Presents one of the main directions of research in the area of design and analysis of feedback stabilizers for distributed parameter systems in structural dynamics. Important progress has been made in this area, driven, to a large extent, by problems in modern structural engineering that require active feedback control mechanisms to stabilize structures which may possess only very weak natural damping. Much of the progress is due to the development of new methods to analyze the stabilizing effects of specific feedback mechanisms. Boundary Stabilization of Thin Plates provides a comprehensive and unified treatment of asymptotic stability of a thin plate when appropriate stabilizing feedback mechanisms acting through forces and moments are introduced along a part of the edge of the plate.
Preface; 1. Introduction: orientation; Background; Connection with exact controllability; 2. Thin plate models: Kirchhoff model; Mindlin-Timoshenko model; von Karman model; A viscoelastic plate model; A linear termoelastic plate model; 3. Boundary feedback stabilization of Mindlin-Timoshenko plates: Orientation: existence, uniqueness, and properties of solutions; Uniform asymptotic stability of solutions; 4. Limits of the Mindlin-Timoshenko system and asymptotic stability of the limit systems: Orientation; The limit of the M-T system as KE 0+; The limit of the M-T system as K; Study of the Kirchhoff system; Uniform asymptotic stability of solutions; Limit of the Kirchhoff system as 0+; 5. Uniform stabilization in some nonlinear plate problems: Uniform stabilization of the Kirchhoff system by nonlinear feedback; Uniform asymptotic energy estimates for a von Karman plate; 6. Boundary feedback stabilization of Kirchhoff plates subject to weak viscoelastic Damping: formulation of the boundary value problem; Existence, uniqueness, and properties of solutions; Asymptotic energy estimates; 7. Uniform asymptotic energy estimates for thermoelastic plates: Orientation; Existence, uniqueness, regularity, and strong stability; Uniform asymptotic energy estimates; Bibliography; Index.