Skip to main content
SpringerLink
Log in

Predicting Limit Cycle of Modified Rayleigh Differential Equation

  • Conference paper
  • First Online:
Advances in Nonlinear Dynamics, Volume I (ICNDA 2023)

Part of the book series: NODYCON Conference Proceedings Series ((NCPS))

Included in the following conference series:

  • 48 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Mostaghel, N., Davis, T.: Representations of coulomb friction for dynamic analysis. Earthq. Eng. Struct. Dyn. 26(5), 541–548 (1997)

    Article  Google Scholar 

  2. Rao, S.S.: Mechanical Vibrations. Prentice Hall, Englewood Cliffs (2010)

    Google Scholar 

  3. Thomson, W.T.: Theory of Vibration with Applications. CRC Press, Boca Raton (2018)

    Book  Google Scholar 

  4. Grimshaw, R.: Nonlinear Ordinary Differential Equations, vol. 2. CRC Press, Boca Raton (1991)

    Google Scholar 

  5. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. John Wiley & Sons, London (2008)

    Google Scholar 

  6. Shaw, S.W.: On the dynamic response of a system with dry friction. J. Sound Vib. 108(2), 305–325 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  7. Marino, L., Cicirello, A., Hills, D.A.: Displacement transmissibility of a coulomb friction oscillator subject to joined base-wall motion. Nonlinear Dyn. 98(4), 2595–2612 (2019)

    Article  Google Scholar 

  8. Feeny, B, Moon, F.C.: Chaos in a forced dry-friction oscillator: experiments and numerical modelling. J. Sound Vib. 170(3), 303–323 (1994)

    Article  ADS  Google Scholar 

  9. Elmer, F.J.: Nonlinear dynamics of dry friction. J. Phys. A: Math. Gener. 30(17), 6057 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  10. Dominic Jordan and Peter Smith. Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers, vol. 11. Oxford University Press, Oxford (2007)

    Book  Google Scholar 

  11. Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, Boca Raton (2018)

    Book  Google Scholar 

  12. Peters, R.D., Pritchett, T.: The not-so-simple harmonic oscillator. Am. J. Phys. 65(11), 1067–1073 (1997)

    Article  ADS  Google Scholar 

  13. Vitorino, M.V., Vieira, A., Rodrigues, M.S.: Effect of sliding friction in harmonic oscillators. Sci. Rep. 7(1), 1–7 (2017)

    Article  Google Scholar 

  14. Den Hartog, J.P.: Forced vibrations with combined coulomb and viscous damping. Trans. ASME 53, 107–115 (1931)

    Google Scholar 

  15. Hundal, M.S.: Response of a base excited system with coulomb and viscous friction. J. Sound Vib. 64(3), 371–378 (1979)

    Article  ADS  Google Scholar 

  16. Hess, D.P., Soom, A.: Normal vibrations and friction at a Hertzian contact under random excitation: perturbation solution. J. Sound Vib. 164(2), 317–326 (1993)

    Article  ADS  Google Scholar 

  17. Ferretti, G., Magnani, G., Rocco, P.: An integral friction model. In: IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA’04. 2004, vol. 2, pp. 1809–1813. IEEE, Piscataway (2004)

    Google Scholar 

  18. Marchewka, A., Abbott, D.S., Beichner, R.J.: Oscillator damped by a constant-magnitude friction force. Am. J. Phys. 72(4), 477–483 (2004)

    Article  ADS  Google Scholar 

  19. Meirovitch, L.: Fundamentals of Vibrations. Waveland Press (2010)

    Google Scholar 

  20. López, M.A., Martínez, R.: A note on the generalized Rayleigh equation: limit cycles and stability. J. Math. Chem. 51(4), 1164–1169 (2013)

    Article  MathSciNet  Google Scholar 

  21. Akbari, M.R., Ganji, D.D., Majidian, A., Ahmadi, A.R.: Solving nonlinear differential equations of Van der pol, Rayleigh and Duffing by AGM. Front. Mech. Eng. 9(2), 177–190 (2014)

    Article  Google Scholar 

  22. Arosh, L.B., Cross, M.C., Lifshitz, R.: Quantum limit cycles and the Rayleigh and Van der pol oscillators. Phys. Rev. Res. 3(1), 013130 (2021)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Prof. K R Y Simha, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, for this valuable input. The authors would like to thank Prof. Andy Ruina, Department of Mechanical Engineering, Cornell University, for his encouragement to pursue this work.

Author information

Authors and Affiliations

  1. Department of Mechanical, Materials and Aerospace Engineering, Indian Institute of Technology Dharwad, Karnataka, India

    Venkoba Shrikanth, Amar K. Gaonkar & Pramod Kumar Verma

Authors
  1. Venkoba Shrikanth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amar K. Gaonkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pramod Kumar Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Venkoba Shrikanth .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Roma, Roma, Italy

    Walter Lacarbonara

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Shrikanth, V., Gaonkar, A.K., Verma, P.K. (2024). Predicting Limit Cycle of Modified Rayleigh Differential Equation. In: Lacarbonara, W. (eds) Advances in Nonlinear Dynamics, Volume I. ICNDA 2023. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-031-50631-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation