Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Transient response of vibration systems with viscous-hysteretic mixed damping using Hilbert transform and effective eigenvalues

  • Bae, S.H. (Nuclear EQ and Safety Center, Korea Institute of Machinery and Materials) ;
  • Jeong, W.B. (School of Mechanical Engineering, Pusan National University) ;
  • Cho, J.R. (Department of Naval Architecture and Ocean Engineering, Hongik University) ;
  • Lee, J.H. (Nuclear EQ and Safety Center, Korea Institute of Machinery and Materials)
  • Received : 2017.01.02
  • Accepted : 2017.06.25
  • Published : 2017.09.25
⟨ Previous Next ⟩

Abstract

This paper presents the time response of a mixed vibration system with the viscous damping and the hysteretic damping. There are two ways to derive the time response of such a vibration system. One is an analytical method, using the contour integral of complex functions to compute the inverse Fourier transforms. The other is an approximate method in which the analytic functions derived by Hilbert transform are expressed in the state space representation, and only the effective eigenvalues are used to efficiently compute the transient response. The unit impulse responses of the two methods are compared and the change in the damping properties which depend on the viscous and hysteretic damping values is investigated. The results showed that the damping properties of a mixed damping vibration system do not present themselves as a linear combination of damping properties.

Keywords

Acknowledgement

Supported by : Korea Institute of Machinery & Materials, Hongik University

References

  1. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  2. Amichi, K. and Atalla, N. (2009), "A new 3D finite element for sandwich beams with a viscoelastic core", J. Vib. Acoust., 131(2), 021010. https://doi.org/10.1115/1.3025828
  3. Arfken, G.B. and Weber, H.J. (2005), Mathematical Methods for Physicists, Academic Press, London.
  4. Bae, S.H., Cho, J.R. and Jeong, W.B. (2016), "Free and transient responses of linear complex stiffness system by Hilbert transform and convolution integral," Smart Struct. Syst., 17(5), 753-771. https://doi.org/10.12989/sss.2016.17.5.753
  5. Bae, S.H., Cho, J.R., Bae, S.R. and Jeong, W.B. (2014), "A discrete convolutional Hilbert transform with the consistent imaginary initial conditions for the time-domain analysis of five-layered viscoelastic sandwich beam", Comput. Meth. Appl. Mech. Eng., 268, 245-263. https://doi.org/10.1016/j.cma.2013.09.010
  6. Barkanov, E., Rikards, R., Holste, C. and Tager, O. (2000), "Transient response of sandwich viscoelastic beams, plates, and shells under impulse loading", Mech. Compos. Mater., 36(3), 215-222. https://doi.org/10.1007/BF02681873
  7. Bonisoli, E. and Mottershead, J.E. (2004), "Complex-damped dynamic systems in the time and frequency domains", J. Shock Vib., 11, 209-225. https://doi.org/10.1155/2004/849417
  8. Chen, J.T. and You, D.W. (1999), "An integral-differential equation approach for the free vibration of a SDOF system with hysteretic damping", Adv. Eng. Softw., 30(1), 43-48. https://doi.org/10.1016/S0965-9978(98)00061-1
  9. Crandall, S.H. (1970), "The role of damping in vibration theory", J. Sound Vib., 11(1), 3-18 https://doi.org/10.1016/S0022-460X(70)80105-5
  10. Feldman, M. (2011), Hilbert Transform in Mechanical Vibration, John Wiley & Sons, Ltd., Chichester, UK.
  11. Gaul, L., Bohlen, S. and Kempfle, S. (1985), "Transient and forced oscillations of systems with constant hysteretic damping", Mech. Res. Commun., 12(4), 187-201. https://doi.org/10.1016/0093-6413(85)90057-6
  12. Genta, G. and Amati, N. (2010), "Hysteretic damping in rotordynamics: An equivalent formulation", J. Sound Vib., 329(22), 4772-4784. https://doi.org/10.1016/j.jsv.2010.04.036
  13. Henwood, D.J. (2002), "Approximating the hysteretic damping matrix by a viscous matrix for modelling in the time domain", J. Sound Vib., 254(3), 575-593. https://doi.org/10.1006/jsvi.2001.4136
  14. Inaudi, J.A. and Makris, N. (1996), "Time-domain analysis of linear hysteretic damping", Earthq. Eng. Struct. D., 25(6), 529-545. https://doi.org/10.1002/(SICI)1096-9845(199606)25:6<529::AID-EQE549>3.0.CO;2-P
  15. Johansson, M. (1999), The Hilbert Transform, Master Thesis, Mathematics, Vaxjo University.
  16. Li, Z., Qiao, G., Sun, Z., Zhao, H. and Guo, R. (2012), "Short baseline positioning with an improved time reversal technique in a multi-path channel", J. Mar. Sci. Appl., 11(2), 251-257. https://doi.org/10.1007/s11804-012-1130-5
  17. Mohammadi, F. and Sedaghati, R. (2012), "Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained viscoelastic core layer", Int. J. Mech. Sci., 54(1), 156-171. https://doi.org/10.1016/j.ijmecsci.2011.10.006
  18. Nashif, A.D., Jones, D.I.G. and Henderson, J.P. (1985), Vibration Damping, Wiley, New York.
  19. Padois, T., Prax, C., Valeau, V. and Marx, D. (2012), "Experimental localization of an acoustic sound source in a wind-tunnel flow by using a numerical time-reversal technique", Acoust. Soc. Am., 132(4), 2397. https://doi.org/10.1121/1.4747015
  20. Soroka, W.W. (2012), "Note on the relations between viscous and structural damping coefficients," J. Aeronaut. Sci., 16(7), 409-410. https://doi.org/10.2514/8.11822
  21. Wang, Q., Yuan, S., Hong, M. and Su, Z. (2015), "On time reversal-based signal enhancement for active lamb wave-based damage identification", Smart Struct. Syst., 15(6), 1463-1479. https://doi.org/10.12989/sss.2015.15.6.1463
  22. Won, S.G., Bae, S.H., Cho, J.R., Bae, S.R. and Jeong, W.B. (2013), "Three-layered damped beam element for forced vibration analysis of symmetric sandwich structures with a viscoelastic core", Finite Elem. Anal. Des., 68, 39-51. https://doi.org/10.1016/j.finel.2013.01.004
  23. Won, S.G., Bae, S.H., Jeong, W.B. and Cho, J.R. (2012), "Forced vibration analysis of damped beam structures with composite cross-section using Timoshenko beam element", Struct. Eng. Mech., 43(1), 15-30. https://doi.org/10.12989/sem.2012.43.1.015
  24. Zhu, H., Hu, Y. and Pi, Y. (2014), "Transverse hysteretic damping characteristics of a serpentine belt: Modeling and experimental investigation", J. Sound Vib., 333(25), 7019-7035. https://doi.org/10.1016/j.jsv.2014.06.020