Abstract
The onset of low-velocity collisions in vibro-impacting systems induces instabilities in the system dynamics that, when not checked, may result in sudden, and unanticipated discontinuous transitions between distinct steady-state responses. This paper illustrates this phenomenology in an example system that includes dry friction. Here, the instability is associated with the zero-velocity contact of an oscillatory unilateral constraint and a stationary mass suspended through a preloaded spring. The analysis summarizes observations on the passive response of the mass under variations in the oscillation amplitude of the constraint. A control strategy is subsequently shown to successfully suppress the instability. The paper concludes with suggestions for applications of this phenomenology as well as a description of similar observation in mechanical systems with or without friction and with rigid as well as compliant contact.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdel-Rahman, E.M., Nayfeh, A.H.: Secondary resonances of electrically actuated resonant microsensors. J. Micromech. Microeng. 13(3), 491–501 (2003)
Dankowicz, H., Jerrelind, J.: Control of Near-grazing Dynamics in Impact Oscillators. P Roy. Soc. A-Math. Phys. 461(2063), 3365–3380 (2005)
Dankowicz, H., Svahn, F.: On the Stabilizability of Near-grazing Dynamics in Impact Oscillators. Int. J. Robust Nonlin. 17, 1405–1429 (2007)
Dankowicz, H., Zhao, X., Misra, S.: Near-grazing Dynamics in Tapping-mode Atomic-force Microscopy. Int. J. Nonlin. Mech. 42, 697–709 (2007)
Long, X.-H., Lin, G., Balachandran, B.: Grazing bifurcations in an elastic structure excited by harmonic impactor motions. Physica D 237(8), 1129–1138 (2008)
Mohr, T., Uhlmann, F.H.: Detecting Thresholds by Means of Jump-Phenomena. In: Proceeedings of 7th IEEE International Conference on Electronics, Circuits and Systems (2000)
Nordmark, A.B.: Effects Due to Low Velocity Impact in Mechanical Oscillators. Int. J. Bifurcat Chaos 2(3), 597–605 (1992)
Paques, J.-J.: Limit switches: Selection for safety. ISA Trans. 33(1), 99–103 (1994)
Pavlovskaia, E., Wiercigroch, M., Grebogi, C.: Modeling of an Impact System with Drift. Phys. Rev. E 64, 056224, 1–9 (2001)
Siddiqi, I., Vijay, R., Pierre, F., Wilson, C.M., Metcalfe, M., Rigetti, C., Frunzio, L., Devoret, M.H.: RF-driven Josephson bifurcation amplifier for quantum measurement. Phys. Rev. Lett. 93(20), 207002, 1–4 (2004)
Svahn, F., Dankowicz, H.: Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions. J. Vib. Control 14(1-2), 255–284 (2008)
Svahn, F., Dankowicz, H.: Controlled Onset of Low-velocity Collisions in a Vibro-impacting System with Friction. Submitted to P. Roy. Soc. A-Math. Phys. (2009)
Turner, K.L., Baskaran, R., Zhang, W.: Using nonlinear dynamics for performance enhancement in resonant micro and nano-scale devices. In: Proceedings of the IEEE Conference on Decision and Control, vol. 3, pp. 2650–2651 (2003)
Zhang, W., Baskaran, R., Turner, K.L.: Effect of Cubic Nonlinearity on Auto-Parametrically Amplified Resonant MEMS Mass Sensor. Sensor Actuat A-Phys. 102(1-2), 139–150 (2002)
Zhang, W., Turner, K.L.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sensor Actuat A-Phys. 122(1), 23–30 (2005)
Zhao, X., Dankowicz, H.: Characterization of Intermittent Contact in Tapping-mode Atomic Force Microscopy. J. Comput. Nonlin. Dyn. 1(2), 109–115 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dankowicz, H., Svahn, F. (2009). Control of Instabilities Induced by Low-Velocity Collisions in a Vibro-Impacting System with Friction. In: Ibrahim, R.A., Babitsky, V.I., Okuma, M. (eds) Vibro-Impact Dynamics of Ocean Systems and Related Problems. Lecture Notes in Applied and Computational Mechanics, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00629-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-00629-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00628-9
Online ISBN: 978-3-642-00629-6
eBook Packages: EngineeringEngineering (R0)