Abstract
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.
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References
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An efficient numerical scheme for solving Eq. (1) in the presence of grazing impacts uses the analytical solutions for the motion between impacts. The (exact) positions ξ (t) are computed in a small number of discrete points t 1,…,t k in each drive period. It is crucial not to miss boundary crossings of ξ (t). These crossings are detected both directly by checking ξ (t 1),.. ξ(t k) and by computing the position ξ(t) at the turning points.
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© 1997 Springer Science+Business Media Dordrecht
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De Weger, J., Binks, D., Molenaar, J., Van De Water, W. (1997). Universal Bifurcations in Impact Oscillators. In: Van Campen, D.H. (eds) IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems. Solid Mechanics and Its Applications, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5778-0_50
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DOI: https://doi.org/10.1007/978-94-011-5778-0_50
Publisher Name: Springer, Dordrecht
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