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 Kármán 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. © 2013 Elsevier Ltd. All rights reserved.

Physically and geometrically non-linear vibrations of thin rectangular plates / Breslavsky, Ivan D.; Amabili, Marco; Legrand, Mathias. - In: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS. - ISSN 0020-7462. - 58:(2014), pp. 30-40. [10.1016/j.ijnonlinmec.2013.08.009]

### 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 Kármán 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. © 2013 Elsevier Ltd. All rights reserved.
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2014
Physically and geometrically non-linear vibrations of thin rectangular plates / Breslavsky, Ivan D.; Amabili, Marco; Legrand, Mathias. - In: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS. - ISSN 0020-7462. - 58:(2014), pp. 30-40. [10.1016/j.ijnonlinmec.2013.08.009]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11381/2814712`
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