Skip to main content
SpringerLink
Log in

Resonance study of fractional-order strongly nonlinear duffing systems

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

This article takes a class of strongly nonlinear Duffing systems with fractional-order terms as the research object, studying their main resonance and conditions for chaos under single-frequency excitation. The approximate analytical solution of the main resonance of the system under single-frequency excitation is obtained by the multi-scale method. The approximate analytical solution is utilized to construct the steady-state motion's amplitude–frequency response equation, and Lyapunov's first method is used to determine the constant solution's stability condition, which is then used to analyze the steady-state motion's stability. The system is examined by using the Melnikov method to identify the circumstances that would appear to result in a transverse intersection of heterodox orbits and the onset of chaos in the system. The amplitude–frequency characteristics of the total response of the system at various excitation frequencies are investigated in numerical simulations using analytical and simulation methods, respectively, and the system makes a comparison of amplitude–frequency curves, confirming that the numerical results and results achieve a consistent trend. The effects of nonlinear stiffness coefficients, excitation amplitude, fractional-order differential term order and fractional-order differential term coefficients on the system's amplitude–frequency response are each examined in turn. A numerical investigation of the effects of system parameters on chaotic motion is then conducted using many kinds of diagrams .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability statement

All data generated or analyzed during this study are included in this published article.

References

  1. P Prommee, P Pienpichayapong, N Manositthichai et al AEU: Archiv fur Elektronik und Ubertragungstechnik: Electronic and Communication. 128 (2021)

  2. A Z Mohammad and A K Ali Journal of Computational and Applied Mathematics. 438 1 (2024)

    Google Scholar 

  3. D Yan, W Wang, Q Chen Chaos Soliton Fract. 133 (2020)

  4. P Y Xiong, F E Alsaadi et al Chaos, Solitons and Fractals.144 (2021)

  5. S Dadras, H R. Momeni Physica A: Physica A. 389 2434 (2010)

  6. L Chaib, A Choucha and S Arif Ain Shams Eng J. 8 113 (2017)

    Article  Google Scholar 

  7. S P Nangrani S S Bhat Asian J Control. 20 403 (2018)

    Article  MathSciNet  Google Scholar 

  8. G Tzounas, I Dassios, M A Murad et al Ieee T Power Syst. 35 4622 (2020)

    Article  Google Scholar 

  9. S A Hosseini Scientia Iranica. 20 1464 (2013)

    Article  Google Scholar 

  10. A Kimiaeifar and A R Saidi Solution & Fractals. 42 2660 (2009)

    Article  ADS  Google Scholar 

  11. K Zhao J Li Chinese Journal of Physics. 77 1796 (2022)

    Article  ADS  Google Scholar 

  12. K B Kachhia, B Krunal Partial Differential Equations in Applied Mathematics. 7 (2023)

  13. P Perdikaris G E Karniadakis Ann Biomed Eng. 42 1012 (2014)

    Article  Google Scholar 

  14. A Raza, M Farman, A Akgül et al Aims Bioeng. 7 194 (2020)

    Article  Google Scholar 

  15. D Kumar D Baleanu Front Phys-Lausanne. 7 81 (2019)

    Article  Google Scholar 

  16. M A Abdou Indian J Phys. 93 537 (2019)

    Article  ADS  Google Scholar 

  17. D Guo, G Yang, X Feng et al J Energy Storage. 30 (2020)

  18. S Sarwar and M M Rashidi Wave Random Complex. 26 365 (2016)

    Article  ADS  Google Scholar 

  19. H M Baskonus, T Mekkaoui, Z Hammouch et al Entropy-Switz. 17 5771 (2015)

    Article  ADS  Google Scholar 

  20. A Yousefpour, H Jahanshahi, J M Munoz-Pacheco et al Chaos Soliton Fract. 130 (2020)

  21. Z Wang and X Huang H Shen Neurocomputing. 83 83 (2012)

    Article  Google Scholar 

  22. K Zhou, Z H Wang, L K Gao et al Chinese Phys B. 24 (2015)

  23. Q Zhou, J Gao, Z Wang et al Ieee T Geosci Remote. 54 1905 (2015)

    Article  ADS  Google Scholar 

  24. F H Li and Z F Li Earthquake Science. 36 81 (2023)

    Article  ADS  Google Scholar 

  25. Y Wang, Y Ning and Y Wang Energies. 13 5901 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

The project is supported by the Fundamental Research Program of Shanxi Province (20210302123207 and 20210302124009), National Natural Science Foundation of China (U22A20188), Shanxi Province Merit-based Funding Project for Scientific and Technological Activities of Returnees Studying Abroad (20230032),Shanxi Patent Transformation Special Plan Project(202201006 and 202202032), Taiyuan University of Science and Technology Joint Training Demonstration Base for Graduate Students (JD2022002), Taiyuan University of Science and Technology Graduate Innovation Project (BY2022004) and the Coordinative Innovation Center of Taiyuan Heavy Machinery Equipment,2022 Huai'an "Huaishang Talent Program" innovation and entrepreneurship team.

Funding

Funding was provided by University-level graduate innovation Project

Author information

Authors and Affiliations

  1. School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Jie Liu, Hailian Gui, Hao Liu & Chen Zhang

  2. Shanxi Provincial Key Laboratory of Metallurgical Device Design Theory and Technology, Taiyuan, 030024, China

    Peng Zhang & Tong Xing

  3. Highend Heavy Machinery Equipment Research Institute, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Tong Xing

  4. China School of Intelligent Engineering, Jin Zhong College of Information, Jinzhong, 030800, China

    Jie Liu

Authors
  1. Jie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hailian Gui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tong Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Chen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jie Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Zhang, P., Gui, H. et al. Resonance study of fractional-order strongly nonlinear duffing systems. Indian J Phys (2024). https://doi.org/10.1007/s12648-024-03080-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12648-024-03080-z

Keywords

Search

Navigation