Skip to main content
SpringerLink
Log in

Nonlinear dynamic characterization of a new hysteretic device: experiments and computations

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The nonlinear dynamical behavior of the hysteretic rheological device proposed in Carboni et al. (J Eng Mech 2014) is investigated. The device can provide nonlinear hysteretic forces to a one-degree-of-freedom (one-dof) mass through suitable assemblies of NiTiNOL and steel wire ropes subject to tension–flexure cycles. The simultaneous occurrence of interwire friction, phase transformations and geometric nonlinearities is the key feature of the obtained material behavior. Frequency-response curves (FRCs) of the system subject to base excitation are obtained numerically via a continuation procedure together with stability analysis and experimentally by carrying out shaking table tests, respectively. The phenomenological identification of the material behaviors through force–displacement cycles, reported in Carboni et al. (J Eng Mech 2014), is employed for the computation of the FRCs and the equivalent damping ratios as function of the displacement amplitude. The different restoring forces give rise to whole new families of nonlinear hysteretic oscillators governed by softening, hardening and softening–hardening behaviors depending on the oscillation amplitude.

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
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Baber, T., Noori, M.: Random vibration of degrading, pinching systems. J. Eng. Mech. 111(8), 1010–1026 (1985)

    Article  Google Scholar 

  2. Baber, T., Noori, M.: Modeling general hysteresis behavior and random vibration application. J. Vib. Acoust. Stress Reliab. Design 108(4), 411–420 (1986)

    Article  Google Scholar 

  3. Baber, T., Wen, Y.: Random vibration hysteretic, degrading systems. J. Eng. Mech. Div. 107(6), 1069–1087 (1981)

    Google Scholar 

  4. Bastien, J., Schatzman, M., Lamarque, C.H.: Study of some rheological models with a finite number of degrees of freedom. Eur. J. Mech. A/Solids 19(2), 277–307 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bernardini, D., Pence, T.J.: Mathematical models for shape memory materials. In: Schwartz, M. (ed.) Smart materials, pp. 20.17–20.28. CRC Press, Boca Raton (2009)

  6. Bouc, R.: Forced vibration of mechanical systems with hysteresis. In: Proceedings of the Fourth Conference on Non-linear Oscillation, Prague, Czechoslovakia (1967)

  7. Capecchi, D.: Periodic response and stability of hysteretic oscillators. Dyn. Stab. Syst. 6(2), 89–106 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  8. Capecchi, D.: Asymptotic motions and stability of the elastoplastic oscillator studied via maps. Int. J. Solids Struct. 30(23), 3303–3314 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Capecchi, D.: Coupling and resonance phenomena in dynamic systems with hysteresis. In: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics: Proceedings of the Iutam Symposium Held in Ithaca, NY, USA, vol. 63. Springer, Berlin, 27 July-1 August 1997 (1998)

  10. Capecchi, D., Vestroni, F.: Steady-state dynamic analysis of hysteretic systems. J. Eng. Mech. 111(12), 1515–1531 (1985)

    Article  Google Scholar 

  11. Capecchi, D., Vestroni, F.: Periodic response of a class of hysteretic oscillators. Int. J. Non-Linear Mech. 25(2), 309–317 (1990)

    Article  MATH  Google Scholar 

  12. Carboni, B., Lacarbonara, W., Auricchio, F.: Hysteresis of multiconfiguration assemblies of nitinol and steel strands: experiments and phenomenological identification. J. Eng. Mech. (2014)

  13. Casalotti, A., Lacarbonara, W.: Nonlinear vibration absorber optimal design via asymptotic approach. In: P. Hagedorn (ed.) IUTAM Symposium on Analytical Methods in Nonlinear Dynamics: Proceedings of the Iutam Symposium Held in Frankfurt, Germany, 6–9 July 2015. Elsevier, Amsterdam (2015)

  14. Caughey, T.: Sinusoidal excitation of a system with bilinear hysteresis. J. Appl. Mech. 27(4), 640–643 (1960)

    Article  MathSciNet  Google Scholar 

  15. Foliente, G.: Hysteresis modeling of wood joints and structural systems. J. Struct. Eng. 121(6), 1013–1022 (1995)

    Article  Google Scholar 

  16. Gendelman, O.V.: Targeted energy transfer in systems with non-polynomial nonlinearity. J. Sound Vib. 315(3), 732–745 (2008)

    Article  Google Scholar 

  17. Gerges, R.: Model for the force–displacement relationship of wire rope springs. J. Aerosp. Eng. 21(1), 1–9 (2008)

    Article  Google Scholar 

  18. Inc M.: Matlab 2010b (1994–2014). Software Trade Mark

  19. Ivshin, Y., Pence, T.: A thermomechanical model for a one variant shape memory material. J. Intell. Mater. Syst. Struct. 5(4), 455–473 (1994)

    Article  MathSciNet  Google Scholar 

  20. Ko, J., Ni, Y., Tian, Q.: Hysteretic behavior and emperical modeling of a wire-cable vibration isolator. Digital Library and Archives of the Virginia Tech University Libraries (1992)

  21. Lacarbonara, W.: Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling. Springer, Berlin (2013)

    Book  Google Scholar 

  22. Lacarbonara, W., Bernardini, D., Vestroni, F.: Periodic and nonperiodic responses of shape-memory oscillators. In: Proceedings of the 18th Biennial ASME Conference on Mechanical Vibration and Noise, pp. 9–12 (2001)

  23. Lacarbonara, W., Bernardini, D., Vestroni, F.: Nonlinear thermomechanical oscillations of shape-memory devices. Int. J. Solids Struct. 41(5), 1209–1234 (2004)

    Article  MATH  Google Scholar 

  24. Lacarbonara, W., Vestroni, F.: Nonclassical responses of oscillators with hysteresis. Nonlinear Dyn. 32(3), 235–258 (2003)

    Article  MATH  Google Scholar 

  25. Lacarbonara, W., Vestroni, F., Capecchi, D.: Poincaré map-based continuation of periodic orbits in dynamic discontinuous and hysteretic systems. In: Proceedings of the 17th Biennial ASME Conference on Mechanical Vibration and Noise, pp. 12–15 (1999)

  26. Lamarque, C.H., Bernardin, F., Bastien, J.: Study of a rheological model with a friction term and a cubic term: deterministic and stochastic cases. Eur. J. Mech. A/Solids 24(4), 572–592 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  27. Lamarque, C.H., Gendelman, O.V., Savadkoohi, A.T., Etcheverria, E.: Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech. 221(1–2), 175–200 (2011)

    Article  MATH  Google Scholar 

  28. Luongo, A., Zulli, D.: Dynamic analysis of externally excited NES-controlled systems via a mixed multiple scale/harmonic balance algorithm. Nonlinear Dyn. 70(3), 2049–2061 (2012)

    Article  MathSciNet  Google Scholar 

  29. Manevitch, L.: The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn. 25(1–3), 95–109 (2001)

  30. Nayfeh, A., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley, New York (1995)

    Book  MATH  Google Scholar 

  31. Ni, Y., Ko, J., Wong, C., Zhan, S.: Modelling and identification of a wire-cable vibration isolator via a cyclic loading test. Proc. Inst. Mech. Eng. Part I 213(3), 163–172 (1999)

    Article  Google Scholar 

  32. Ni, Y., Koh, J., Wong, C., Zhan, S.: Modelling and identification of a wire-cable vibration isolator via a cyclic loading test. pt. 2: identification and response prediction. Proc. Inst. Mech. Eng. Pt. 213, 173–182 (1999)

    Google Scholar 

  33. Okuizumi, N., Kimura, K.: Multiple time scale analysis of hysteretic systems subjected to harmonic excitation. J. Sound Vib. 272(3), 675–701 (2004)

    Article  Google Scholar 

  34. Sauter, D., Hagedorn, P.: On the hysteresis of wire cables in stockbridge dampers. Int. J. Non-linear Mech. 37(8), 1453–1459 (2002)

    Article  MATH  Google Scholar 

  35. Sireteanu, T., Giuclea, M., Mitu, A.: Identification of an extended bouc-wen model with application to seismic protection through hysteretic devices. Comput. Mech. 45(5), 431–441 (2010)

    Article  MATH  Google Scholar 

  36. Visintin, A.: Differential Models of Hysteresis, vol. 111. Springer Science & Business Media, Berlin (2013)

    Google Scholar 

  37. Wen, Y.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. 102(2), 249–263 (1976)

    Google Scholar 

Download references

Acknowledgments

The partial support of the Italian Ministry of Education, University and Scientific Research (2010–2011 PRIN Grant No. 2010BFXRHS-002) and of Sapienza University (Grant No. C26A13JPY9) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza University of Rome, Via Eudossiana 18, 00184, Rome, Italy

    Biagio Carboni & Walter Lacarbonara

Authors
  1. Biagio Carboni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Walter Lacarbonara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Walter Lacarbonara.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carboni, B., Lacarbonara, W. Nonlinear dynamic characterization of a new hysteretic device: experiments and computations. Nonlinear Dyn 83, 23–39 (2016). https://doi.org/10.1007/s11071-015-2305-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2305-9

Keywords

Search

Navigation