Vibration of a Square Hyperelastic Plate Around Statically Pre-Loaded State

Ivan Breslavsky (1, 2) , Mathias Legrand (2, 1) , Marco Amabili (2)

1 Structural Dynamics and Vibration Laboratory [Montréal]
2 Department of Mechanical Engineering [Montréal]

Static deflection and free nonlinear vibrations of thin square plate made of biological material are investigated. The involved physical nonlinearity is described through Neo-Hookean, Mooney-Rivlin and Ogden hyperelastic laws; geometrical nonlinearity is modelled by Novozhilov nonlinear shell theory. The problem is solved by sequentially constructing the local models that describe the behavior of plate in the vicinity of a certain static configuration. These models are the systems of ordinary differential equations with quadratic and cubic nonlinear terms in displacement, which allows application of techniques used in analysis of thin-walled structures of physically linear materials. The comparison of static and dynamic results obtained with different material models is carried out.

Domaines: Vibrations [physics.class-ph]; Mécanique des structures [physics.class-ph]

Ivan Breslavsky, Mathias Legrand, Marco Amabili. Vibration of a Square Hyperelastic Plate Around Statically Pre-Loaded State. ASME IDETC/CIE Conference, Aug 2014, Buffalo, United States. ⟨10.1115/DETC2014-35382⟩. ⟨hal-01195752⟩