Skip to main content

Experimental Analysis of a Nonlinear Piecewise Multi-degrees-of-Freedom System

  • 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:

  • 61 Accesses

Abstract

The growing industrial demand for lightweight and low-carbon emission systems is eroding the safety factors adopted in the linear design of vehicles and structures. This exposes the ultimately nonlinear nature of mechanical systems, creating the need for a better understanding of their nonlinear behaviour. In this context, we have experimentally investigated the dynamic behaviour of a nonlinear two-degree-of-freedom mechanical system with piecewise stiffness characteristics. The system is clamped at both ends, and one constraint is directly excited by a shaker. The system allows the adjustment of non-contact gaps and stiffness of the piecewise characteristic and provides a valuable resource for the validation and verification of numerical studies in this field. The experimental results show the very rich dynamics of the system, revealing the presence of quasi-periodic, chaos, and multi-periodic responses as well as branches of bifurcating stable solutions.

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

Access this chapter

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. Wagg, D., Neild, S.: Nonlinear Vibration with Control: For Flexible and Adaptive Structures, vol. 218, 2nd edn. Springer, Berlin (2015). http://www.springer.com/series/6557

    Book  Google Scholar 

  2. Noël, J.P., Kerschen, G.: Mech. Syst. Signal Process. 83, 2 (2017). https://doi.org/10.1016/j.ymssp.2016.07.020

    Article  ADS  Google Scholar 

  3. Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C.: Mech. Syst. Signal Process. 20(3), 505 (2006)

    Article  ADS  Google Scholar 

  4. Yang, T., Zhou, S., Fang, S., Qin, W., Inman, D.J.: Appl. Phys. Rev. 8 (2021). https://doi.org/10.1063/5.0051432

  5. Hajjaj, A.Z., Jaber, N., Ilyas, S., Alfosail, F.K., Younis, M.I.: Int. J. Non-Linear Mech. 119 (2020). https://doi.org/10.1016/j.ijnonlinmec.2019.103328

  6. Sharma, S., Coetzee, E.B., Lowenberg, M.H., Neild, S.A., Krauskopf, B.: Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 373 (2015). https://doi.org/10.1098/rsta.2014.0406

  7. Younesian, D., Hosseinkhani, A., Askari, H., Esmailzadeh, E.: Nonlinear Dyn. 97, 853 (2019). https://doi.org/10.1007/s11071-019-04977-9

    Article  Google Scholar 

  8. di Bernardo, M., Budd, C., Champneys, A., Kowalczyk, P.: Piecewise-Smooth Dynamical Systems: Theory and Applications, 1st edn. Springer, London (2009)

    Google Scholar 

  9. Chin, W., Ott, E., Nusse, H.E., Grebogi, C.: Phys. Rev. E pp. 4427–4444 (1994). https://doi.org/10.1103/Phys. https://hal.archives-ouvertes.fr/hal-01386141

  10. Yin, S., Ji, J., Wen, G.: Int. J. Mech. Sci. 156, 106 (2019). https://doi.org/10.1016/j.ijmecsci.2019.03.023

    Article  Google Scholar 

  11. Vasconcellos, R., Abdelkefi, A., Hajj, M.R., Marques, F.D.: Commun. Nonlinear Sci. Numer. Simul. 19, 1611 (2014). https://doi.org/10.1016/j.cnsns.2013.09.022

    Article  ADS  MathSciNet  Google Scholar 

  12. Ing, J., Pavlovskaia, E., Wiercigroch, M.: In: IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, pp. 135–143 (2010). www.springer.com/series/7695

  13. Saunders, B.E., Vasconcellos, R., Kuether, R.J., Abdelkefi, A.: Int. J. Mech. Sci. 210 (2021). https://doi.org/10.1016/j.ijmecsci.2021.106729

  14. Alcorta, R., Baguet, S., Prabel, B., Piteau, P., Jacquet-Richardet, G.: Nonlinear Dyn. 98, 2939 (2019). https://doi.org/10.1007/s11071-019-05245-6

    Article  Google Scholar 

  15. Martinelli, C., Coraddu, A., Cammarano, A.: Nonlinear Dyn. 111 (2023). https://doi.org/10.1007/s11071-023-08293-1

  16. Shaw, S., Holmes, P.J.: J. Sound Vib. (1983). https://hal.archives-ouvertes.fr/hal-01509017

  17. Andreaus, U., De Angelis, M.: Nonlinear Dyn. 84, 1447 (2016). https://doi.org/10.1007/s11071-015-2581-4

    Article  Google Scholar 

  18. Saunders, B.E., Vasconcellos, R., Kuether, R.J., Abdelkefi, A.: Nonlinear Dyn. 107, 1479 (2022). https://doi.org/10.1007/s11071-021-06436-w

    Article  Google Scholar 

  19. Dai, H., Yue, X., Yuan, J., Xie, D., Atluri, S.N.: Nonlinear Dyn. 81, 169 (2015). https://doi.org/10.1007/s11071-015-1980-x

    Article  Google Scholar 

  20. Chávez, J.P., Pavlovskaia, E., Wiercigroch, M.: Nonlinear Dyn. 77, 213 (2014). https://doi.org/10.1007/s11071-014-1285-5

    Article  Google Scholar 

  21. Chávez, J.P., Liu, Y., Pavlovskaia, E., Wiercigroch, M.: Commun. Nonlinear Sci. Numer. Simul. 37, 102 (2016). https://doi.org/10.1016/j.cnsns.2016.01.009

    Article  ADS  MathSciNet  Google Scholar 

  22. Lelkes, J., Kalmár-Nagy, T.: Nonlinear Dyn. 103, 2997 (2021). https://doi.org/10.1007/s11071-020-05725-0

    Article  Google Scholar 

  23. Castrichini, A., Wilson, T., Saltari, F., Mastroddi, F., Viceconti, N., Cooper, J.E.: J. Aircraft 57, 333 (2020). https://doi.org/10.2514/1.C035602

    Article  Google Scholar 

  24. Huang, R., Zhou, X.: AIAA J. 59, 2641 (2021). https://doi.org/10.2514/1.J059347

    Article  ADS  Google Scholar 

  25. Mélot, A., Benaïcha, Y., Rigaud, E., Perret-Liaudet, J., Thouverez, F.: J. Sound Vib. 516 (2022). https://doi.org/10.1016/j.jsv.2021.116495

  26. Wang, C., Zhang, Q., Wang, W.: J. Sound Vib. 399, 169 (2017). https://doi.org/10.1016/j.jsv.2017.02.048

    Article  ADS  Google Scholar 

  27. Fasihi, A., Shahgholi, M., Ghahremani, S.: J. Vib. Control 0, 1 (2021). https://doi.org/10.1177/1077546321993585

  28. Geng, X.F., Ding, H.: J. Sound Vib. 520 (2022). https://doi.org/10.1016/j.jsv.2021.116667

  29. deLangre, E., Lebreton, G.: In: ASME 8th International Conference on Pressure Vessel Technology, p. 33 (1996)

    Google Scholar 

  30. Wiercigroch, M.: Chaos Solitons Fractals 11, 2429 (2000). www.elsevier.nl/locate/chaos

    Article  ADS  MathSciNet  Google Scholar 

  31. Geng, X.F., Ding, H., Mao, X.Y., Chen, L.Q.: Mech. Syst. Signal Process. 156 (2021). https://doi.org/10.1016/j.ymssp.2021.107625

  32. Wang, X., Geng, X.F., Mao, X.Y., Ding, H., Jing, X.J., Chen, L.Q.: Mech. Syst. Signal Process. 172 (2022). https://doi.org/10.1016/j.ymssp.2022.109001

  33. Ewins, D.J.: Modal Testing: Theory, Practice and Application. John Wiley & Sons, London (2009)

    Google Scholar 

  34. Worden, K., Tomlinson, G.R.: Nonlinearity in Structural Dynamics: Detection, Identification and Modelling. CRC Press, Boca Raton (2001)

    Book  Google Scholar 

  35. Cammarano, A., Hill, T.L., Neild, S.A., Wagg, D.J.: Nonlinear Dyn. 77, 311 (2014). https://doi.org/10.1007/s11071-014-1295-3

    Article  Google Scholar 

  36. Natsiavas, S.: J. Sound Vib. 165, 439 (1993). https://doi.org/10.1006/jsvi.1993.1269. https://hal.science/hal-01510834

  37. Martinelli, C., Coraddu, A., Cammarano, A.: Enlighten Research Data (2023). https://doi.org/10.5525/gla.researchdata.1471

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cristiano Martinelli .

Editor information

Editors and Affiliations

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

Martinelli, C., Coraddu, A., Cammarano, A. (2024). Experimental Analysis of a Nonlinear Piecewise Multi-degrees-of-Freedom System. 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_56

Download citation

Publish with us

Policies and ethics