We give experimental evidence for a new bifurcation structure that arises when smooth dynamical systems cross a boundary. Our experiment concerns a driven impacting leaf-spring oscillator with a very precise control of the driving amplitude. The results are in surprisingly good agreement with the predictions of a simple nonlinear mapping that is valid near grazing impact (i.e. impact with zero velocity). The agreement is surprising because a multitude of vibration modes of the spring is excited upon impact whereas the mapping is two-dimensional. Additionally, we consider the case where the impact is not instantaneous due to collisions with a nonrigid stop. This case can be captured by a mapping and we find strong support for the universality of impact phenomena, even in systems that have nonidealities.
|Title of host publication||Interaction between dynamics and control in advanced mechanical systems : proceedings of the IUTAM symposium, 21-26 April, 1996, Eindhoven, the Netherlands|
|Editors||D.H. Campen, van|
|Publication status||Published - 1996|
|Name||Solid Mechanics and its Applications|
Weger, de, J. G., Binks, D. J., Molenaar, J., & Water, van de, W. (1996). Universal bifurcations in impact oscillators. In D. H. Campen, van (Ed.), Interaction between dynamics and control in advanced mechanical systems : proceedings of the IUTAM symposium, 21-26 April, 1996, Eindhoven, the Netherlands (pp. 417-424). (Solid Mechanics and its Applications; Vol. 52).