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multilayer plate

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Exact controllability of a multilayer Rao-Nakra platewith clamped boundary conditions
Scott W. Hansen, Oleg Imanuvilov
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 4 / October 2011

Published online by Cambridge University Press:

08 November 2010, pp. 1101-1132

Print publication:

October 2011
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Exact controllabilityresults 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 “sandwichplate” system due to Rao and Nakra. The multilayer version involves a number ofLamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controlsare assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for thecoupled 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.