Abstract
Continuation and path following methods have been applied to many nonlinear problems in mathematics and physics. There is less widespread application of these methods, however, to structural systems. Since structural buckling and stability problems are primarily concerned with system behavior as a control parameter (most often the load) varies, they are particularly well suited for continuation methods and bifurcation analysis. In this work, the continuation package AUTO is utilized to calculate post-buckled configurations, natural frequencies, and mode shapes of flat plates. Additionally, the continuation analysis identifies bifurcation points and is also adapted to plate configurations that include slight initial imperfections. Finally, the path following methods are also applied to track the unstable snap-through solution and natural frequencies of post-buckled plates subject to a transverse load.
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References
Murphy KD (1994) Theoretical and experimental studies in nonlinear dynamics and stability of elastic structures. PhD thesis, Duke University
Hui D, Leissa AW (1983) Effects of geometric imperfections on vibrations of biaxially compressed rectangular flat plates. J Appl Mech 50:750–756
Ilanko S (2002) Vibration and post-buckling of in-plane loaded rectangular plates using a multiterm Galerkin’s methods. J Appl Mech 69:589–592
Doedel E, Keller HB, Kernevez JP (1991) Numerical analysis and control of bifurcation problems (II): bifurcation in ininite dimensions. Int J Bifurcat Chaos 1:745–772
Chen H, Virgin LN (2004) Dynamic analysis of modal shifting and mode jumping in thermally buckled plates. J Sound Vib 278:233–256
Seydel R (1991) Tutorial on continuation. Int J Bifurcat Chaos 1:3–11
Seydel R (2010) Practical bifurcation and stability analysis. Springer, New York
Doedel EJ, Oldeman BE (2009) AUTO-07P: continuation and bifurcation software for ordinary differential equations. Concordia University, Oct 2009
Strogatz SH (2001) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview Press, Cambridge,
Meirovitch L (2001) Fundamentals of vibrations. McGraw-Hill, Boston
Dowell EH (1975) Aeroelasticity of plates and shells. Noordhoff International, Leyden
Bulson PS (1970) The stability of flat plates. Chatto and Windus, London
Acknowledgements
The authors would like to acknowledge the NASA Graduate Student Researchers Program (GSRP) grant NNX09AJ17H and the Air Force Office of Scientific Research grant FA9550-09-1-0204 for support.
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© 2012 The Society for Experimental Mechanics, Inc. 2012
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Lyman, T.C., Virgin, L.N., Davis, R.B. (2012). Application of Continuation Methods to Nonlinear Post-buckled Structures. In: Adams, D., Kerschen, G., Carrella, A. (eds) Topics in Nonlinear Dynamics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2416-1_20
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DOI: https://doi.org/10.1007/978-1-4614-2416-1_20
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