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Free Vibration Identification of the Geometrically Nonlinear Isolator with Elastic Rings by Using Hilbert Transform

  • Zhan Hu
  • Xing Wang
  • Gangtie Zheng
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

The geometrically nonlinear isolator formed by a pair of elastic circular springs in the push-pull configuration has the symmetrical hardening stiffness under static compression and tension. Thus, it could be a potential solution to satisfy the dual isolation requirements of steady-state vibrations and transient shocks in the engineering application. The nonlinear transmissibility of this isolator under large-amplitude sinusoidal excitations has been investigated theoretically and experimentally in our previous research. In this paper, the Hilbert transform is applied to identify the geometrically nonlinear isolator with measured free vibration responses in the time domain. The measured responses are acquired by a laser vibrometer with large initial deformations. Since all the involved instantaneous modal parameters contain fast oscillations around their average values, the empirical mode decomposition is employed to smooth the identified results of the instantaneous frequency and damping coefficient. It is found that the backbone curve obtained experimentally conforms well to the previously measured frequency responses. The identified nonlinear stiffness and damping force characteristics of this geometrically nonlinear isolator have good agreements with the results from the theoretically calculation and the frequency-domain test in our previous research. Therefore, this research provides an efficient approach to analyze the dynamic characteristics of the geometrically nonlinear isolator with push-pull configuration rings and is also beneficial to design the parameters of this isolator.

Keywords

System identification Free vibration Geometrical nonlinearity Hilbert transform Instantaneous modal frequency 

References

  1. 1.
    Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314(3), 371–452 (2008)CrossRefGoogle Scholar
  2. 2.
    Tse, P.C., Lai, T.C., So, C.K., et al.: Large deflection of elastic composite circular springs under uniaxial compression. Int J Non Linear Mech. 29(5), 781–798 (1994)CrossRefMATHGoogle Scholar
  3. 3.
    Tse, P.C., Lung, C.T.: Large deflections of elastic composite circular springs under uniaxial tension. Int J Non Linear Mech. 35(2), 293–307 (2000)CrossRefMATHGoogle Scholar
  4. 4.
    Tse, P.C., Lai, T.C., So, C.K.: A note on large deflection of elastic composite circular springs under tension and in push-pull configuration. Compos. Struct. 40(3), 223–230 (1997)CrossRefGoogle Scholar
  5. 5.
    Hu, Z., Zheng, G.: A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings. Mech. Syst. Signal Process. 76, 634–648 (2016)CrossRefGoogle Scholar
  6. 6.
    Feldman, M.: Hilbert transform in vibration analysis. Mech. Syst. Signal Process. 25(3), 735–802 (2011)CrossRefGoogle Scholar
  7. 7.
    Feldman, M.: Non-linear free vibration identification via the Hilbert transform[J]. J. Sound Vib. 208(3), 475–489 (1997)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Feldman, M.: Time-varying vibration decomposition and analysis based on the Hilbert transform. J. Sound Vib. 295(3), 518–530 (2006)CrossRefMATHGoogle Scholar
  9. 9.
    Davies, P., Hammond, J.K. (eds.): The use of envelope and instantaneous phase methods for the response of oscillatory nonlinear systems to transients. In: Proceedings of the Fifth IMAC, vol. II, pp. 1460–1466 (1987)Google Scholar
  10. 10.
    Huang, N.E., Shen, Z., Long, S.R.: New view of nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech. 31, 417–457 (1999)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Rato, R.T., Ortigueira, M.D., Batista, A.G.: On the HHT, its problems, and some solutions. Mech. Syst. Signal Process. 22(6), 1374–1394 (2008)CrossRefGoogle Scholar
  12. 12.
    Capecchi, D., Vestroni, F.: Periodic response of a class of hysteretic oscillators. Int. J. Non-linear Mech. 25(2), 309–317 (1990)CrossRefMATHGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2017

Authors and Affiliations

  1. 1.School of Aerospace EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Mechanical EngineeringUniversity of BristolBristolUK

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