Research on Vibration Suppression of Nonlinear Energy Sink Under Dual-Frequency Excitation

  • B. Sun
  • Z. Q. WuEmail author
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 69)


Most of modern civil turbofan engines adopt the dual-rotor layout, which introduces the typical dual-frequency excitation into the dynamic models. This work sets a single degree of freedom (SDOF) linear oscillator for the main system, and establishes the dynamic models of that coupled with the SDOF linear dynamic vibration absorber (DVA) and different configurations of nonlinear energy sink (NES). In view of the typical flutter mechanism of wing, the modal frequency of the first-order symmetric twist typical state of wing is introduced into dynamic models. With the wing, low and high characteristic frequency ratio (1:2.67:12.66) for the typical dual-rotor aero-engine in cruise, the fourth-order Runge-Kutta algorithm is employed for analysis. According to the energy criteria for the dynamic vibration absorber optimization, focusing on the effects of the characteristic frequency ratio on the kinetic energy of the primary mass, total system energy etc., numerical simulation results of comparison can indicate that reducing the torsional vibration of wing by NES is feasible, and NES has better vibration suppression effect than the traditional linear DVA with certain set of parameters under the dual-frequency excitation. In addition, the vibration suppression effects of the SDOF, two-DOF serial and parallel NES on the main oscillator system are focused on. Under the condition that the characteristic parameters of the main system and additive total mass of the vibration absorber remain unchanged, results show the two-DOF parallel NES has the best vibration energy suppression effect under dual-frequency excitation.


NES Civil aero-engine Dual-frequency excitation Vibration suppression optimization 



This work was supported by the National Basic Research Program of China (No. 2014CB046805) and the National Natural Science Foundation of China (No. 11372211, No. 11672349).


  1. 1.
    Yan, L.T., Wang, D.Y.: Vibration features from rubbing between rotor and casing for a dual-shaft aeroengine. J. Aerosp. Power (1998). (in Chinese)Google Scholar
  2. 2.
    Depriest, J.: Aircraft engine attachment and vibration control. Manufacturing (2000)Google Scholar
  3. 3.
    Han, J., Gao, D.P., Hu, X., et al.: Research on beat vibration of dual-rotor for aero-engine. Acta Aeronaut. et Astronaut. Sin. 28(6), 1369–1373 (2007). (in Chinese)Google Scholar
  4. 4.
    Chen, Y., He, E.M., Hu, X.Z., et al.: Exploring wing-mounted engine vibration transmission for new generation airplanes with turbofan engines of high bypass ratio. J. Northwest. Polytechn. Univ. 30(3), 384–389 (2012). (in Chinese)Google Scholar
  5. 5.
    Ouyang, Y.F., Ming, Y.: Research on rub-impact fault vibration characteristics of aeroengine dual-rotor system. Mech. Eng. 11, 65–71 (2016). (in Chinese)Google Scholar
  6. 6.
    Xiao, F., Yang, H.Z., Lu, Q.J., et al.: Vortex-induced parametric resonance of top tensioned riser based on bi-frequency excitation. Ocean. Eng. 31(2), 28–34 (2013). (in Chinese)Google Scholar
  7. 7.
    Xiao, F., Yang, H.Z.: Hill stability prediction of deep-sea steel catenary riser. Shanghai Jiao Tong Univ. 48(4), 583–588 (2014). (in Chinese)Google Scholar
  8. 8.
    Gendelman, O.V., Starosvetsky, Y.: FELDMAN M, Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes. Nonlinear Dyn. 51(1), 31–46 (2007)CrossRefGoogle Scholar
  9. 9.
    Starosvetsky, Y., Gendelman, O.V.: Attractors of harmonically forced linear oscillator with attached nonlinear energy sink II: Optimization of a nonlinear vibration absorber [J]. Nonlinear Dyn. 51(1–2), 47–57 (2008)zbMATHGoogle Scholar
  10. 10.
    Starosvetsky, Y., Gendelman, O.V.: Interaction of nonlinear energy sink with a two degrees of freedom linear system Internal resonance. J. Sound Vib. 329(10), 1836–1852 (2010)CrossRefGoogle Scholar
  11. 11.
    Starosvetsky, Y., Gendelman, O.V.: Response regimes in forced system with non-linear energy sink: quasi-periodic and random forcing. Nonlinear Dyn. 64(1), 177–195 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kong, X.R., Zhang, Y.C.: Vibration suppression of a two-degree-of-freedom nonlinear energy sink under harmonic excitation. Acta Aeronaut. et Astronaut. Sin. 33(6), 1020–1029 (2012). (in Chinese)MathSciNetGoogle Scholar
  13. 13.
    Zhang, Y.C., Kong, X.R.: Initial conditions for targeted energy transfer in coupled nonlinear oscillators. J. Harbin Inst. Technol. 44(07), 21–26 (2012). (in Chinese)MathSciNetGoogle Scholar
  14. 14.
    Zhang, Y.C.: Dynamics of a nonlinear energy sink used for suppressing two-separated resonance peaks. Spacecr. Environ. Eng. 32(05), 477–483 (2015). (in Chinese)Google Scholar
  15. 15.
    Xiong, H., Kong, X.R., Liu, Y.: Influence of structural damping on a system with nonlinear energy sinks. J. Vib. Shock 11, 116–121 (2015). (in Chinese)Google Scholar
  16. 16.
    Xiong, H., Kong, X.R., Liu, Y.: Energy transfer and dissipation of a class of nonlinear absorber and its parameter design. J. Vib. Eng. 28(5), 785–792 (2015). (in Chinese)Google Scholar
  17. 17.
    Hubbard, S.A., McFarland, D.M., Bergman, L.A., et al.: Targeted energy transfer between a model flexible wing and nonlinear energy sink. J. Aircr. 47(6), 1918–1931 (2010)CrossRefGoogle Scholar
  18. 18.
    Hubbard, S.A., McFarland, D.M., Bergman, L.A., et al.: Targeted energy transfer between a swept wing and winglet-housed nonlinear energy sink. AIAA J. 52(12), 2633–2651 (2014)CrossRefGoogle Scholar
  19. 19.
    Boroson, E., Missoum, S., Mattei, P.O., Vergez, C.: Optimization under uncertainty of parallel nonlinear energy sinks. J. Sound Vib. 394, 451–464 (2017)CrossRefGoogle Scholar
  20. 20.
    Ahmadabadi, Z.N., Khadem, S.E.: Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech. Mach. Theory 50(50), 134–149 (2012)CrossRefGoogle Scholar
  21. 21.
    Kani, M., Khadem, S.E., Pashaei, M.H., et al.: Design and performance analysis of a nonlinear energy sink attached to a beam with different support conditions. Arch. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 230(4), 527–542 (2016)Google Scholar
  22. 22.
    Liu, C.Y., Sun, X.H., Ma, X.: Vibration and flutter characteristics analysis of wing finite element model. Comput. Aided Eng. 15(s1), 53–55 (2006). (in Chinese)Google Scholar
  23. 23.
    Zhang, H. B., Zhang, G. G.: Research on flutter characteristics of wing structure with variable parameters. In: Proceedings of the Thirteenth National Conference on Air Elasticity (2013). (in Chinese)Google Scholar
  24. 24.
    Gendelman, O.V.: Targeted energy transfer in systems with external and self-excitation. Arch. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225(9), 2007–2043 (2011)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Department of Mechanics, School of Mechanical EngineeringTianjin UniversityTianjinPeople’s Republic of China
  2. 2.Department of Aircraft, School of Aeronautical EngineeringCivil Aviation University of ChinaTianjinPeople’s Republic of China

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