Abstract
A key feature of many nonlinear dynamical systems is the presence of co-existing solutions, i.e, nonlinear systems are often sensitive to initial conditions. While there have been many studies to explore this behavior from a numerical perspective, in which case it is trivial to prescribe initial conditions (for example using a regular grid), this is more challenging from an experimental perspective. This paper will discuss the basins of attraction in a simple mechanical experiment. By applying both small and large stochastic perturbations to steady-state behavior, it is possible to interrogate the initial condition space and map-out basins of attraction as system parameters are changed. This tends to provide a more complete picture of possible behavior than conventional bifurcation diagrams with their focus on local steady-state behavior.
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Acknowledgements
This work was partially supported by the US Air Force, AFOSR Grant no. FA9550-09-1-0201, and NSF grant 0927186 (Dynamical Systems).
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© 2014 The Society for Experimental Mechanics, Inc.
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Virgin, L.N., Waite, J.J., Wiebe, R. (2014). Co-existing Responses in a Harmonically-Excited Nonlinear Structural System. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04522-1_1
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DOI: https://doi.org/10.1007/978-3-319-04522-1_1
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