Skip to main content

Advertisement

SpringerLink
Log in

Vibration attenuation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force using nonlinear energy sink

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

This paper studies the effect of a number of smooth nonlinear energy sinks (NESs) on the vibration mitigation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force. The NESs have a linear damping and an essentially nonlinear stiffness. Two NESs in the perpendicular directions are located on the bearing body. The equations of motion are derived and numerically solved. In order to optimize the parameters of the NESs, a genetic algorithm is utilized. For different values of the system parameters, periodic, two-periodic (2T) and qusai-periodic motions, occur in the system. It is shown that the NESs reduce effectively vibration of the rotor-bearing system in an operating speed range. However, the type of motion does not change in the most rotational speeds of rotor. Furthermore, for lower values of damping, the NESs demonstrate a high performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

c :

The radial clearance of the bearing

c r , c 0, \( C_{nes} \) :

The dampings of rotor, bearing, and NES

e :

The eccentricity of journal

l :

The length of bearing

m, m 0, m nes :

The masses of rotor, bearing, and NES

K 1, K 2 :

The linear and nonlinear stiffnesses of the bearing foundation

K nes :

The essentially nonlinear stiffness of NES

K s :

The stiffness of rotating shaft

X b , Y b :

The displacements of bearing along the X- and Y- directions, respectively

X j , Y j :

The displacements of journal along the X- and Y- directions, respectively

X n , Y n :

The displacements of NESs along the X- and Y- directions, respectively

X r , Y r :

The displacements of rotor along the X- and Y- directions, respectively

ɛ = e/c :

The dimensionless eccentricity of the journal

(ϕ = ωt):

The rotational angle of the rotor

μ :

The dynamic viscosity of oil

θ :

The angle of minimum thickness of oil film

ρ :

The mass eccentricity of the rotor

ω :

The rotational speed of the rotor

References

  1. Adiletta G, Guido AR, Rossi C (1997) Nonlinear dynamics of a rigid unbalanced rotor in journal bearings part I: theoretical analysis. Nonlinear Dyn 14:57–87

    Article  MATH  Google Scholar 

  2. Adiletta G, Guido AR, Rossi C (1997) Nonlinear dynamics of a rigid unbalanced rotor in journal bearings part II: experimental analysis. Nonlinear Dyn 14:157–189

    Article  MATH  Google Scholar 

  3. Dai X, Shen Z, Wei H (2001) On the vibration of rotor-bearing system with squeeze film damper in an energy storage flywheel. Int J Mech Sci 43:2525–2540

    Article  MATH  Google Scholar 

  4. Frulla G (2000) Rigid rotor dynamic stability using Floquet theory. Eur J Mechan A/Solids 19:139–150

    Article  ADS  MATH  Google Scholar 

  5. Tiago AN, Silva N, Maia MM (2011) Elastically restrained Bernoulli–Euler beams applied to rotary machinery modeling. Acta Mech Sin 27(1):56–62

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Byers L, Gandhi F (2009) Embedded absorbers for helicopter rotor lag damping. J Sound Vib 325:705–721

    Article  ADS  Google Scholar 

  7. Chang-Jian CW, Chen CK (2009) Chaotic response and bifurcation analysis of a flexible rotor supported by porous and non-porous bearings with nonlinear suspension. Nonlinear Anal Real World Appl 10:1114–1138

    Article  MATH  Google Scholar 

  8. Chang-Jian CW, Chen CK (2007) Chaos and bifurcation of a flexible rub-impact rotor supported by oil film bearings with nonlinear suspension. Mech Mach Theory 42:312–333

    Article  MATH  Google Scholar 

  9. Chang-Jian CW, Chen CK (2009) Chaos of rub–impact rotor supported by bearings with nonlinear suspension. Tribol Int 42:426–439

    Article  Google Scholar 

  10. Shahgholi M, Khadem SE (2013) Resonances of an in-extensional asymmetrical spinning shaft with speed fluctuations. Meccanica 48(1):103–120

    Article  MathSciNet  MATH  Google Scholar 

  11. Najafi A, Ghazavi MR, Jafari AA (2014) Application of Krein’s theorem and bifurcation theory for stability analysis of a bladed rotor. Meccanica 49:1507–1526

    Article  MathSciNet  MATH  Google Scholar 

  12. Han Q, Zhai J, Wang M, Guan T (2014) Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum. Meccanica 49(10):2335–2357

    Article  MathSciNet  MATH  Google Scholar 

  13. Gendelman OV, Vakakis AF, Manevitch LI, Closkey RM (2001) Energy pumping in nonlinear mechanical oscillators I: dynamics of the underlying Hamiltonian system. J Appl Mech 68:34–41

    Article  MathSciNet  MATH  Google Scholar 

  14. Vakakis AF (2001) Inducing passive nonlinear energy sinks in linear vibrating systems. J Vib Acoust 123(3):324–332

    Article  Google Scholar 

  15. Ahmadabadi ZN, Khadem SE (2012) Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech Mach Theory 50:134–149

    Article  Google Scholar 

  16. Georgiades F, Vakakis AF (2009) Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear attachments. Int J Solids Struct 46:2330–2353

    Article  MATH  Google Scholar 

  17. Georgiades F, Vakakis AF (2007) Dynamics of a linear beam with an attached local nonlinear energy sink. Commun Nonlinear Sci Numer Simul 12:643–651

    Article  ADS  MATH  Google Scholar 

  18. Ahmadabadi ZN, Khadem SE (2012) Self-excited oscillations attenuation of drill-string system using nonlinear energy sink. J Mech Eng Sci. doi:10.1177/0954406212447226

    Google Scholar 

  19. Georgiades F, Vakakis AF, Kerschen G (2007) Broadband passive targeted energy pumping from a linear dispersive rod to a lightweight essentially non-linear end attachment. Int J Non-Linear Mech 42:773–788

    Article  Google Scholar 

  20. Samani FS, Pellicano F (2009) Vibration reduction on beams subjected to moving loads using linear and nonlinear dynamic absorbers. J Sound Vib 325:742–754

    Article  ADS  Google Scholar 

  21. Avramov KV, Gendelman OV (2010) On interaction of vibrating beam with essentially nonlinear absorber. Meccanica 45(3):355–365

    Article  MathSciNet  MATH  Google Scholar 

  22. Lamarque CH, Savadkoohi AT (2014) Dynamical behavior of a Bouc–Wen type oscillator coupled to a nonlinear energy sink. Meccanica 49(8):1917–1928

    Article  MathSciNet  MATH  Google Scholar 

  23. Lamarque CH, Savadkoohi AT (2014) Targeted energy transfer between a system with a set of Saint-Venant elements and a nonlinear energy sink. Continuum Mech Thermodyn. doi:10.1007/s00161-014-0354-9

    MATH  Google Scholar 

  24. Weiss M, Savadkoohi AT, Gendelman OV, Lamarque CH (2014) Dynamical behavior of a mechanical system including Saint-Venant component coupled to a non-linear energy sink. Int J Non-Linear Mech 63:10–18

    Article  Google Scholar 

  25. Domany E, Gendelman OV (2013) Dynamic responses and mitigation of limit cycle oscillations in Van der Pol-Duffing oscillator with nonlinear energy sink. J Sound Vib 332:5489–5507

    Article  ADS  Google Scholar 

  26. Perchikov N, Gendelman OV (2015) Dynamics and stability of a discrete breather in a harmonically excited chain with vibro-impact on-site potential. Phys D 292–293:8–28

    Article  MathSciNet  Google Scholar 

  27. Vaurigaud B, Manevitch LI, Lamarque CH (2011) Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer. J Sound Vib 330(11):2580–2595

    Article  ADS  Google Scholar 

  28. Ahmadabadi ZN, Khadem SE (2012) Annihilation of high-amplitude periodic responses of a forced two degrees-of-freedom oscillatory system using nonlinear energy sink. J Vib Control. doi:10.1177/1077546312456226

    Google Scholar 

  29. Younesian D, Nankali A, Motieyan E (2011) Optimal nonlinear energy sinks in vibration mitigation of the beams traversed by successive moving loads. Journal of Solid Mechanics 3(4):323–331

    Google Scholar 

  30. Ahmadabadi ZN, Khadem SE (2012) Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device. J Sound Vib 333:4444–4457

    Article  Google Scholar 

  31. Viguie R, Kerschen G (2009) Nonlinear Vibration absorber coupled to a nonlinear primary system: a tuning methodology. J Sound Vib 326:780–793

    Article  ADS  Google Scholar 

  32. Bab S, Khadem SE, Shahgholi M (2014) Vibration mitigation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force using nonlinear energy sink. Int J Non-Linear Mech. doi:10.1016/j.ijnonlinmec.2014.08.016i

    Google Scholar 

  33. Angelo L, Zulli D (2012) Dynamic analysis of externally excited NES-controlled systems via a mixed Multiple Scale/Harmonic Balance algorithm. Nonlinear Dynamic 70:2049–2061

    Article  MathSciNet  Google Scholar 

  34. Mehmood A, Nayfeh AH, Hajj MR (2014) Effects of a non-linear energy sink (NES) on vortex-induced vibrations of a circular cylinder. Nonlinear Dyn 77(3):667–680

    Article  Google Scholar 

  35. Guo C, AL-Shudeifat MA, Vakakis AF, Bergman LA, McFarland DM, Yan J (2014) Vibration reduction in unbalanced hollow rotor systems with nonlinear energy sinks. Nonlinear Dynamic. doi:10.1007/s11071-014-1684-7

    Google Scholar 

  36. Genta G (2005) Dynamics of Rotating Systems, 1st edn. Springer, Berlin

    Book  MATH  Google Scholar 

  37. Nayfeh AH, Holden AV (2004) Applied nonlinear dynamics. Wiley-Interscience, Hoboken

    Google Scholar 

  38. Wang L, Cao DQ, Huang W (2010) nonlinear coupled dynamics of flexible blade–rotor–bearing systems. Tribol Int 43:759–778

    Article  Google Scholar 

  39. Varney P, Green I (2015) Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor–stator contact system. J Sound Vib 336(3):207–226

    Article  ADS  Google Scholar 

  40. API (1996) API Publication 684: Tutorial on the API standard paragraphs covering rotor dynamics and balancing: an introduction to lateral critical and train torsional analysis and rotor balancing, API

  41. Dimond M (2000) Vibration characteristics of industrial gas turbines, shaft centerlines

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tarbiat Modares University, P.O. Box 14115-177, Tehran, Iran

    Saeed Bab & Siamak E. Khadem

  2. Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, P.O. Box 16785-136, Tehran, Iran

    Majid Shahgholi

Authors
  1. Saeed Bab
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siamak E. Khadem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Majid Shahgholi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Siamak E. Khadem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bab, S., Khadem, S.E. & Shahgholi, M. Vibration attenuation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force using nonlinear energy sink. Meccanica 50, 2441–2460 (2015). https://doi.org/10.1007/s11012-015-0156-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-015-0156-6

Keywords

Search

Navigation