Abstract
Dynamical systems containing contact/impact between parts can be modeled as piecewise-smooth reduced-order models. The most common example is freeplay, which can manifest as a loose support, worn hinges, or backlash. Freeplay causes very complex, nonlinear responses in a system that range from isolated resonances to grazing bifurcations to chaos. This can be an issue because classical solution methods, such as direct time integration (e.g., Runge-Kutta) or harmonic balance methods, can fail to accurately detect some of the nonlinear behavior or fail to run altogether. To deal with this limitation, researchers often approximate piecewise freeplay terms in the equations of motion using continuous, fully smooth functions. While this strategy can be convenient, it may not always be appropriate for use. For example, past investigation on freeplay in an aeroelastic control surface showed that, compared to the exact piecewise representation, some approximations are not as effective at capturing freeplay behavior as other ones. Another potential issue is the effectiveness of continuous representations at capturing grazing contacts and grazing-type bifurcations. These can cause the system to transition to high-amplitude responses with frequent contact/impact and be particularly damaging. In this work, a bifurcation study is performed on a model of a forced Duffing oscillator with freeplay nonlinearity. Various representations are used to approximate the freeplay including polynomial, absolute value, and hyperbolic tangent representations. Bifurcation analysis results for each type are compared to results using the exact piecewise-smooth representation computed using MATLAB® Event Location. The effectiveness of each representation is compared and ranked in terms of numerical accuracy, ability to capture multiple response types, ability to predict chaos, and computation time.
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Acknowledgments
The authors B. Saunders and A. Abdelkefi gratefully acknowledge the support from Sandia National Laboratories. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the US Government. This paper is also supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc. for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2020-13766 C. R. Vasconcellos acknowledges the financial support of the Brazilian agency CAPES (grant 88881.302889/2018-01).
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Saunders, B.E., Vasconcellos, R.M.G., Kuether, R.J., Abdelkefi, A. (2022). Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations. In: Kerschen, G., Brake, M.R., Renson, L. (eds) Nonlinear Structures & Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-77135-5_9
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DOI: https://doi.org/10.1007/978-3-030-77135-5_9
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