The Resource Boundary stabilization of thin plates, John E. Lagnese, (electronic resource)
Boundary stabilization of thin plates, John E. Lagnese, (electronic resource)
 Summary
 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. In particular, primary emphasis is placed on the derivation of explicit estimates of the asymptotic decay rate of the energy of the plate that are uniform with respect to the initial energy of the plate, that is, on uniform stabilization results. The method that is systematically employed throughout this book is the use of multipliers as the basis for the derivation of a priori asymptotic estimates on plate energy. It is only in recent years that the power of the multiplier method in the context of boundary stabilization of hyperbolic partial differential equations came to be realized. One of the more surprising applications of the method appears in Chapter 5, where it is used to derive asymptotic decay rates for the energy of the nonlinear von Karman plate, even though the technique is ostensibly a linear one
 Language
 eng
 Extent
 1 electronic text (viii, 176 p.)
 Contents

 Preface
 Chapter 1. Introduction: Orientation; Background; Connection with exact controllability
 Chapter 2. Thin plate models: Kirchhoff model; MindlinTimoshenko model; Von Karman model; A viscoelastic plate model; A linear thermoelastic plate model
 Chapter 3. Boundary feedback stabilization of MindlinTimoshenko plates: Orientation: existence, uniqueness, and properties of solutions; Uniform asymptotic stability of solutions
 Chapter 4. Limits of the MindlinTimoshenko system and asymptotic stability of the limit systems: orientation; The limit of the MT System as KÊ 0+; The limit of the MT System as K ; Study of the Kirchhoff system; uniform asymptotic stability of solutions; Limit of the Kirchhoff System as 0+
 Chapter 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
 Chapter 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
 Chapter 7. Uniform asymptotic energy estimates for thermoelastic plates: Orientation; existence, uniqueness, regularity, and strong stability; Uniform asymptotic energy estimates
 Bibliography
 Index
 Isbn
 9781611970821
 Label
 Boundary stabilization of thin plates
 Title
 Boundary stabilization of thin plates
 Statement of responsibility
 John E. Lagnese
 Language
 eng
 Summary
 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. In particular, primary emphasis is placed on the derivation of explicit estimates of the asymptotic decay rate of the energy of the plate that are uniform with respect to the initial energy of the plate, that is, on uniform stabilization results. The method that is systematically employed throughout this book is the use of multipliers as the basis for the derivation of a priori asymptotic estimates on plate energy. It is only in recent years that the power of the multiplier method in the context of boundary stabilization of hyperbolic partial differential equations came to be realized. One of the more surprising applications of the method appears in Chapter 5, where it is used to derive asymptotic decay rates for the energy of the nonlinear von Karman plate, even though the technique is ostensibly a linear one
 Additional physical form
 Also available in print version.
 Cataloging source
 CaBNVSL
 Illustrations
 illustrations
 Index
 index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SIAM studies in applied mathematics
 Series volume
 vol. 10
 Target audience
 adult
 Label
 Boundary stabilization of thin plates, John E. Lagnese, (electronic resource)
 Link
 http://libproxy.rpi.edu/login?url=http://epubs.siam.org/ebooks/siam/studies_in_applied_and_numerical_mathematics/am10
 Bibliography note
 Includes bibliographical references (p. 171174) and index
 Color
 black and white
 Contents
 Preface  Chapter 1. Introduction: Orientation; Background; Connection with exact controllability  Chapter 2. Thin plate models: Kirchhoff model; MindlinTimoshenko model; Von Karman model; A viscoelastic plate model; A linear thermoelastic plate model  Chapter 3. Boundary feedback stabilization of MindlinTimoshenko plates: Orientation: existence, uniqueness, and properties of solutions; Uniform asymptotic stability of solutions  Chapter 4. Limits of the MindlinTimoshenko system and asymptotic stability of the limit systems: orientation; The limit of the MT System as KÊ 0+; The limit of the MT System as K ; Study of the Kirchhoff system; uniform asymptotic stability of solutions; Limit of the Kirchhoff System as 0+  Chapter 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  Chapter 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  Chapter 7. Uniform asymptotic energy estimates for thermoelastic plates: Orientation; existence, uniqueness, regularity, and strong stability; Uniform asymptotic energy estimates  Bibliography  Index
 http://library.link/vocab/cover_art
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 unknown
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 {'f': 'http://opac.lib.rpi.edu/record=b3128728'}
 Extent
 1 electronic text (viii, 176 p.)
 File format
 multiple file formats
 Form of item
 online
 Governing access note
 Restricted to subscribers or individual electronic text purchasers
 Isbn
 9781611970821
 Isbn Type
 (electronic bk.)
 Other physical details
 ill., digital file.
 Publisher number
 AM10
 Reformatting quality
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 Specific material designation
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