pidl R. Consideration on road transport vibration simulation techniques for packaging testing purposes, Acta Technica Jaurinensis, Vol 10. No. 2, 2017, pp. 137–147.

    • Search Google Scholar
    • Export Citation
  • [7]

    Stépán G. Delay-differential equation models for machine tool chatter, Dynamics and Chaos in Manufacturing Processes, Vol. 471152935, 1998, pp. 165-192.

    • Search Google Scholar
    • Export Citation
  • [8]

    Schiffer A , Ivanyi A. Vibration of transformer sheets using non-linear characteristics, Journal of Physics, Conference Series, Vol. 268:, 2011, paper 012027.

    • Search Google Scholar
    • Export Citation
  • [9]

    Peluffo-Ordonez D. H. , Rodríguez-Sotelo J. L., Revelo-Fuelagán E. J., Ospina-Aguirre C., Olivard-Tost G. Generalized Bonhoeffer-van der Pol oscillator for modeling cardiac pulse: Preliminary results, 2015 IEEE 2nd Colombian Conference on Automatic Control, Manizales, Colombia, 14-16 October 2015, DOI: 10.1109/CCAC.2015.7345211

    • Search Google Scholar
    • Export Citation
  • [10]

    Facchinetti M. L. , Langre E., Biolley F. Vortex shedding modeling using diffusive van der Pol oscillators, Comptes Rendus Mécanique, Vol. 330, No 7, 2002, pp. 451–456.

    • Search Google Scholar
    • Export Citation
  • [11]

    Dumitrescu I. , Bachir S., Cordeau D., Paillot J. M., Iordache M. Modeling and characterization of oscillator circuits by Van Der Pol model using parameter estimation, Journal of Circuits, Systems, and Computers, Vol. 21. No. 5. 2012, paper 1250043.

    • Search Google Scholar
    • Export Citation
  • [12]

    Chian A. C. L. Complex systems approach to economic dynamics, Springer-Verlag, Berlin Heidelberg, 2007.

  • [13]

    Wang L. Reliable design of tunnel diode and resonant tunnelling diode based microwave sources, PhD Thesis, University of Glasgow, 2012.

    • Search Google Scholar
    • Export Citation
  • [14]

    Garay B. Nonlinear dynamical systems (in Hungarian), Pázmány Péter Catholic University, 2013, http://www.tankonyvtar.hu/en/tartalom/tamop412A/2011-0052_20_nemlinearis_dinamikus_rendszerek/index.html (last visited 12 November 2017).

    • Search Google Scholar
    • Export Citation
  • [15]

    Khalil H. K. Nonlinear systems, Prentice Hall, 1999.

  • [16]

    Bayat M. , Pakar I. On the approximate analytical solution to non-linear oscillation systems, Shock and Vibration, Vol. 20, No. 1, 2013, pp. 4–52.

    • Search Google Scholar
    • Export Citation
  • [17]

    Abdelhafez H. M. Solution of excited non-linear oscillators under damping effects using the modified differential transform method, Mathematics, Vol. 4, No. 1. 2016, p. 12.

    • Search Google Scholar
    • Export Citation
  • [18]

    Maróti Gy. Investigating parameterized model of n-gonal wheel’s motion, Pollack Periodica, Vol. 6, No. 2, 2011, pp. 4–36.

  • [19]

    Maróti Gy. Finding closed-form solutions of beam vibration, Pollack Periodica, Vol. 6, No. 1, 2011, pp. 4–154.

  • [20]

    Lynch S. Dynamical systems with applications using maple, Birkhäuser Boston, 2010.

  • [21]

    Perjési-Hámori I. Two dimensional mathematical model of heat-transmission using MAPLE, IFAC-PapersOnLine, Vol. 48, No. 1, 2015 pp. 689–690.

    • Search Google Scholar
    • Export Citation
  • [22]

    Hajdu F. Numerical examination of a nonlinear circuit element (in Hungarian), Proceedings of the 5th Interdisciplinary Doctoral Conference Conference, Pécs, Hungary, 27-29 May 2016, pp. 142–154.

    • Search Google Scholar
    • Export Citation
  • [23]

    Hajdu F. , Molnárka Gy. Parallelization of numerical examination of nonlinear systems using Maple, Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Pécs, Hungary, 30-31 May 2017, Civil-Comp Press, Stirlingshire, UK, Paper 30.

    • Search Google Scholar
    • Export Citation
  • [24]

    Aguierre L. A. A tutorial introduction to nonlinear dynamics and chaos, Part 1, Tools and benchmarks, SBA Controle & Automacao, Vol. 7, No. 1, 1996, pp. 4–49.

    • Search Google Scholar
    • Export Citation
  • [25]

    Kuznetsov Y. A. Elements of applied bifurcation theory, Springer, 1998.

  • [26]

    Garay B. M. , Indig B. Chaos in Vallis’ asymmetric Lorenz model for El Niño, Chaos, Solitons & Fractals, Vol. 75, 2015, pp. 3–262.

  • [27]

    Hajdu F. , Molnárka Gy. Numerical examination of a system model with a nonlinear component, Proceedings of the 8th International Scientific and Expert Conference, Trnava, Slovakia, 19-21 October 2016, pp. 12–16.

    • Search Google Scholar
    • Export Citation
  • [28]

    Billings S. A. , Boaghe O. M. The response spectrum map, a frequency domain equivalent to the bifurcation diagram, International Journal of Bifurcation and Chaos, Vol. 11, No. 7, 2001, pp. 4–1975.

    • Search Google Scholar
    • Export Citation
  • [29]

    Kuczmann M. Fourier transform and controlling of flux in scalar hysteresis measurement, Physica B: Condensed Matter, Vol. 403 No.2-3, 2008 pp. 410–413.

    • Search Google Scholar
    • Export Citation
  • [30]

    Maple soft: new features in Maple 17, Signal processing, https://www.maplesoft.com/products/maple/new_features/maple17/signal_processing.aspx, (last visited 1 October 2017).

  • [31]

    Sári Z. Investigation of multi-valued, hysteresis-type nonlinearities in numerical field problems, PhD Thesis, Budapest University of Technology and Economics, 2012.

    • Search Google Scholar
    • Export Citation
  • [32]

    Sykora H. T. , Wedig W. V., Bachrathy D., Stépán G. Approximation of top Lyapunov exponent of stochastic delayed turning model using Fokker-Planck approach, Proceedings of the 9th European Nonlinear Dynamics Conference, Budapest, Hungary, 25-30 June 2017, Paper 429

    • Search Google Scholar
    • Export Citation
  • [33]

    Liu K. , Wang H., Xiao J., Taha Z. Analysis of human standing balance by largest Lyapunov exponent, Computational Intelligence and Neuroscience, 2015, Paper 158478.

    • Search Google Scholar
    • Export Citation
  • [34]

    Ivancevic V. G. , Ivancevic T. High-dimensional chaotic and attractor systems, Springer Netherlands, 2007.

  • [35]

    Égert J. , Jezsó K. Mechanics-vibrations (in Hungarian), Széchenyi István University, Győr, Hungary, 2006.

  • [36]

    Takashi K. Duffing oscillator, Scholarpedia, http://www.scholarpedia.org/article/Duffing_oscillator (last visited: 26.03.2018).

  • [37]

    Tam J. I. , Holmes P. Revisiting a magneto-elastic strange attractor, Journal of Sound and Vibration, Vol. 333, No. 6, 2014, pp. 4–1780.

    • Search Google Scholar
    • Export Citation
  • [38]

    Mojrzisch S. , Wallaschek J., Bremer J. An experimental method for the phase controlled frequency response measurement of nonlinear vibration systems, Proceedings in Applied Mathematics and Mechanics, Vol. 12, No. 1, 2012, pp. 4–254.

    • Search Google Scholar
    • Export Citation
  • [39]

    Donoso G. , Ladera C. L. Nonlinear dynamics of a magnetically driven Duffing-type spring–magnet oscillator in the static magnetic field of a coil, European Journal of Physics, Vol. 33, No. 6, 2012, pp. 4–1486.

    • Search Google Scholar
    • Export Citation
  • [40]

    Cottone F. , Basset P., Vocca H., Gammaitoni L. Electromagnetic buckled beam oscillator for enhanced vibration energy harvesting, IEEE International Conference on Green Computing and Communications, Besancon, France, 20-23 November 2012, doi: 10.1109/GreenCom.2012.151.

    • Search Google Scholar
    • Export Citation
  • [41]

    Litak G. , Borowiec M., Friswell M. I., Szabelski K. Chaotic vibration of a quarter-car model excited by the road surface profile, Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 7, 2008, pp. 4–1383.

    • Search Google Scholar
    • Export Citation
  • [42]

    Barbosa R. S. Vehicle dynamic response due to pavement roughness, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 33, No. 3, 2011, doi: 10.1590/S1678-58782011000300005

    • Search Google Scholar
    • Export Citation
  • [43]

    Fakhraei J. , Khanlo H. M., Ghayour M. Chaotic behaviors of a ground vehicle oscillating system with passengers, Scientia Iranica, Vol. 24, No. 3, 2017, pp. 4–1068.

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand
Cover Pollack Periodica
Pollack Periodica
Print ISSN:
1788-1994
Online ISSN:
1788-3911

Senior editors

Editor(s)-in-Chief: Iványi, Amália

Editor(s)-in-Chief: Iványi, Péter

 

Scientific Secretary

Miklós M. Iványi

Editorial Board

  • Bálint Bachmann (Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Jeno Balogh (Department of Civil Engineering Technology, Metropolitan State University of Denver, Denver, Colorado, USA)
  • Radu Bancila (Department of Geotechnical Engineering and Terrestrial Communications Ways, Faculty of Civil Engineering and Architecture, “Politehnica” University Timisoara, Romania)
  • Charalambos C. Baniotopolous (Department of Civil Engineering, Chair of Sustainable Energy Systems, Director of Resilience Centre, School of Engineering, University of Birmingham, U.K.)
  • Oszkar Biro (Graz University of Technology, Institute of Fundamentals and Theory in Electrical Engineering, Austria)
  • Ágnes Borsos (Institute of Architecture, Department of Interior, Applied and Creative Design, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Matteo Bruggi (Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Italy)
  • Petra Bujňáková (Department of Structures and Bridges, Faculty of Civil Engineering, University of Žilina, Slovakia)
  • Anikó Borbála Csébfalvi (Department of Civil Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Mirjana S. Devetaković (Faculty of Architecture, University of Belgrade, Serbia)
  • Szabolcs Fischer (Department of Transport Infrastructure and Water Resources Engineering, Faculty of Architerture, Civil Engineering and Transport Sciences Széchenyi István University, Győr, Hungary)
  • Radomir Folic (Department of Civil Engineering, Faculty of Technical Sciences, University of Novi Sad Serbia)
  • Jana Frankovská (Department of Geotechnics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
  • János Gyergyák (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Kay Hameyer (Chair in Electromagnetic Energy Conversion, Institute of Electrical Machines, Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Germany)
  • Elena Helerea (Dept. of Electrical Engineering and Applied Physics, Faculty of Electrical Engineering and Computer Science, Transilvania University of Brasov, Romania)
  • Ákos Hutter (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technolgy, University of Pécs, Hungary)
  • Károly Jármai (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
  • Teuta Jashari-Kajtazi (Department of Architecture, Faculty of Civil Engineering and Architecture, University of Prishtina, Kosovo)
  • Róbert Kersner (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Rita Kiss  (Biomechanical Cooperation Center, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary)
  • István Kistelegdi  (Department of Building Structures and Energy Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Stanislav Kmeť (President of University Science Park TECHNICOM, Technical University of Kosice, Slovakia)
  • Imre Kocsis  (Department of Basic Engineering Research, Faculty of Engineering, University of Debrecen, Hungary)
  • László T. Kóczy (Department of Information Sciences, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, University of Győr, Hungary)
  • Dražan Kozak (Faculty of Mechanical Engineering, Josip Juraj Strossmayer University of Osijek, Croatia)
  • György L. Kovács (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Balázs Géza Kövesdi (Department of Structural Engineering, Faculty of Civil Engineering, Budapest University of Engineering and Economics, Budapest, Hungary)
  • Tomáš Krejčí (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
  • Jaroslav Kruis (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
  • Miklós Kuczmann (Department of Automations, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, Széchenyi István University, Győr, Hungary)
  • Tibor Kukai (Department of Engineering Studies, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Maria Jesus Lamela-Rey (Departamento de Construcción e Ingeniería de Fabricación, University of Oviedo, Spain)
  • János Lógó  (Department of Structural Mechanics, Faculty of Civil Engineering, Budapest University of Technology and Economics, Hungary)
  • Carmen Mihaela Lungoci (Faculty of Electrical Engineering and Computer Science, Universitatea Transilvania Brasov, Romania)
  • Frédéric Magoulés (Department of Mathematics and Informatics for Complex Systems, Centrale Supélec, Université Paris Saclay, France)
  • Gabriella Medvegy (Department of Interior, Applied and Creative Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Tamás Molnár (Department of Visual Studies, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Ferenc Orbán (Department of Mechanical Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Zoltán Orbán (Department of Civil Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Dmitrii Rachinskii (Department of Mathematical Sciences, The University of Texas at Dallas, Texas, USA)
  • Chro Radha (Chro Ali Hamaradha) (Sulaimani Polytechnic University, Technical College of Engineering, Department of City Planning, Kurdistan Region, Iraq)
  • Maurizio Repetto (Department of Energy “Galileo Ferraris”, Politecnico di Torino, Italy)
  • Zoltán Sári (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Grzegorz Sierpiński (Department of Transport Systems and Traffic Engineering, Faculty of Transport, Silesian University of Technology, Katowice, Poland)
  • Zoltán Siménfalvi (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
  • Andrej Šoltész (Department of Hydrology, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
  • Zsolt Szabó (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Hungary)
  • Mykola Sysyn (Chair of Planning and Design of Railway Infrastructure, Institute of Railway Systems and Public Transport, Technical University of Dresden, Germany)
  • András Timár (Faculty of Engineering and Information Technology, University of Pécs, Hungary)
  • Barry H. V. Topping (Heriot-Watt University, UK, Faculty of Engineering and Information Technology, University of Pécs, Hungary)

POLLACK PERIODICA
Pollack Mihály Faculty of Engineering
Institute: University of Pécs
Address: Boszorkány utca 2. H–7624 Pécs, Hungary
Phone/Fax: (36 72) 503 650

E-mail: peter.ivanyi@mik.pte.hu 

or amalia.ivanyi@mik.pte.hu

Indexing and Abstracting Services:

  • SCOPUS
  • CABELLS Journalytics

 

2023  
Scopus  
CiteScore 1.5
CiteScore rank Q3 (Civil and Structural Engineering)
SNIP 0.849
Scimago  
SJR index 0.288
SJR Q rank Q3

Pollack Periodica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025 Online subsscription: 381 EUR / 420 USD
Print + online subscription: 456 EUR / 520 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

 

2023  
Scopus  
CiteScore 1.5
CiteScore rank Q3 (Civil and Structural Engineering)
SNIP 0.849
Scimago  
SJR index 0.288
SJR Q rank Q3

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jun 2024 4 0 0
Jul 2024 4 0 0
Aug 2024 15 0 0
Sep 2024 4 0 0
Oct 2024 14 0 0
Nov 2024 0 0 0
Dec 2024 0 0 0