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Mitigation of structural vibrations by hysteretic oscillators in internal resonance

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Abstract

The present paper deals with the dynamics of a two-degrees-of freedom system consisting of a nonlinear absorber attached to a primary linear structure under external excitations. The nonlinear attachment exhibits a hysteretic restoring force modeled with the classic Bouc–Wen law [hysteretic vibration absorber (HVA)]; furthermore, the mechanical characteristics of the nonlinear oscillator are tuned to regulate the ratio between the two natural frequencies and to lead the system near to internal resonance conditions. The steady-state periodic solutions are investigated, and particular attention is given to the study of modal interactions by means of frequency response curves for various excitation levels. A parametric investigation is performed to analytically detect the conditions for the occurrence of (n : 1) internal resonances for low and high external excitations. Finally, specific resonance conditions have been found under which the nonlinear attachment produces a notable reduction of the vibration amplitude of the primary system for a wide range of the excitation level. The aim of the paper is therefore twofold: the first purpose is to investigate the effect of the hysteretic dam** on the passive mitigation of structural vibrations. The second purpose is to improve the system capacity of mitigating structural vibrations, by optimally choosing the characteristics of the HVA.

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References

  1. Hartog, J.D.: Mechanical Vibrations. McGraw-Hill, New York (1934)

    MATH  Google Scholar 

  2. Haxton, R., Barr, A.: The autoparametric vibration absorber. J. Eng. Ind. 94, 119–125 (1972)

    Article  Google Scholar 

  3. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  4. Nayfeh, A.H., Balachandran, B.: Modal interactions in dynamical and structural systems. Appl. Mech. Rev. 42(11S), S175–S201 (1989)

    Article  MathSciNet  Google Scholar 

  5. Vakakis, A.F.: Intentional utilization of strong nonlinearity in structural dynamics. Proc. Eng. 199, 70–77 (2017)

    Article  Google Scholar 

  6. Natsiavas, S.: Steady state oscillations and stability of non-linear dynamic vibration absorbers. J. Sound Vib. 156, 227–245 (1992)

    Article  Google Scholar 

  7. Bernardini, D., Vestroni, F.: Hysteretic modeling of shape-memory alloy vibration reduction devices. J. Mater. Proces. Manuf. Sci. 9, 101–112 (2000)

    Article  Google Scholar 

  8. Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Kerschen, G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50, 651–677 (2007)

    Article  Google Scholar 

  9. Tso, M.H., Yuan, J., Wong, W.O.: Design and experimental study of a hybrid vibration absorber for global vibration control. Eng. Struct. 56, 1058–1069 (2013)

    Article  Google Scholar 

  10. Carpineto, N., Lacarbonara, W., Vestroni, F.: Hysteretic tuned mass dampers for structural vibration mitigation. J. Sound Vib. 333, 1302–1318 (2013)

    Article  Google Scholar 

  11. Carboni, B., Lacarbonara, W.: Nonlinear dynamic characterization of a new hysteretic device: experiments and computations. Nonlinear Dyn. 83, 23–39 (2016)

    Article  Google Scholar 

  12. Tang, B., Brennan, M.J., Gatti, G., Ferguson, N.S.: Experimental characterization of a nonlinear vibration absorber using free vibration. J. Sound Vib. 367, 159–169 (2016)

    Article  Google Scholar 

  13. Tsiatas, G.C., Charalampakis, A.E.: A new hysteretic nonlinear energy sink (HNES). Commun. Nonlinear Sci. Numer. Simul. 60, 1–11 (2018)

    Article  Google Scholar 

  14. Vakakis, A.F.: Designing a linear structure with a local nonlinear attachment for enhanced energy pum**. Meccanica 38(6), 677–686 (2003)

    Article  MathSciNet  Google Scholar 

  15. Vakakis, A.F., Manevitch, L., Gendelman, O., Bergman, L.: Dynamics of linear discrete systems connected to local, essentially non-linear attachments. J. Sound Vib. 264(3), 559–577 (2003)

    Article  Google Scholar 

  16. Vakakis, A.F., Rand, R.H.: Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities. Int. J. Non-linear Mech. 39(7), 1079–1091 (2004)

    Article  Google Scholar 

  17. Kerschen, G., Lee, Y.S., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Irreversible passive energy transfer in coupled oscillators with essential nonlinearity. SIAM J. Appl. Math. 66(2), 648–679 (2006)

    Article  MathSciNet  Google Scholar 

  18. Savadkoohi, A.T., Lamarque, C.-H., Contessa, M.V.: Trap** vibratory energy of main linear structures by coupling light systems with geometrical and material non-linearities. Int. J. Non-linear Mech. 80, 3–13 (2016)

    Article  Google Scholar 

  19. Shaw, J., Shaw, S.W., Haddow, A.G.: On the response of the non-linear vibration absorber. Int. J. Non-linear Mech. 24(4), 281–293 (1989)

    Article  Google Scholar 

  20. Laxalde, D., Thouverez, F., Sinou, J.-J.: Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber. Int. J. Non-linear Mech. 41, 969–978 (2006)

    Article  Google Scholar 

  21. Ji, J.C.: Design of a nonlinear vibration absorber using three-to-one internal resonances. Mech. Syst. Signal Process. 42(1–2), 236–246 (2014)

    Article  Google Scholar 

  22. Casalotti, A., Lacarbonara, W.: Tailoring of pinched hysteresis for nonlinear vibration absorption via asymptotic analysis. Int. J. Non-linear Mech. 94, 59–71 (2017)

    Article  Google Scholar 

  23. Viguié, R., Kerschen, G.: Nonlinear vibration absorber coupled to a nonlinear primary system: a tuning methodology. J. Sound Vib. 326(3–5), 780–793 (2009)

    Article  Google Scholar 

  24. Brennan, M.J., Gatti, G.: The characteristics of a nonlinear vibration neutralizer. J. Sound Vib. 331(13), 3158–3171 (2012)

    Article  Google Scholar 

  25. Vakakis, A.F.: Non-similar normal oscillations in a strongly non-linear discrete system. J. Sound Vib. 158(2), 341–361 (1992)

    Article  MathSciNet  Google Scholar 

  26. Gendelman, O.V.: Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn. 37, 115–128 (2004)

    Article  MathSciNet  Google Scholar 

  27. Vestroni, F., Noori, M.: Hysteresis in mechanical systems: modeling and dynamic response. Int. J. Non-linear Mech. 37(8), 1261–1262 (2002)

    Article  Google Scholar 

  28. Capecchi, D., Vestroni, F.: Asymptotic response of a two DOF elastoplastic system under harmonic excitation. Internal resonance case. Nonlinear Dyn. 7, 317–333 (1995)

    Article  Google Scholar 

  29. Masiani, R., Capecchi, D., Vestroni, F.: Resonant and coupled response of hysteretic two-degree-of-freedom systems using harmonic balance method. Int. J. Non-linear Mech. 37, 1421–1434 (2002)

    Article  Google Scholar 

  30. Awrejcewicz, J., Dzyubak, L., Lamarque, C.H.: Modelling of hysteresis using Masing–Bouc–Wen’s framework and search of conditions for the chaotic responses. Commun. Nonlinear Sci. Numer. Simul. 13, 939–958 (2008)

    Article  MathSciNet  Google Scholar 

  31. Casini, P., Vestroni, F.: Nonlinear resonances of hysteretic oscillators. Acta Mech. 229, 939–952 (2018)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  34. Casini, P., Giannini, O., Vestroni, F.: Effect of dam** on the nonlinear modal characteristics of a piecewice-smooth system through harmonic forced response. Mech. Syst. Signal Process. 36, 540–548 (2013)

    Article  Google Scholar 

  35. Bouc, R.: Forced vibrations of mechanical systems with hysteresis. In: Proceedings of the Fourth Conference on Non-linear Oscillations, Prague, (1967)

  36. Wen, Y.K.: Method of random vibration of hysteretic systems. ASCE J. Eng. Mech. 102(2), 249–263 (1976)

    Google Scholar 

  37. Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis Bouc–Wen model, a survey. Arch. Comput. Methods Eng. 16, 161–188 (2009)

    Article  Google Scholar 

  38. Erlicher, S., Bursi, O.S.: Bouc–Wen type models with stiffness degradation: thermodynamic analysis and applications. ASCE J. Eng. Mech. 134(10), 843–855 (2008)

    Article  Google Scholar 

  39. Basili, M., Casini, P., Morelli, L., Vestroni, F.: A hysteretic vibration absorber to mitigate vibrations of train noise barriers. In: XIIIth International Conference on Recent Advances in Structural Dynamics, Lyon, France, (2019)

  40. Casini, P., Vestroni, F.: Characterization of bifurcating non-linear normal modes in piecewise linear mechanical systems. Int. J. Non-linear Mech. 46, 42–150 (2011)

    Article  Google Scholar 

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Acknowledgements

This work has been partially supported by the MIUR (Ministry of Education, University and Research) under the grant PRIN-2015, 2015TTJN95, P.I. Fabrizio Vestroni, “Identification and Monitoring of Complex Structural Systems”.

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  1. Dipartimento di Ingegneria Strutturale e Geotecnica (DISG), Università di Roma “La Sapienza”, Roma, Italy

    Fabrizio Vestroni & Paolo Casini

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  1. Fabrizio Vestroni
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  2. Paolo Casini
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Correspondence to Paolo Casini.

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Vestroni, F., Casini, P. Mitigation of structural vibrations by hysteretic oscillators in internal resonance. Nonlinear Dyn 99, 505–518 (2020). https://doi.org/10.1007/s11071-019-05129-9

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