Skip to main content
Log in

Stick-slip vibration of a moving oscillator on an axially flexible beam

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

This study investigates the stick-slip vibration between an axially flexible beam fixed at both ends and an oscillator moving on the beam. After deriving the equations of motion for the stick and slip states, the stick-slip vibrations between the oscillator and the beam are analyzed. In addition, to obtain the irregularly changed contact position due to the axial deformation of the beam and oscillator movement, a mathematical expression for the contact position is derived. It is found that the long-period stick-slip vibration is influenced mainly by the oscillator and the short-period vibration is influenced mainly by axial deformation of the beam. Furthermore, the dynamic responses show that even if a high damping ratio is applied to the oscillator, stick-slip vibration due to axial deformation of the beam can occur. Finally, the analysis shows that a kind of the internal resonance occurs between the oscillator and the beam when the harmonics of the natural frequency of the oscillator match the natural frequencies of the beam.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. M. Gibert, G. Fadel and M. F. Daqaq, On the stick-slip dynamics in ultrasonic additive manufacturing, Journal of Sound and Vibration, 332 (2013) 4680–4695.

    Article  Google Scholar 

  2. M. Sparham, A. A. D. Sarhan, N. A. Mardi, M. Dahari and M. Hamdi, Cutting force analysis to estimate the friction force in linear guideways of CNC machine, Measurement, 85 (2016) 65–79.

    Article  Google Scholar 

  3. S. C. Chang and H. P. Lin, Chaos attitude motion and chaos control in an automotive wiper system, International Journal of Solids and Structures, 41 (2004) 3491–3504.

    Article  Google Scholar 

  4. C. Chevennement-Roux, R. Grenouillat, T. Dreher, P. Alliot, E. Aubry, J. P. Lainé and L. Jézéquel, Wiper systems with flexible structures-instabilities analysis and correlation with a theoretical model, SAE Technical Paper, 2005-01-2375 (2005).

    Google Scholar 

  5. A. Koenen and A. Sanon, Tribological and vibroacoustic behavior of a contact between rubber and glass (application to wiper blade), Tribology International, 40 (2007) 1484–1491.

    Article  Google Scholar 

  6. Z. Wang and K. T. Chau, Control of chaotic vibration in automotive wiper systems, Chaos, Solitons & Fractals, 39 (2009) 168–181.

    Article  Google Scholar 

  7. A. Ammar, M. Yousif and I. Rahim, Investigate stick-slip intervals with one equation of motion and analyse the effect of the friction noise, International Journal of Scientific and Technology Research, 2 (2013) 96–111.

    Google Scholar 

  8. H. I. Won and J. Chung, Stick-slip vibration of an oscillator with damping, Nonlinear Dynamics, 86 (2016) 257–267.

    Article  Google Scholar 

  9. L. Tang, X. Zhu, X. Qian and C. Shi, Effects of weight on bit on torsional stick-slip vibration of oilwell drill string, Journal of Mechanical Science and Technology, 31 (2017) 4589–4597.

    Article  Google Scholar 

  10. U. Galvanetto and S. R. Bishop, Dynamics of a simple damped oscillator undergoing stick-slip vibrations, Meccanica, 34 (1999) 337–347.

    Article  MathSciNet  Google Scholar 

  11. S. Chatterjee, Non-linear control of friction-induced selfexcited vibration, International Journal of Non-Linear Mechanics, 42 (2007) 459–469.

    Article  MathSciNet  Google Scholar 

  12. A. Saha and P. Wahi, An analytical study of time-delayed control of friction-induced vibrations in a system with a dynamic friction model, International Journal of Non-Linear Mechanics, 63 (2014) 60–70.

    Article  Google Scholar 

  13. A. Papangelo, M. Ciavarella and N. Hoffmann, Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening-strengthening friction law: Analytical results and comparison with experiments, Nonlinear Dynamics, 90 (2017) 2037–2046.

    Article  Google Scholar 

  14. Z. Veraszto and G. Stepan, Nonlinear dynamics of hardwarein-the-loop experiments on stick-slip phenomena, International Journal of Non-Linear Mechanics, 94 (2017) 380–391.

    Article  Google Scholar 

  15. J. Wojewoda, A. Stefański, M. Wiercigroch and T. Kapitaniak, Estimation of Lyapunov exponents for a system with sensitive friction model, Archive of Applied Mechanics, 79 (2009) 667–677.

    Article  Google Scholar 

  16. A. Saha, M. Wiercigroch, K. Jankowski, P. Wahi and A. Stefański, Investigation of two different friction models from the perspective of friction-induced vibrations, Tribology International, 90 (2015) 185–197.

    Article  Google Scholar 

  17. A. Saha, P. Wahi, M. Wiercigroch and A. Stefański, A modified LuGre friction model for an accurate prediction of friction force in the pure sliding regime, International Journal of Non-Linear Mechanics, 80 (2016) 122–131.

    Article  Google Scholar 

  18. N. Hoffmann and L. Gaul, Effects of damping on mode - coupling instability in friction induced oscillations, ZAMM - Journal of Applied Mathematics and Mechanics, 83 (2003) 524–534.

    Article  Google Scholar 

  19. J. J. Sinou and L. Jezequel, Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping, European Journal of Mechanics -A/Solids, 26 (2007) 106–122.

    Article  Google Scholar 

  20. M. Pascal, New events in stick-slip oscillators behaviour, Journal of Applied Mathematics and Mechanics, 75 (2011) 283–288.

    Article  MathSciNet  Google Scholar 

  21. M. Pascal, New limit cycles of dry friction oscillators under harmonic load, Nonlinear Dynamics, 70 (2012) 1435–1443.

    Article  MathSciNet  Google Scholar 

  22. M. Pascal, A new model of dry friction oscillator colliding with a rigid obstacle, Nonlinear Dynamics, 91 (2018) 2541–2550.

    Article  Google Scholar 

  23. J. Tian, T. Zhang, L. Dai, W. Cheng, L. Yang and C. Yuan, Dynamic characteristics and test analysis of a new drilling downhole tool with anti-stick-slip features, Journal of Mechanical Science and Technology, 32 (2018) 4941–4949.

    Article  Google Scholar 

  24. F. Xia, P. Wolfs and C. Cole, On the motion of the structure varying multibody systems with two-dimensional dry friction, Journal of Mechanical Science and Technology, 19 (2005) 927–935.

    Article  Google Scholar 

  25. H. Ouyang, J. E. Mottershead, M. P. Cartmell and M. I. Friswell, Friction-induced parametric resonances in discs: effect of a negative friction-velocity relationship, Journal of Sound and Vibration, 209 (1998) 251–264.

    Article  Google Scholar 

  26. J. Heilig and J. Wauer, Stability of a nonlinear brake system at high operating speeds, Nonlinear Dynamics, 34 (2003) 235–247.

    Article  Google Scholar 

  27. M. A. Heckl and I. D. Abrahams, Curve squeal of train wheels, part 1: Mathematical model for its generation, Journal of Sound and Vibration, 229 (2000) 669–693.

    Article  Google Scholar 

  28. H. Ouyang, J. E. Mottershead, M. P. Cartmell and D. J. Brookfield, Friction-induced vibration of an elastic slider on a vibrating disc, International Journal of Mechanical Science, 41 (1999) 325–336.

    Article  Google Scholar 

  29. Z. Li, H. Ouyang and Z. Guan, Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment, Nonlinear Dynamics, 87 (2017) 1045–1067.

    Article  Google Scholar 

  30. V. N. Pilipchuk, R. A. Ibrahim and P. G. Blaschke, Disc brake ring-element modeling involving friction-induced vibration, Journal of Vibration and Control, 8 (2002) 1085–1104.

    Article  Google Scholar 

  31. D. Tonazzi, F. Massi, A. Culla, L. Baillet, A. Fregolent and Y. Berthier, Instability scenarios between elastic media under frictional contact, Mechanical Systems and Signal Processing, 40 (2013) 754–766.

    Article  Google Scholar 

  32. H. M. Sedighi, K. H. Shirazi and K. Naderan-Tahan, Stick-slip vibrations of layered structures undergoing large deflection and dry friction at the interface, Journal of Vibration and Acoustics, 135 (2013) 061006.

    Article  Google Scholar 

  33. S. Yamagishi and S. Morishita, Friction vibration modeling with detachment and adhesion by Cellular Automata, Journal of Computational Science, 11 (2015) 226–232.

    Article  Google Scholar 

  34. J. Chung and G. M. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method, Journal of Applied Mechanics, 60 (1993) 371–375.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (NRF-2018R1D1A1B07050187).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jintai Chung.

Additional information

Recommended by Editor No-cheol Park

Jun-gi Hong received his B.S. degree in 2012 from the Department of Mechanical Engineering at Hanyang University. He is currently a Ph.D. candidate in the Department of Mechanical Engineering at Hanyang University. His research interests are the stick-slip vibration of mechanical systems with a relative motion and BSR noise reductions of vehicles and home appliances.

Jaewon Kim received his B.S. degree in 2012 and Ph.D. degree in 2019 from the Department of Mechanical Engineering at Hanyang University. His research interests are the dynamics of robot manipulator and the vibration and noise reductions of rotating machines and vehicles.

Jintai Chung received his B.S. and M.S. degrees from the Department of Mechanical Engineering at Seoul National University in 1984 and 1986, respectively. He obtained his Ph.D. degree from the Department of Mechanical Engineering at University of Michigan, Ann Arbor in 1992. He is currently a Professor in the Department of Mechanical Engineering at Hanyang University. His research interests are vibration and noise reductions of rotating machines, vehicles and home appliances.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hong, Jg., Kim, J. & Chung, J. Stick-slip vibration of a moving oscillator on an axially flexible beam. J Mech Sci Technol 34, 541–553 (2020). https://doi.org/10.1007/s12206-020-0102-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0102-y

Keywords

Navigation