Meccanica

, Volume 52, Issue 4–5, pp 763–779 | Cite as

Numerical and experimental investigations of a rotating nonlinear energy sink

  • Mohammad A. AL-Shudeifat
  • Nicholas E. Wierschem
  • Lawrence A. Bergman
  • Alexander F. Vakakis
Article

Abstract

In this work, passive nonlinear targeted energy transfer (TET) is addressed by numerically and experimentally investigating a lightweight rotating nonlinear energy sink (NES) which is coupled to a primary two-degree-of-freedom linear oscillator through an essentially nonlinear (i.e., non-linearizable) inertial nonlinearity. It is found that the rotating NES passively absorbs and rapidly dissipates a considerable portion of impulse energy initially induced in the primary oscillator. The parameters of the rotating NES are optimized numerically for optimal performance under intermediate and strong loads. The fundamental mechanism for effective TET to the NES is the excitation of its rotational nonlinear mode, since its oscillatory mode dissipates far less energy. This involves a highly energetic and intense resonance capture of the transient nonlinear dynamics at the lowest modal frequency of the primary system; this is studied in detail by constructing an appropriate frequency–energy plot. A series of experimental tests is then performed to validate the theoretical predictions. Based on the obtained numerical and experimental results, the performance of the rotating NES is found to be comparable to other current translational NES designs; however, the proposed rotating device is less complicated and more compact than current types of NESs.

Keywords

Targeted energy transfer Rotating nonlinear energy sink Inertial nonlinearity 

References

  1. 1.
    Vakakis AF, Gendelman OV, Kerschen G, Bergman LA, McFarland DM, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems, I and II. Springer, BerlinMATHGoogle Scholar
  2. 2.
    Gendelman O, Manevitch LI, Vakakis AF, McCloskey R (2001) Energy pumping in nonlinear mechanical oscillators: part I—dynamics of the underlying Hamiltonian systems. J Appl Mech 68(1):34–41MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Vakakis AF, Gendelman O (2001) Energy pumping in nonlinear mechanical oscillators: part II—resonance capture. J Appl Mech 68(1):42–48MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Lee YS, Kerschen G, Vakakis AF, Panagopoulos P, Bergman L, McFarland DM (2005) Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment. Phys D 204(1–2):41–69MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gourdon E, Alexander NA, Taylor CA, Lamarque CH, Pernot S (2007) Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J Sound Vib 300:522–551ADSCrossRefGoogle Scholar
  6. 6.
    Quinn DD, Gendelman O, Kerschen G, Sapsis TP, Bergman LA, Vakakis AF (2008) Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance capture: part I. J Sound Vib 311:1228–1248ADSCrossRefGoogle Scholar
  7. 7.
    Sapsis TP, Vakakis AF, Gendelman OV, Bergman LA, Kerschen G, Quinn DD (2009) Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: part II, analytical study. J Sound Vib 325:297–320ADSCrossRefGoogle Scholar
  8. 8.
    Michael McFarland D, Bergman LA, Vakakis AF (2005) Experimental study of non-linear energy pumping occurring at a single fast frequency. Int J Non-Linear Mech 40:891–899CrossRefMATHGoogle Scholar
  9. 9.
    Sapsis TP, Quinn DD, Vakakis AF, Bergman LA (2012) Effective stiffening and damping enhancement of structures with strongly nonlinear local attachments. J Vib Acoust 134:011016-1CrossRefGoogle Scholar
  10. 10.
    Sigalov G, Gendelman OV, AL-Shudeifat MA, Manevitch LI, Vakakis AF, Bergman LA (2012) Resonance captures and targeted energy transfers in an inertially coupled rotational nonlinear energy sink. Nonlinear Dyn 69:1693–1704MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sigalov G, Gendelman OV, Al-Shudeifat M, Manevitch LI, Vakakis AF, Bergman LA (2012) Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling. Chaos 22:013118ADSMathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Gendelman OV, Sigalov G, Manevitch LI, Mane M, Vakakis AF, Bergman LA (2012) Dynamics of an eccentric rotational nonlinear energy sink. J Appl Mech 79:011012CrossRefGoogle Scholar
  13. 13.
    Tripepi C (2009) Application of targeted energy transfer (TET) techniques to the seismic protection of symmetric and eccentric steel structures, Ph.D. thesis. Università Mediterranea di Reggio CalabriaGoogle Scholar
  14. 14.
    Pantelidis CP, Ma X (1997) Linear and nonlinear pounding of structural systems. Comput Struct 66(1):79–92CrossRefGoogle Scholar
  15. 15.
    Nucera F, Vakakis AF, McFarland DM, Bergman LA, Kerschen G (2007) Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn 50:651–677CrossRefMATHGoogle Scholar
  16. 16.
    Karayannis I, Vakakis AF, Georgiades F (2008) Vibro-impact attachments as shock absorbers. Proc IMechE J Mech Eng Sci 222(1):1899–1908CrossRefGoogle Scholar
  17. 17.
    Nucera F, McFarland DM, Bergman LA, Vakakis AF (2010) Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: I. Computational results. J Sound Vib 329(15):2973–2994ADSCrossRefGoogle Scholar
  18. 18.
    Lee YS, Nucera F, Vakakis AF, McFarland DM, Bergman LA (2009) Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Phys D 238(18):1868–1896CrossRefMATHGoogle Scholar
  19. 19.
    Georgiadis F, Vakakis AF, McFarland DM, Bergman LA (2005) Shock isolation through passive energy pumping caused by non-smooth nonlinearities. Int J Bifurc Chaos 15(6):1–13CrossRefGoogle Scholar
  20. 20.
    Karayannis I, Vakakis AF, Georgiades F (2008) Vibro-impact attachments as shock absorbers. Proc IMechE J Mech Eng Sci 222(C10):1899–1908CrossRefGoogle Scholar
  21. 21.
    AL-Shudeifat MA, Wierschem N, Quinn DD, Vakakis AF, Bergman LA, Spencer BF Jr (2013) Numerical and experimental investigation of a highly effective single-sided vibro-impact nonlinear energy sink for shock mitigation. Int J Non-Linear Mech 52:96–109CrossRefGoogle Scholar
  22. 22.
    Manevitch LI, Sigalov G, Romeo F, Bergman LA, Vakakis A (2014) Dynamics of a linear oscillator coupled to a bistable light attachment: analytical study. J Appl Mech 81(4):041011CrossRefGoogle Scholar
  23. 23.
    AL-Shudeifat MA (2014) Highly efficient nonlinear energy sink. Nonlinear Dyn 76(4):1905–1920MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Romeo F, Sigalov G, Bergman LA, Vakakis AF (2015) Dynamics of a linear oscillator coupled to a bistable light attachment: numerical study. J Comput Nonlinear Dyn 10(1):011007CrossRefGoogle Scholar
  25. 25.
    Gendelman OV (2012) Analytic treatment of a system with a vibro-impact nonlinear energy sink. J Sound Vib 331(21):4599–4608ADSCrossRefGoogle Scholar
  26. 26.
    Gendelman OV, Alloni A (2015) Dynamics of forced system with vibro-impact energy sink. J Sound Vib 358:301–314ADSCrossRefGoogle Scholar
  27. 27.
    Alexander NA, Schilder F (2009) Exploring the performance of a nonlinear tuned mass damper. J Sound Vib 319(1):445–462ADSCrossRefGoogle Scholar
  28. 28.
    Habib G, Detroux T, Viguié R, Kerschen G (2015) Nonlinear generalization of Den Hartog’s equal-peak method. Mech Syst Signal Process 52:17–28ADSCrossRefGoogle Scholar
  29. 29.
    Jiang X, McFarland DM, Bergman LA, Vakakis AF (2003) Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dyn 33(1):87–102CrossRefMATHGoogle Scholar
  30. 30.
    Savadkoohi AT, Vaurigaud B, Lamarque CH, Pernot S (2012) Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments. Nonlinear Dyn 67(1):37–46MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Lee YS, Kerschen G, McFarland DM, Hill WJ, Nichkawde C, Strganac TW, Bergman LA, Vakakis AF (2007) Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments. AIAA J 45(10):2391–2400ADSCrossRefGoogle Scholar
  32. 32.
    McFarland DM, Kerschen G, Kowtko JJ, Lee YS, Bergman LA, Vakakis AF (2005) Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J Acoust Soc Am 118:791–799ADSCrossRefMATHGoogle Scholar
  33. 33.
    Georgiades F, Vakakis AF (2009) Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear end attachments. Int J Solids Struct 46(11–12):2330–2353CrossRefMATHGoogle Scholar
  34. 34.
    AL-Shudeifat MA, Vakakis AF, Bergman LA (2016) Shock mitigation by means of low- to high-frequency nonlinear targeted energy transfers of a large-scale structure. J Comput Nonlinear Dyn 11(2). doi:10.1115/1.4030540
  35. 35.
    Quinn DD, Wierschem N, Hubbard S, AL-Shudeifat MA, Ott RJ, McFarland DM, Vakakis AF, Bergman LA (2012) Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments. J Multi-body Dyn 226(2):122–146Google Scholar
  36. 36.
    Kerschen G, Peeters M, Golinval JC, Vakakis A (2009) Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech Syst Signal Process 23:170–194ADSCrossRefGoogle Scholar
  37. 37.
    Peeters M, Viguié R, Sérandour G, Kerschen G, Golinval J-C (2009) Nonlinear normal modes, part II: toward a practical computation using numerical continuation techniques. Mech Syst Signal Process 23(1):195–216. doi:10.1016/j.ymssp.2008.04.003 ADSCrossRefGoogle Scholar
  38. 38.
    Wierschem N, Luo J, Quinn DD, Hubbard S, Al-Shudeifat MA, McFarland M, Vakakis AF, Bergman LA, Spencer BF Jr (2012) Passive damping enhancement of a two-degree-of-freedom system through a strongly nonlinear two-degree-of-freedom attachment. J Sound Vib 331(25):5393–5407ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Mohammad A. AL-Shudeifat
    • 1
  • Nicholas E. Wierschem
    • 2
  • Lawrence A. Bergman
    • 3
  • Alexander F. Vakakis
    • 4
  1. 1.Aerospace EngineeringKhalifa University of Science, Technology and ResearchAbu DhabiUAE
  2. 2.Civil and Environmental EngineeringUniversity of Tennessee, KnoxvilleKnoxvilleUSA
  3. 3.Aerospace EngineeringUniversity of Illinois at Urbana – ChampaignUrbanaUSA
  4. 4.Mechanical Science and EngineeringUniversity of Illinois at Urbana – ChampaignUrbanaUSA

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