Vibration and Damping in Distributed Systems, Volume I [Kõva köide]

Vibration, Wave Propagation and Damping in One Space Dimension: Review
of Lumped Parameter Control Systems. A First Example of DPS-A Vibrating
String. Boundary Stabilization of a Vibrating String. Stabilization of a
Vibrating Thin Beam. Vibrating Beam Continued: Boundary Feedback
Stabilization. The Wave Propagation Method for a Vibrating String with
Boundary Damping. The Wave Propagation Method for a Vibrating Beam with
Boundary Damping. Mechanical Designs of Dampers Satisfying Stabilizing
Boundary Conditions on a Beam. Point Controllers and Stabilizers Located in
the Middle of the Span I: Vibrating Strings. Point Controllers and
Stabilizers Located in the Middle of the Span II: Vibrating Beams. Further
Examples of Damping and Vibration. Damping Devices in One-Dimensional
Acoustic Systems. Other Structural Vibration Models. Functional Analysis:
Metric Spaces and Vector Spaces. Bounded Linear Transformations. The Basic
Principles of Linear Analysis. Some Important Properties in Hilbert Spaces.
The Gram-Schmidt Orthonormalization Process and Orthonormal Basis. Dual
Spaces. The Tri-Space Setting V c H c V*. The Weak and �Weak* Convergence.
Closable and Closed Linear Operators. Adjoint and Symmetric Operators.
Resolvent and Spectrum. Compact Operators. Compact Symmetric Operators. The
Lebesgue Measure and Integral. Distributions, Sobolev Spaces and Boundary
Value Problems: Distributions. The Fourier Transform of Tempered
Distributions. Sobolev Spaces and Imbedding Theorems. The Trace Theorems.
Poincaré Type Inequalities. Regularity of Solutions for Boundary Value
Problems. Strongly Continuous Semigroups of Evolution: Strongly Continuous
Semigroups. Contraction Semigroups Generated by Dissipative Operators in a
Hilbert Space. The Generation of Co-Semigroups in a Banach Space. The Fourier
Inversion Formula. Adjoint Semigroups. The Lumer-Phillips Theorem for the
Generation of Contraction Co-Semigroups in a Banach Space. Example of
Co-Contraction Semigroups Corresponding to Conservative or Damped Distributed
Parameter Systems. The Adjoint Operators Corresponding to BVP with
Dissipative B.C. Asymptotic Stability and Exponential Decay of Energy: Weak
Stability and Asymptotic Stability. Characterizing Conditions for Uniform
Exponential Stability I: LP Summability Test. Characterizing Conditions for
Uniform Exponential Stability II: Frequency Domain Test. Characterizing
Conditions for Uniform Exponential Stability III: Eigenfunction Test.
Applications to the Wave, Beam and Schrödinger Equations. Nonhomogeneous
Evolution Equations. An Asymptotic Result. Russell's Exact Controllability
Via Exponential Stabilizability. The Method of Energy Identities: Uniform
Exponential Decay of Energy of the Wave Equation with Distributed Viscous
Damping. Derivation of Energy Identities Using More Multipliers. Decay of
Energy of the Wave Equation Exterior to a Star-Shaped Scatterer. Uniform
Exponential Decay of Energy of the Wave Equation on a Bounded Domain with
Partly Dissipative Boundary. The Loss of Energy Due to Expanding Boundary.
Serially Connected Beams with Damping at Joints and the Boundary. Exponential
Decay of Energy of a Thin Kirchhoff Plate with Boundary Damping. Holomorphic
Semigroups Corresponding to Structures with Strong Damping: Holomorphic
Semigroups and Differentiable Semigroups. Fractional Powers of Unbounded
Linear Operators. Holomorphic Semigroups Corresponding to the Heat Equation.
Holomorphic Semigroups Associated with Linear Elastic Systems with Structural
Damping. Other Models of Structural Damping. Appendices: The Riesz Index of
an Eigenvalue. The Fundamental Solution of a Time-Dependent Evolution
Equation. Dispersive Waves. Bibliography. Index.