Skip to main content
SpringerLink
Log in

Targeted energy transfers in vibro-impact oscillators for seismic mitigation

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

Abstract

In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate ‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems.

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

Similar content being viewed by others

References

  1. Arnold, V.I. (ed.): Dynamical Systems III, Encyclopaedia of Mathematical Sciences, vol. 3. Springer, Berlin and New York (1988).

    Google Scholar 

  2. Babitsky, V.I.: Theory of Vibro-Impact Systems. Springer, Berlin and New York (1998)

    MATH  Google Scholar 

  3. Blazejczyk-Okolewska, B.: Analysis of an Impact damper of vibration. Chaos Solitons Fractals 12, 1983–1988 (2001)

    Article  Google Scholar 

  4. Brogliato, B.: Nonsmooth Mechanics. Springer, Berlin and New York (1999)

    MATH  Google Scholar 

  5. Emaci, E., Nayfeh, T.A., Vakakis, A.F.: Numerical and experimental study of nonlinear localization in a flexible structure with vibro-impacts. Zeitschrift fur Angewandte Mathematik und Mechanik – ZAMM (J. Appl. Math. Mech.) 77(7), 527–541 (1997)

    MATH  Google Scholar 

  6. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic, Dordrecht (1988)

  7. Gendelman, O., Manevitch, L. I., Vakakis, A. F., M'Closkey, R.: Energy pumping in nonlinear mechanical oscillators: Part I – Dynamics of the underlying Hamiltonian systems. J. Appl. Mech. 68, 34–41 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Georgiadis, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Shock isolation through passive energy pumping caused by non-smooth nonlinearities. Int. J. Bif. Chaos (special issue on: Non-Smooth Dynamical Systems: Recent Trends and Perspectives) 15(6), 1–13 (2005)

    Google Scholar 

  9. Housner, G.W., Bergman, L.A., Caughey, T.K., Chassiakos, A.G., Claus, R.O., Masri, S.F., Skelton, R.E., Soong, T.T., Spencer, B.F., Yao, J.T.P.: Structural control: past, present and future. ASCE J. Eng. Mech. 123(9) (1997)

  10. Kerschen, G.: On the model validation in non-linear structural dynamics. PhD Dissertation, University of Liege, Department of Aerospace, Mechanics and Materials Engineering (2002)

  11. Kerschen, G., Vakakis, A.F., Lee Young S., McFarland, D.M., Kowtko, J., Bergman, L.A.: Energy transfers in a system of two coupled oscillators with essential nonlinearity: 1:1 resonance manifold and transient bridging orbits. Nonlinear Dyn. 42(3), 283–303 (2005)

    Article  MATH  Google Scholar 

  12. Kerschen, G., Lee, Y. Sup., 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 (2006a)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kerschen, G., Gendelman, O., Vakakis, A.F., Bergman, L.A., McFarland, D.M.: Impulsive periodic and quasi-periodic orbits of coupled oscillators with essential stiffness nonlinearity. Communications in Nonlinear Science and Numerical Simulation (submitted) (2006b)

  14. Kryzhevich, S.G., Pliss, V.A.: Chaotic modes of oscillation of a vibro-impact system. J. Appl. Math. Mech.- PMM 69, 13–26 (2005)

    Article  MathSciNet  Google Scholar 

  15. Leine, R.I., Nijmeijer, H.: Dynamics and Bifurcations in Non-Smooth Mechanical Systems. Springer-Verlag, Berlin (2004)

  16. Masri, S.F., Caughey, T.K.: On the stability of the impact damper. J. Appl. Mech. 33(3), 586–592 (1966)

    MathSciNet  Google Scholar 

  17. Masri, S.F., Ibrahim, A.M.: Response of the impact damper to nonstationary random excitation. J. Acous. Soc. Am. 53(1), 200–211 (1973)

    Article  Google Scholar 

  18. Neishtadt, A.I.: Scattering by resonances. Celest. Mech. Dyn. Astron. 65, 1–20 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nucera, F.: Nonlinear energy pumping as a strategy for seismic protection. PhD Thesis, University of Calabria at Arcavacata of Rende, Cosenza, Italy (2005)

  20. Peterka, F., Blazejczyk-Okolewska, B.: Some aspects of the dynamical behavior of the impact damper. J. Vib. Control 11, 459–479 (2005)

    Article  Google Scholar 

  21. Pfeiffer, F., Glocker, Ch.: Contacts in multibody systems. J. Appl. Math. Mech. 64(5), 773–782 (2000)

    Article  Google Scholar 

  22. Quinn, D., Rand, R.H.: The dynamics of resonance capture. Nonlinear Dyn. 8, 1–20 (1995)

    MathSciNet  Google Scholar 

  23. Spencer, Jr. B.F., Christenson, R.E., Dyke, S.J.: Next generation benchmark control problem for seismically excited buildings. In: Proceedings of 2nd World Conference on Structural Control, Wiley, New York, Vol. 2, pp. 1135–1360. (1999)

    Google Scholar 

  24. Shaw, S.W., Rand, R.H.: The transition to chaos in a simple mechanical system. Int. J. Non-Linear Mech. 24, 41–56 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  25. Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  26. Sun, J.Q., Luo, A.: Bifurcation and Chaos in Complex Systems, vol. 1. Elsevier, Oxford, UK (2006)

  27. Thota, P., Dankowicz, H.: Continuous and discontinuous grazing bifurcations in impacting oscillators. Physica D 214, 187–197 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Vakakis, A. F.: Inducing passive nonlinear energy sinks in vibrating systems. J. Vib. Acous. 123, 324–332 (2001)

    Article  Google Scholar 

  29. Vakakis, A. F., Gendelman, O.: Energy pumping in nonlinear mechanical oscillators: Part II – Resonance capture. J. Appl. Mech. 68, 42–48 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  30. Vakakis, A.F., Manevitch, L.I., Mikhlin, Yu.V., Pilipchuk, V.N., Zevin, A.A.: Normal Modes and Localization in Nonlinear Systems. Wiley Interscience, New York (1996)

    MATH  Google Scholar 

  31. Vakakis, A.F.: Shock isolation through the use of nonlinear energy sinks. J. Vib. Control (commemorative issue on the occasion of Professor Friedrich G. Pfeiffer's 65th birthday) 9(1–2), 79–93 (2003)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Materials, Mediterranean University of Reggio Calabria, Reggio Calabria, Italy

    F. Nucera

  2. Division of Mechanics, National Technical University of Athens, Athens, Greece

    A. F. Vakakis

  3. Department of Mechanical and Industrial Engineering (adjunct), University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    A. F. Vakakis

  4. Department of Aerospace Engineering (adjunct), University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    A. F. Vakakis

  5. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    D. M. McFarland & L. A. Bergman

  6. Department of Materials, Mechanical and Aerospace Engineering, University of Liége, Liege, Belgium

    G. Kerschen

Authors
  1. F. Nucera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Vakakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. M. McFarland
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. A. Bergman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Kerschen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. F. Vakakis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nucera, F., Vakakis, A.F., McFarland, D.M. et al. Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn 50, 651–677 (2007). https://doi.org/10.1007/s11071-006-9189-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-006-9189-7

Keywords

Search

Navigation