%0 Journal Article
%T Conservative numerical methods for the Full von Kármán plate equations
%+ Acoustics and Audio Group
%+ Laboratoire des Sciences de l'Information et des Systèmes : Ingénierie Numérique des Systèmes Mécaniques (LSIS- INSM)
%+ Unité de Mécanique (UME)
%+ Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219)
%A Bilbao, Stefan
%A Thomas, Olivier
%A Touzé, Cyril
%A Ducceschi, Michele
%< avec comité de lecture
%@ 0749-159X
%J Numerical Methods for Partial Differential Equations
%I Wiley
%V 31
%N 6
%8 2015-11
%D 2015
%R 10.1002/num.21974
%Z Mathematics [math]/Analysis of PDEs [math.AP]
%Z Mathematics [math]/Numerical Analysis [math.NA]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph]Journal articles
%X This article is concerned with the numerical solution of the full dynamical von Karman plateequations for geometrically nonlinear (large-amplitude) vibration. This system is composed ofthree equations describing the time evolution of the transverse displacement field, as well as thetwo longitudinal displacements. Particular emphasis is put on developing a family of numericalschemes which, when losses are absent, are exactly energy conserving. The methodology thusextends previous work on the simple von Karman system, for which longitudinal inertia effectsare neglected, resulting in a set of two equations for the transverse displacement and an Airystress function. Both the semi-discrete (in time) and fully discrete schemes are developed.From the numerical energy conservation property, it is possible to arrive at sufficient conditionsfor numerical stability, under strongly nonlinear conditions. Simulation results are presented,illustrating various features of plate vibration at high amplitudes, as well as the numericalenergy conservation property, using both simple finite difference as well as Fourier spectraldiscretisations.
%G English
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01206323/document
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01206323/file/NMPDE_SBOTCTMD.pdf
%L hal-01206323
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-01206323
%~ CEA
%~ ENSTA
%~ CNRS
%~ UNIV-AMU
%~ INSMI
%~ LSIS-INSM
%~ ENSTA_UME
%~ CEA-UPSAY
%~ TDS-MACS
%~ UNIV-PARIS-SACLAY
%~ CEA-UPSAY-SACLAY
%~ ENSTA-SACLAY
%~ EDF