Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions

¹ Department of Mathematics, Iowa State University, Ames, IA 50011, USA.shansen@orion.math.iastate.edu .
² Department of Mathematics, Colorado State University, Ft. Collins, CO 80523, USA.

Received: 7 November 2008
Revised: 24 February 2010
Revised: 3 May 2010

Abstract

Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for the coupled system are based on some new Carleman estimates for the Kirchhoff plate as well as some known Carleman estimates due to Imanuvilov and Yamamoto for the Lamé system.