Physically and geometrically non-linear vibrations of thin rectangular plates

Abstract : Static deflection as well as free and forced large-amplitude vibrations of thin rectangular rubber plates under uniformly distributed pressure are investigated. Both physical, through a neo-Hookean constitutive law to describe the non-linear elastic deformation of the material, and geometrical non-linearities are accounted for. The deflections of a thin initially flat plate are described by the von Karman non-linear plate theory. A method for building a local model, which approximates the plate behavior around a deformed configuration, is proposed. This local model takes the form of a system of ordinary differential equations with quadratic and cubic non-linearities. The corresponding results are compared to the exact solution and are found to be accurate. Two models reflecting both physical and geometrical non-linearities and geometrical non-linearities only are compared. It is found that the sensitivity of the deflection to the physically induced non-linearities at moderate strains is significant.
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International Journal of Non-Linear Mechanics, Elsevier, 2013, 58, pp.30-40. 〈10.1016/j.ijnonlinmec.2013.08.009〉
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Ivan Breslavsky, Marco Amabili, Mathias Legrand. Physically and geometrically non-linear vibrations of thin rectangular plates. International Journal of Non-Linear Mechanics, Elsevier, 2013, 58, pp.30-40. 〈10.1016/j.ijnonlinmec.2013.08.009〉. 〈hal-00864370〉

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