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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Stick-Slip Instability in a Compliant Bistable Double-Slider Mechanism

Journal of Applied Nonlinear Dynamics 10(4) (2021) 775--789 | DOI:10.5890/JAND.2021.12.013

Alborz Niknam , Kambiz Farhang

Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale,\\ 1263 Lincoln Drive, Carbondale, IL 62901-6899, USA

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A This paper investigates friction-induced instability in a Single Degree-of-Freedom, pseudo-rigid-body representation of a bistable compliant mechanism composed of two sliders connected with a massless rigid link. The friction force is a function of the state variables through Stribeck effect and variable contact force due to the structural nonlinearity of the mechanism. A Constant normal force ensures the mass-belt contact during oscillation. It is shown that the steady-state response of the vibrating mechanism depends on the belt velocity, applied normal load, and stiffness. The applied normal force and belt velocity, as bifurcation parameters, are used to define the number and location of equilibrium points and their corresponding stability.


  1. [1]  Howell, L.L. (2001), Compliant mechanisms, John Wiley & Sons.
  2. [2]  Kota, S., Lu, K.-J., Kreiner, Z., Trease, B., Arenas, J., and Geiger, J. (2005), Design and application of compliant mechanisms for surgical tools, J. Biomech. Eng., 127, 981-989.
  3. [3]  Kota, S., Hetrick, J.A., Osborn, R., Paul, D., Pendleton, E., Flick, P., and Tilmann, C. (2003), Design and application of compliant mechanisms for morphing aircraft structures, in: Industrial and Commercial Applications of Smart Structures Technologies, pp. 24-34.
  4. [4]  Jensen, B.D. and Howell, L.L. (2004), Bistable configurations of compliant mechanisms modeled using four links and translational joints, J. Mech. Des., 126, 657-666.
  5. [5]  Chen, G., Gou, Y., and Zhang, A. (2011), Synthesis of compliant multistable mechanisms through use of a single bistable mechanism, J. Mech. Des., 133, 81007-81009.
  6. [6]  S\"{o}nmez, \"{U} and Tutum, C.C. (2008), A Compliant bistable mechanism design incorporating elastica buckling beam theory and pseudo-rigid-body model, J. Mech. Des., 130, 42304-42314.
  7. [7]  Jensen, B.D., Howell, L.L., and Salmon, L.G. (1999), Design of two-link, in-plane, bistable compliant micro-mechanisms, J. Mech. Des., 121, 416-423.
  8. [8]  Niknam, A. and Farhang, K. (2018), Vibration instability in a large motion bistable compliant mechanism due to stribeck friction, J. Vib. Acoust.,
  9. [9]  Berger, E. (2002), Friction modeling for dynamic system simulation, Appl. Mech. Rev., 55, 535.
  10. [10]  Ibrahim, R.A. (1994), Friction-induced vibration, chatter, squeal, and chaos---Part II: dynamics and modeling, Appl. Mech. Rev., 47, 227-253.
  11. [11]  Ibrahim, R.A. (1994), Friction-induced vibration, chatter, squeal, and chaos---Part I: mechanics of contact and friction, Appl. Mech. Rev., 47, 209-226.
  12. [12]  Kovalyshen, Y. (2015), Understanding root cause of stick-slip vibrations in deep drilling with drag bits, Int. J. Non. Linear. Mech., 67, 331-341.
  13. [13]  Sarker, M., Rideout, D.G., and Butt, S.D. (2017), Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction, J. Pet. Sci. Eng., 150, 272-287.
  14. [14]  Mirzababaei, S. and Filip, P. (2017), Impact of humidity on wear of automotive friction materials, Wear., 376-377, 717-726.
  15. [15]  Le Rouzic, J., Le Bot, A., Perret-Liaudet, J., Guibert, M., Rusanov, A., Douminge, L., Bretagnol, F., and Mazuyer, D. (2013), Friction-induced vibration by Stribeck's Law: Application to wiper blade squeal noise, Tribol. Lett., 49, 563-572.
  16. [16]  Hetzler, H., Schwarzer, D., and Seemann, W. (2007), Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise, Commun. Nonlinear Sci. Numer. Simul., 12, 83-99.
  17. [17]  Juel Thomsen, J. and Fidlin, A. (2003), Analytical approximations for stick-slip vibration amplitudes, Int. J. Non. Linear. Mech., 38, 389-403.
  18. [18]  Niknam, A. and Farhang, K. (2019), Friction-induced vibration due to mode-coupling and intermittent contact loss, J. Vib. Acoust. 141, 021012 (10 pages).
  19. [19]  Hoffmann, N. and Gaul, L. (2004), A sufficient criterion for the onset of sprag-slip oscillations, Arch. Appl. Mech., 73, 650-660.
  20. [20]  Sinou, J.-J., Thouverez, F., and Jezequel, L. (2003), Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model, J. Sound Vib., 265, 527-559.
  21. [21]  Dupont, P.E. and Bapna, D. (1996), Perturbation stability of frictional sliding with varying normal force, J. Vib. Acoust., 118, 491-497.
  22. [22]  Dupont, P.E. and Bapna, D. (1994), Stability of sliding frictional surfaces with varying normal force, J. Vib. Acoust., 116, 237-242.
  23. [23]  Luo, A.C.J. and Gegg, B.C. (2006), On the mechanism of stick and nonstick, periodic motions in a periodically forced, linear oscillator with dry friction, J. Vib. Acoust., 128, 97-105.
  24. [24]  Luo, A.C.J. and Huang, J. (2012), Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator, Nonlinear Anal. Real World Appl., 13, 241-257.
  25. [25]  Luo, A.C.J. and Gegg, B.C. (2006), Dynamics of a harmonically excited oscillator with dry-friction on a sinusoidally time-varying, traveling surface, Int. J. Bifurc. Chaos., 16, 3539-3566.
  26. [26]  Luo, A.C.J. and Gegg, B.C. (2006), Periodic motions in a periodically forced oscillator moving on an oscillating belt with dry friction, ASME Journal of Computational and Nonlinear Dynamics, 1, 212-220.
  27. [27]  Luo, A.C.J. and Zwiegart Jr, P. (2008), Existence and analytical predictions of periodic motions in a periodically forced, nonlinear friction oscillator, J. Sound Vib., 309, 129-149.
  28. [28]  Won, H.I. and Chung, J. (2016), Stick--slip vibration of an oscillator with damping, Nonlinear Dyn., 86, 257-267.