Location of Repository

Dynamics of an impact oscillator near a degenerate graze

By D.R.J. Chillingworth

Abstract

We give a complete analysis of low-velocity dynamics close to grazing<br/>for a generic one degree of freedom impact oscillator. <br/>This includes nondegenerate (quadratic) grazing and minimally<br/>degenerate (cubic) grazing, corresponding respectively to nondegenerate<br/>and degenerate chatter. We also describe the dynamics associated<br/>with generic one-parameter bifurcation at a more degenerate (quartic)<br/>graze, showing in particular how this gives rise to the often-observed<br/>highly convoluted structure in the stable manifolds of chattering orbits.<br/>The approach adopted is geometric, using methods from singularity theory

Topics: TJ, QA
Year: 2010
OAI identifier: oai:eprints.soton.ac.uk:71868
Provided by: e-Prints Soton

Suggested articles

Preview

Citations

  1. (1988). A doi
  2. (1983). A periodically forced piecewise linear oscillator doi
  3. (2002). and Askari A doi
  4. (1987). and Tondl A doi
  5. (1959). Andronov A A, Vitt A A and doi
  6. (2006). Asymptotic analysis of chattering oscillations for an impacting inverted pendulum doi
  7. (2008). Bifurcations in nonsmooth dynamical systems doi
  8. (1986). Catastrophe Theory, 2nd ed
  9. (2008). Champneys A R and Kowalczyk P doi
  10. (1982). Chaos after period doubling bifurcations in the resonance of an impact oscillator Phys Lett 91A 5{8 doi
  11. (1995). Chaotic regular and unbounded behaviour in the elastic impact oscillator doi
  12. (2001). Chatter sticking and chaotic impacting motion in a two-degree of freedom impact oscillator doi
  13. (1994). Chattering and related behaviour in impact oscillators Phil Trans R Soc London A doi
  14. (1995). Clie A
  15. (2005). Control of near-grazing dynamics in impact oscillators Proc Roy Soc London A doi
  16. (1984). Curves and Singularities (Cambridge: doi
  17. (2002). Discontinuity geometry for an impact oscillator doi
  18. (1992). Dynamical complexities of forced impacting systems Phil Trans R Soc London A doi
  19. (2004). Dynamics of a two degree of freedom vibro-impact system with multiple motion limiting constraints doi
  20. (2007). Experimental and numerical veri of bifurcations and chaos in cam-follower impacting systems doi
  21. (2006). Fidlin A doi
  22. (1989). Geometry of singular sets Math Proc Cambridge Philos Soc doi
  23. (1987). Global dynamics of a vibro-impacting linear oscillator doi
  24. (1994). Grazing bifurcation in impact oscillators doi
  25. (1999). Grazing bifurcations and basins of attraction in an impact-friction oscillator doi
  26. (2003). Hybrid dynamics of two coupled oscillators that can impact a stop doi
  27. (1994). Impact oscillations: linear theory of stability and doi
  28. (1992). Local and global stability of a piecewise linear oscillator Phil Trans R Soc London A doi
  29. (2007). Mathematical models of gear rattle in Roots blower vacuum pumps doi
  30. (2003). Modelling of vibro-impact system driven by beat frequency doi
  31. (1984). Motion pictures: an application of singularity theory doi
  32. (1991). Non-periodic motion caused by grazing incidence in an impact oscillator doi
  33. (1985). Nonlinear Oscillations in Physical Systems (Princeton: doi
  34. (1999). Nonsmooth Mechanics London: Springer-Verlag)Dynamics of an impact oscillator near a degenerate graze 32
  35. (1955). On singularities of mappings of Euclidean spaces I doi
  36. (1984). On the motion of the oset impact oscillator
  37. (1985). Outlines and their duals Proc London doi
  38. (1971). Partially hyperbolic points doi
  39. (2005). Partially hyperbolic dynamical systems doi
  40. (2000). Rigid-body dynamics with friction and impact doi
  41. (1987). The vibro-impact response of a harmonically excited and preloaded onedimensional linear oscillator doi
  42. (1988). Theory of Vibro-Impact Systems and Applications, doi
  43. (1992). Transition to chaotic motion in mechanical systems with impacts J Sound and Vibration 154 95{115Dynamics of an impact oscillator near a degenerate graze 33
  44. (2006). Unfolding degenerate grazing dynamics in impact actuators doi
  45. (1997). Universal limit mapping in grazing bifurcations doi
  46. (2008). Unstable manifolds of a limit cycle near grazing doi
  47. (1992). W Singularities in vibro-impact dynamics doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.