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Plate vibration suppression by optimizing friction threshold at its bolted supports

  • Sara Hallajisani
  • Hamed KashaniEmail author
  • A. S. Nobari
Article
  • 4 Downloads

Abstract

Hysteretic behavior due to some nonlinear sources is a common phenomenon in many mechanical systems. One of the sources of this behavior in such systems is dry friction in bolted or riveted joints. The dynamic response of a randomly excited thin rectangular plate with bolted supports at the boundaries is considered. Friction in bolted supports is modeled by Jenkins’ bilinear hysteresis element. Equivalent-Linearization technique, a Closed-Form technique and Moment-Closure technique are employed to obtain response statistics. Equivalent damping due to hysteretic supports is obtained versus instantaneous amplitude of the system and also the sliding threshold. Then optimum friction threshold for minimizing response amplitude is obtained versus other system parameters. Further, the Mont-Carlo simulation developed to verify the results. Results show that sliding at the bolted supports has significant effect on mean square value of transverse vibration amplitude and there is an optimum sliding threshold in which overall variance of system response is minimum.

Keywords

Bilinear hysteresis Bolted support Hysteretic system Optimum friction level Plate vibration Random excitation 

References

  1. 1.
    Ouyang H, Oldfield M, Mottershead J (2006) Experimental and theoretical studies of a bolted joint excited by a torsional dynamic load. Int J Mech Sci 48:1447–1455CrossRefGoogle Scholar
  2. 2.
    Song Y et al (2004) Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements. Sound Vib 273:249–276CrossRefGoogle Scholar
  3. 3.
    Ikhouane F, Rodellar J (2005) On the hysteretic Bouc-Wen model. Nonlinear Dyn 42:63–78CrossRefzbMATHGoogle Scholar
  4. 4.
    Iwan W, Lute L (1968) Response of the bilinear hysteretic system to stationary random excitation. J Acoust Soc Am 43:545–552CrossRefGoogle Scholar
  5. 5.
    Liao X, Jianrun Z, Xiyan X (2016) Analytical model of bolted joint structure and its nonlinear dynamic characteristics in transient excitation. J Shock Vib 2016(3):1–11Google Scholar
  6. 6.
    Oldfield M, Ouyang H (2005) Simplified models of bolted joints under harmonic loading. Comput Struct 84(1):25–33CrossRefGoogle Scholar
  7. 7.
    Butcher E, Argatov I (2011) On the Iwan models for lap-type bolted joints. Int J Non-Linear Mech 46(2):347–356CrossRefGoogle Scholar
  8. 8.
    Pilipchuk V et al (2015) Transient friction-induced vibrations in a 2-DOF model of brakes. Sound Vib 344:297–312CrossRefGoogle Scholar
  9. 9.
    Al-bender F, Lamparet V (2005) The generalized Maxwell-slip model; A novel model for friction simulation and compensation. IEEE Trans Autom Control 50:1883–1887MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Dong L (2018) A modified IWAN model for micro-slip in the context of dampers for turbine blade dynamics. Mech Syst Signal Proc 2019(121):14–30Google Scholar
  11. 11.
    Dong W (2018) Reduced-order modeling approach for frictional stick-slip behaviors of joint interface. Mech Syst Signal Proc 2018(103):131–138Google Scholar
  12. 12.
    Padthe AK et al (2008) Duhem modeling of friction-induced hysteresis. IEEE Control Syst 28:90–107MathSciNetzbMATHGoogle Scholar
  13. 13.
    Pozo F et al (2008) Nonlinear modeling of hysteretic systems with double hysteretic loops using position and acceleration information. Nonlinear Dyn 57:1–12MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lacarbonara W, Vestroni F (2003) Nonclassical responses of oscillators with hysteresis. Nonlinear Dyn 32(3):235–258CrossRefzbMATHGoogle Scholar
  15. 15.
    Dowell E (1986) Damping in beams and plates due to slipping at the support boundaries. J Sound Vib 105(2):243–253CrossRefGoogle Scholar
  16. 16.
    Jezequel L (1981) Structural damping by slip in joints. Design Engineering Technical Conference, Hartford, Connecticut, ASME Paper 81-DET-139 pp 20–23Google Scholar
  17. 17.
    Binde AA, Ferri AA (1992) Damping and vibration of beams with various types of frictional support conditions. ASME J Vib Acoust 114:289–296CrossRefGoogle Scholar
  18. 18.
    Caughey T (1963) Equivalent linearization techniques. J Acoust Soc Am 35(11):1706–1711MathSciNetCrossRefGoogle Scholar
  19. 19.
    Iwan W, Asano K (1984) An alternative approach to the random response of bilinear hysteretic systems. Earthq Eng Struct Dyn 12(2):229–236CrossRefGoogle Scholar
  20. 20.
    Zuguang Y (2003) Response analysis of randomly excited nonlinear systems with symmetric weighting Preisach hysteresis. Acta Mech Sinica 19(4):365–370MathSciNetCrossRefGoogle Scholar
  21. 21.
    Cai GQ, Lin YK (1990) On randomly excited hysteretic structures. J Appl Mech 57:442–448CrossRefzbMATHGoogle Scholar
  22. 22.
    Zhu W, Ying Q (2002) Random response of Preisach hysteretic systems. J Sound Vib 254(1):37–49CrossRefGoogle Scholar
  23. 23.
    Waubke H, Haessig F (2016) Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation. J Sound Vib 382:258–273CrossRefGoogle Scholar
  24. 24.
    Waubke H, Haessig F (2017) Transient response of one-degree-of-freedom systems with Bouc-hysteresis excited by white noise. Proc Eng 199:1146–1151CrossRefGoogle Scholar
  25. 25.
    Wang Y, Huang Z, Jin X (2018) Approximately analytical technique for random response of LuGre friction system. Int J Non-Linear Mech 104:1–7CrossRefGoogle Scholar
  26. 26.
    Iwan W, Asano K (1984) An alternative approach to the random response of bilinear hysteretic systems. Earthq Eng Struct Dyn 12:229–236CrossRefGoogle Scholar
  27. 27.
    Wen Y (1960) Equivalent linearization for hysteretic systems under random excitation. J Appl Mech 27:649–652MathSciNetCrossRefGoogle Scholar
  28. 28.
    Reddy J (2006) Theory and analysis of elastic plates and shells. CRC Press Book, Boca RatonGoogle Scholar
  29. 29.
    Wijker J (2009) Random vibrations in spacecraft structures design: theory and applications. Springer, BerlinCrossRefzbMATHGoogle Scholar
  30. 30.
    Newland D (1993) An introduction to random vibrations, spectral and wavelet analysis. Longman Scientific & Technical, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Space StructuresAerospace Research InstituteTehranIran
  2. 2.Aerospace Department and Center of Excellence in Computational Aerospace EngineeringAmirkabir University of TechnologyTehranIran

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