Timoshenko's plate equation as a singular limit of the dynamical von Karman system

We consider the full nonlinear dynamic von Karman system of equations which models large deflections of thin plates and show how the so-called Timoshe nko and Berger models for thin plates may be obtained as singular limits of the von Karman system when a suitable parameter tends to zero. We also sho w that in the case where the plate is of infinite measure this limit proces s gives the usual linear plate model. Therefore the nonlinear term of the s ystem vanishes asymptotically when the domain has infinite measure. Strong convergence is also discussed: It holds under additional compatibility cond itions on the initial data. Our results extend a previous work by the autho rs on the corresponding 1 - D models. (C) 2000 Editions scientifiques et me dicales Elsevier SAS.