Dynamical Inverse Problems: Theory and Application [electronic resource] /
International Centre for Mechanical Sciences.
Gladwell, Graham M. L.editor.
Morassi, Antonino.editor.
The papers in this volume present an overview of the gerneral aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Description based upon print version of record.
Title Page; Copyright Page; PREFACE; Table of Contents; Matrix Inverse Eigenvalue Problems; 1 Lecture 1. Classical Inverse Problems; 1.1 Introduction; 1.2 The Rayleigh Quotient; 1.3 Inverse Problems for a Jacobian Matrix; 2 Lecture 2. Applications and Extensions; 2.1 A Minimal Mass Problem; 2.2 Another Spring-Mass Inverse Problem; 2.3 Inverse Problems for a Pentadiagonal Matrix; 2.4 Periodic Jacobi Matrices; 2.5 Graph Theory; 3 Lecture 3. Isospectral Systems; 3.1 Reversing Factors; 3.2 The QR Algorithm; 3.3 Positivity; 4 Lecture 4. Toda Flow; 4.1 The Basic Equations
4.2 Application of Toda FlowBibliography; An Introduction to Classical Inverse Eigenvalue Problems; 1 Introduction; 2 Properties of the Dirichlet Eigenvalue Problem; 3 Uniqueness Results: the Borg's Approach; 3.1 Symmetric Potential and Dirichlet Boundary Conditions; 3.2 Symmetric Potential and Neumann Boundary Conditions; 3.3 Generic L2 Potential; 4 Uniqueness Towards Stability; 4.1 Hochstadt's Formula; 4.2 A Local Stability Result; 5 A Local Existence Result; 6 An Euler-Bernoulli Inverse Eigenvalue Problem; Bibliography
A Least Squares Functional for Solving Inverse Sturm-Liouville Problems1 Inverse Problems with Least Squares; 1.1 Gradient Flow; 2 The Inverse Sturm-Liouville Problem; 2.1 Examples; 3 Recovering boundary conditions; 3.1 Examples; 4 Theory; 4.1 Manifolds; 4.2 From the Wronskian to a Scalar Product; 4.3 Linear Independence of the Eigenfunctions; 4.4 Exponential Convergence; 4.5 Other spectral Data; 4.6 Isospectral Manifolds; 5 Similar Algorithms; Bibliography; Boundary Control Method in Dynamical Inverse Problems - An Introductory Course; 1 Introduction; 1.1 About the paper
1.2 Comment, notation, convention1.3 Acknowledgements; 2 Forward problem; 2.1 Statement; 2.2 Integral equation and generalized solutions; 2.3 Fundamental solution; 2.4 Properties of waves; 2.5 Extended problem 1 and locality; 3 String as dynamical system; 3.1 System αT; 3.2 Controllability; 3.3 Wave basis; 3.4 Truncation; 3.5 Amplitude formula; 3.6 Special BCP; 3.7 Gelfand-Levitan-Krein equations; 4 Inverse Problem; 4.1 Statement; 4.2 Solving inverse problem; 4.3 Visualization of waves; APPENDIX; 5 Forward problem; 5.1 Statement; 5.2 Integral equation and generalized solutions
5.3 Fundamental solution5.4 Properties of waves; 5.5 Extended problem 1 and locality; 5.6 Matrix reply function; 5.7 Slow waves; 6 Beam as dynamical system; 6.1 System αT; 6.2 Controllability; 6.3 Wave basis; 6.4 Truncation and AF; 6.5 Special BCP; 7 Inverse Problem; 7.1 Statement; 7.2 Solving the inverse problem; 7.3 Visualization of waves; 7.4 Finite beam; 7.5 Comments and remarks; Bibliography; Dynamic Characterization and Damage Identification; 1 Introduction; 2 Identification of Modal Parameters; 2.1 Frequency Response Function Method; 2.2 Peak Picking; 2.3 Singular Value Decomposition
2.4 The S. Sisto School
Includes bibliographical references.
The papers in this volume present an overview of the gerneral aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Vibration.
Dynamical systems.
Dynamics.
Civil engineering.
System theory.
Ergodic theory.
Vibration, Dynamical Systems, Control.
Civil Engineering.
Systems Theory, Control.
Dynamical Systems and Ergodic Theory.
Courses and lectures /