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Asymmetric bifurcations in a pressurised circular thin plate under initial tension |
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| Institution: | 1. Dept. of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA;2. Dept. of Mechanical Engineering, Gannon University, Erie, PA, USA;1. DipMat, Università degli studi di Salerno, Italy;2. DICATAM, Università degli studi di Brescia, Italy;1. International Research Center on Mathematics and Mechanics of Complex Systems, University of L?Aquila, 67100 L?Aquila, Italy;2. Dipartimento di Ingegneria Civile, Edile-Architettura e Ambientale, University of L?Aquila, 67100 L?Aquila, Italy;1. Carnegie Mellon University in Qatar, P.O. Box 24866 Doha, Qatar;2. Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, United States;1. Department of Aerospace Engineering, IIT Madras, Chennai, 600036, India;2. Department of Aerospace Engineering, PEC University of Technology, Sector 12, Chandigarh, 160012, India |
| Abstract: | It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl–von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon. |
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