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Stochastic interrogation of competing responses in a nonlinear distributed system

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Abstract

In this paper, we examine the potential for coexisting responses in a harmonically forced buckled beam. It is shown experimentally that such structures may present many more responses than might be observed using frequency sweep-up and sweep-down testing, with some responses being observed only very infrequently. The primary contribution of this work is the experimental approximation of the basins of attraction of the competing behaviors using stochastic interrogation, which uses strong, but random, perturbations to map out the initial conditions that tend to each attractor. This procedure is especially difficult in experimental studies of distributed systems; hence, we focus on the process of stochastic interrogation itself and strictly in an experimental context.

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Acknowledgments

This work was partially supported by Universal Technology Corporation contract # FA8650-10-D-3037. The authors also wish to thank Tim Beberniss for his help in the laboratory.

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Author notes

  1. R. Wiebe

    Present address: Department of Civil and Environmental Engineering, University of Washington, 201 More Hall, Box 352700, Seattle, WA, 98195, USA

Authors and Affiliations

  1. Universal Technology Corporation, Structural Sciences Center, Air Force Research Laboratory, Wright-Patterson AFB, OH, 45433, USA

    R. Wiebe

  2. School of Engineering, Duke University, Hudson Hall, Box 90300, Durham, NC, 27708, USA

    L. N. Virgin

  3. Structural Sciences Center, Air Force Research Laboratory, Wright-Patterson AFB, OH, 45433, USA

    S. M. Spottswood

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  1. R. Wiebe
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  2. L. N. Virgin
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  3. S. M. Spottswood
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Correspondence to R. Wiebe.

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Wiebe, R., Virgin, L.N. & Spottswood, S.M. Stochastic interrogation of competing responses in a nonlinear distributed system. Nonlinear Dyn 79, 607–615 (2015). https://doi.org/10.1007/s11071-014-1689-2

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  • DOI: https://doi.org/10.1007/s11071-014-1689-2

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