Abstract
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.
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References
Nayak, R.: Contact vibrations. J. Sound Vib. 22, 297–322 (1972)
Hess, D., Soom, A.: Normal vibrations and friction under harmonic loads: Part 1: Hertzian contact. ASME J. Tribol. 113, 80–86 (1991)
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)
Carson, R., Johnson, K.: Surface corrugations spontaneously generated in a rolling contact disc machine. Wear 17, 59–72 (1971)
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)
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)
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)
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)
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)
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)
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)
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)
Stephenson, A.: On induced stability. Philos. Mag. 15, 233–236 (1908)
Hirsch, P.: Das pendel mit oszillierendem Aufhängepunkt. Z. Angew. Math. Mech. 10, 41–52 (1930)
Kapitza, P.L.: Dynamic stability of a pendulum with an oscillating point of suspension. Z. Eksp. Teor. Fiz. 21, 588–597 (1951) (in Russian)
Thomsen, J.J.: Some general effects of strong high-frequency excitation: stiffening, biasing, and smoothening. J. Sound Vib. 253, 807–831 (2002)
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)
Hansen, M.H.: Effect of high-frequency excitation on natural frequencies of spinning discs. J. Sound Vib. 234, 577–589 (2000)
Tcherniak, D., Thomsen, J.J.: Slow effect of fast harmonic excitation for elastic structures. Nonlinear Dyn. 17, 227–246 (1988)
Mann, B.P., Koplow, M.A.: Symmetry breaking bifurcations of a parametrically excited pendulum. Nonlinear Dyn. 46, 427–437 (2006)
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)
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)
Belhaq, M., Sah, S.M.: Horizontal fast excitation in delayed van der Pol oscillator. Commun. Nonlinear Sci. Numer. Simul. 13, 1706–1713 (2008)
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)
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)
Belhaq, M., Fahsi, A.: Hysteresis suppression for primary and subharmonic 3:1 resonances using fast excitation. Nonlinear Dyn. 57, 275–287 (2009)
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)
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1979)
Blekhman, I.I.: Vibrational Mechanics—Nonlinear Dynamic Effects, General Approach, Application. Singapore, World Scientific (2000)
Thomsen, J.J.: Vibrations and Stability: Advanced Theory, Analysis, and Tools. Springer, Berlin (2003)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)
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Bichri, A., Belhaq, M. & Perret-Liaudet, J. Control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator. Nonlinear Dyn 63, 51–60 (2011). https://doi.org/10.1007/s11071-010-9784-5
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DOI: https://doi.org/10.1007/s11071-010-9784-5