Bifurcation Analysis of a Piecewise-Smooth Freeplay System 77 (a) (b) Fig. 1 (a) Schematic of the Duffing-freeplay system and (b) 3D bifurcation diagrams showing the effects of contact stiffness on the Duffingfreeplay system for m=5 kg, ωn =5Hz, ζ =0.03, α=7∗ 10 8 N/m3, p=4N, j 1 =j2 =0.4mm, x0 =0.32mm Acknowledgments The authors B. Saunders and A. Abdelkefi gratefully acknowledge the support from Sandia National Laboratories. This study 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 study 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. SAND2020-13605 C. R. Vasconcellos acknowledges the financial support of the Brazilian agency CAPES (grant 88881.302889/2018-01). References 1. Yang, Y., Xia, W., Han, J., Song, Y., Wang, J., Dai, Y.: Vibration analysis for tooth crack detection in a spur gear system with clearance nonlinearity. Int. J. Mech. Sci. 157–158, 648–661 (2019). https://doi.org/10.1016/j.ijmecsci.2019.05.012 2. Dai, H., Yue, X., Yuan, J., Xie, D., Atluri, S.N.: A comparison of classical Runge-Kutta And Henon’s methods for capturing chaos and chaotic transients in an aeroelastic system with freeplay nonlinearity. Nonlinear Dyn. 81, 169–188 (2015). https://doi.org/10.1007/s11071-015-1980-x 3. Shaw, S.W.: The dynamics of a harmonically excited system having rigid amplitude constraints, Part 1: Subharmonic motions and local bifurcations. ASME J Appl Mech. 52(2), 453–458 (1985). https://doi.org/10.1115/1.3169068 4. De Langre, E., Lebreton, G.: An experimental and numerical analysis of chaotic motion in vibration with impact. In: ASME 8th International Conference on Pressure Vessel Technology, Montreal, Quebec, Canada (1996) 5. Vasconcellos, R., Abdelkefi, A., Hajj, M.R., Marques, F.D.: Grazing bifurcation in aeroelastic systems with freeplay nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 19(5), 1611–1625. https://doi.org/10.1016/j.cnsns.2013.09.022 6. Vasconcellos, R.M.G., Abdelkefi, A., Marques, F.D., Hajj, M.R.: Characterization of Grazing bifurcation in airfoils with control surface freeplay nonlinearity. In: Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014, Porto, Portugal (2014)
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