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

https://doi.org/10.1016/S0021-7824(00)00149-5Get rights and content
Under an Elsevier user license
open archive

Abstract

We consider the full nonlinear dynamic von Kármán system of equations which models large deflections of thin plates and show how the so-called Timoshenko and Berger models for thin plates may be obtained as singular limits of the von Kármán system when a suitable parameter tends to zero. We also show that in the case where the plate is of infinite measure this limit process gives the usual linear plate model. Therefore the nonlinear term of the system vanishes asymptotically when the domain has infinite measure. Strong convergence is also discussed: It holds under additional compatibility conditions on the initial data. Our results extend a previous work by the authors on the corresponding 1−D models.

Cited by (0)

1

Partially supported by a Grant of CNPq and PRONEX (MCT, Brazil).

2

Supported by Grants PB 96-0663 and the DGES (Spain), ERB FMRX CT 960033 of the European Union.