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Boundary Stabilization of Thin Plates

Boundary Stabilization of Thin Plates

£47.99

Part of Studies in Applied and Numerical Mathematics

  • Date Published: March 1990
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898712377

£ 47.99
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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  • 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.

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    Product details

    • Date Published: March 1990
    • format: Hardback
    • isbn: 9780898712377
    • length: 184 pages
    • dimensions: 235 x 160 x 15 mm
    • weight: 0.469kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    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 KÊ 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.

  • Author

    John E. Lagnese

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