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Bichri, Amine; Belhaq, Mohamed; Perret-Liaudet, Joël

Control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator. (English) Zbl 1215.70016

Nonlinear Dyn. 63, No. 1-2, 51-60 (2011).
Summary: The control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator is investigated analytically and numerically in this paper. The control strategy is introduced via a fast excitation and attention is focused on the response near the primary resonance. The fast excitation is added to the basic harmonic force, either through a harmonic force applied from above, or via a harmonic base displacement added from bellow, or by considering the stiffness of the oscillator as a periodically and rapidly varying in time. The results reveal that the threshold of vibroimpact response initiated by jump phenomenon near the primary resonance can be shifted toward lower or higher frequencies of the slow dynamic system depending on the fast excitation taken into consideration. It was also shown that the most realistic and practical way for controlling the vibroimpact dynamics is the introduction of a fast harmonic base displacement.

Cited in 2 Documents

MSC:

70Q05 Control of mechanical systems
70K70 Systems with slow and fast motions for nonlinear problems in mechanics

Keywords:

Hertzian contact; vibroimpact; high-frequency excitation; active control; perturbation analysis
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\textit{A. Bichri} et al., Nonlinear Dyn. 63, No. 1--2, 51--60 (2011; Zbl 1215.70016)
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References:

[1] Nayak, R.: Contact vibrations. J. Sound Vib. 22, 297–322 (1972) · Zbl 0236.70027
[2] Hess, D., Soom, A.: Normal vibrations and friction under harmonic loads: Part 1: Hertzian contact. ASME J. Tribol. 113, 80–86 (1991)
[3] Sabot, J., Krempf, P., Janolin, C.: Nonlinear vibrations of a sphere–plane contact excited by a normal load. J. Sound Vib. 214, 359–375 (1998)
[4] Carson, R., Johnson, K.: Surface corrugations spontaneously generated in a rolling contact disc machine. Wear 17, 59–72 (1971)
[5] Soom, A., Chen, J.W.: Simulation of random surface roughness-induced contact vibrations at Hertzian contacts during steady sliding. ASME J. Tribol. 108, 123–127 (1986)
[6] Mann, B.P., Carter, R.E., Hazra, S.S.: Experimental study of an impact oscillator with viscoelastic and Hertzian contact. Nonlinear Dyn. 50, 587–596 (2007) · Zbl 1177.70003
[7] Rong, H., Wanga, X., Xu, W., Fang, F.: Resonant response of a non-linear vibro-impact system to combined deterministic harmonic and random excitations. Int. J. Non-Linear Mech. 45, 474–481 (2010)
[8] Rigaud, E., Perret-Liaudet, P.: Experiments and numerical results on nonlinear vibrations of an impacting Hertzian contact. Part 1: Harmonic excitation. J. Sound Vib. 265, 289–307 (2003)
[9] Perret-Liaudet, J., Rigaud, E.: Response of an impacting Hertzian contact to an order-2 subharmonic excitation: Theory and experiments. J. Sound Vib. 296, 319–333 (2003)
[10] Perret-Liaudet, J., Rigaud, E.: Superharmonic resonance of order 2 for an impacting Hertzian contact oscillator: Theory and experiments. J. Comput. Nonlinear Dyn. 2, 190–196 (2007)
[11] Hess, D., Soom, A., Kim, C.: Normal vibrations and friction at a Hertzian contact under random excitation: Theory and experiments. J. Sound Vib. 153, 491–508 (1992) · Zbl 0925.73754
[12] Perret-Liaudet, J., Rigaud, E.: Experiments and numerical results on nonlinear vibrations of an impacting Hertzian contact. Part 2: Random excitation. J. Sound Vib. 265, 309–327 (2003)
[13] Stephenson, A.: On induced stability. Philos. Mag. 15, 233–236 (1908) · JFM 39.0768.01
[14] Hirsch, P.: Das pendel mit oszillierendem Aufhängepunkt. Z. Angew. Math. Mech. 10, 41–52 (1930) · JFM 56.0683.01
[15] Kapitza, P.L.: Dynamic stability of a pendulum with an oscillating point of suspension. Z. Eksp. Teor. Fiz. 21, 588–597 (1951) (in Russian)
[16] Thomsen, J.J.: Some general effects of strong high-frequency excitation: stiffening, biasing, and smoothening. J. Sound Vib. 253, 807–831 (2002)
[17] Jensen, J.S., Tcherniak, D.M., Thomsen, J.J.: Stiffening effects of high-frequency excitation: experiments for an axially loaded beam. J. Appl. Mech. 253, 397–402 (2000) · Zbl 1110.74497
[18] Hansen, M.H.: Effect of high-frequency excitation on natural frequencies of spinning discs. J. Sound Vib. 234, 577–589 (2000)
[19] Tcherniak, D., Thomsen, J.J.: Slow effect of fast harmonic excitation for elastic structures. Nonlinear Dyn. 17, 227–246 (1988) · Zbl 0933.74032
[20] Mann, B.P., Koplow, M.A.: Symmetry breaking bifurcations of a parametrically excited pendulum. Nonlinear Dyn. 46, 427–437 (2006) · Zbl 1170.70359
[21] Sah, S.M., Belhaq, M.: Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator. Chaos Solitons Fractals 37, 1489–1496 (2008) · Zbl 1142.34332
[22] Belhaq, M., Sah, S.M.: Fast parametrically excited van der Pol oscillator with time delay state feedback. Int. J. Non-Linear Mech. 43, 124–130 (2008)
[23] Belhaq, M., Sah, S.M.: Horizontal fast excitation in delayed van der Pol oscillator. Commun. Nonlinear Sci. Numer. Simul. 13, 1706–1713 (2008) · Zbl 1142.34332
[24] Belhaq, M., Fahsi, A.: 2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator. Nonlinear Dyn. 53, 139–152 (2008) · Zbl 1170.70344
[25] Fahsi, A., Belhaq, M., Lakrad, F.: Suppression of hysteresis in a forced van der Pol–Duffing oscillator. Commun. Nonlinear Sci. Numer. Simul. 14, 1609–1616 (2009) · Zbl 1221.34126
[26] Belhaq, M., Fahsi, A.: Hysteresis suppression for primary and subharmonic 3:1 resonances using fast excitation. Nonlinear Dyn. 57, 275–287 (2009) · Zbl 1176.70021
[27] Lakrad, F., Belhaq, M.: Suppression of pull-in instability in MEMS using a high-frequency actuation. Commun. Nonlinear Sci. Numer. Simul. 15, 3640–3646 (2010) · Zbl 05958123
[28] Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1979) · Zbl 0599.73108
[29] Blekhman, I.I.: Vibrational Mechanics–Nonlinear Dynamic Effects, General Approach, Application. Singapore, World Scientific (2000)
[30] Thomsen, J.J.: Vibrations and Stability: Advanced Theory, Analysis, and Tools. Springer, Berlin (2003) · Zbl 1086.70001
[31] Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)
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