Mathematical Control and Related Fields (MCRF)

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

Pages: 189 - 230, Volume 1, Issue 2, June 2011      doi:10.3934/mcrf.2011.1.189

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Scott W. Hansen - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)
Oleg Yu Imanuvilov - Department of Mathematics, Colorado State University, Ft. Collins, CO 80523, United States (email)

Abstract: Exact controllability of a multilayer plate system with free boundary conditions are obtained by the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a three-layer "sandwich plate'' system due to Rao and Nakra. In the multilayer version, $m$ shear deformable layers alternate with $m+1$ layers modeled under Kirchoff plate assumptions. The resulting system involves $m+1$ Lamé systems coupled with a scalar Kirchhoff plate equation. The controls are taken to be distributed in a neighborhood of the boundary. This paper is the sequel to [2] in which only clamped and hinged boundary conditions are considered.

Keywords:  Carleman estimates, exact controllability, multilayer plate, Lamé system.
Mathematics Subject Classification:  Primary: 93B05, 93C20; Secondary: 74K20.

Received: October 2010;      Revised: April 2011;      Available Online: June 2011.