Construction d'un modèle d'évolution de plaques avec terme d'inerte de rotation

SummaryIn a previous work, we have shown how the asymptotic expansion method (with the thickness as the « small » parameter) applied to the linear Hellinger-Reissner evolution model for an elastic plate ofRo3 yields a justification of the classical evolution equation for the transverse displacement of a plate with thickness 2e $$2\varrho e\frac{{\partial ^2 \zeta }}{{\partial t^2 }} + \frac{2}{3}\frac{E}{{1 - v^2 }}e^3 \Delta ^2 \zeta = \int\limits_{ - e}^e {f3.} $$ Pursuing farther the analysis of the asymptotic expansion and considering in particular the first corrector, we are led here to the plate model $$2\varrho e\frac{{\partial ^2 \zeta }}{{\partial t^2 }} + \frac{2}{3}\frac{E}{{1 - v^2 }}e^3 \Delta ^2 \zeta - \frac{{34 - 14v}}{{15(1 - v)}}\varrho e^2 \Delta \zeta '' = \int\limits_{ - e}^e {f3.} $$ Equations of the same form have been proposed notably by N. F. Morozov, G. Duvaut, J. L. Lions and are called equations with rotational inertia term. The applicability of such models is studied and sharp convergence estimates are given.