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

[+] Author Affiliations
Ivan D. Breslavskyi, Mathias Legrand, Marco Amabili

McGill University, Montréal, QC, Canada

Paper No. DETC2014-35382, pp. V008T11A030; 5 pages
doi:10.1115/DETC2014-35382
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 26th Conference on Mechanical Vibration and Noise
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4641-4
  • Copyright © 2014 by ASME

abstract

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 modeled 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.

Copyright © 2014 by ASME
Topics: Vibration

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