Dynamical Inverse Problems: Theory and Application
Invited Lecturers
- Mikhail Igorevich Belishev (Steklov Mathematical Institute, St. Petersburg, Russian Federation )
- 5 lectures on: Forward and inverse problems for the telegraph and string equations. The Sondhi-Gopinath approach. The local approach by A. Blagovestchenskii. One-dimensional scalar Boundary Control (BC) method; amplitude formula and visualization of waves. BC-algorithms and numerical testing. Two-velocity beam; slow waves; controllablity. Elements of the multidimensional BC-method.
- Graham M.L. Gladwell (University of Waterloo, Ontario, Canada)
- 5 lectures on: Classical inverse problems for in-line systems: rods in longitudinal vibration and beams in flexural vibration. Formation of isospectral systems and construction of isospectral finite-element models of membranes. Introduction to inverse mode problems. Throughout the lectures, emphasis will be placed on ways of choosing data that lead to a realistic system.
- Antonino Morassi (Università di Udine, Italy)
- 5 lectures on: Classical approaches to the inversion of one-dimensional scalar Sturm-Liouville problems. Introduction to the inverse eigenvalue problem for Euler-Bernoulli beams. Damage identification in vibrating beams from finite spectral data. A class of inverse dynamical problems for a coupled system composed by two connected beams.
- John E. Mottershead (University of Liverpool, UK)
- 5 lectures on: Dynamic methods of vibration control based on passive modification that do not require to know or to evaluate the inertia, stiffness and damping matrices. A receptance method in active vibration control for which state observers and model reduction techniques are totally unnecessary. Formulations of multi-input state feedback and output feedback, illustrated by numerical and practical experimental results with stability robustness and the treatment of time delay.
- Assad A. Oberai (Rensselaer Polytechnic Institute, NY, USA)
- 5 lectures on: Biomechanical imaging for the determination of the spatial distribution of the mechanical properties of tissue from the knowledge of its displacement field. Description of experimental methods. Determination of the shear modulus from quasi-static displacement measurements. Nonlinear elasticity imaging; efficient and robust numerical techniques. Poroelastic imaging. Viscoelastic imaging.
- Norbert Röhrl (University of Stuttgart, Germany)
- 4 lectures on: Variational methods for solving inverse spectral Sturm-Liouville problems. Definition of functionals which have global minima precisely at the solutions of the inverse problem and introduction of suitable numerical minimization procedures.
- Fabrizio Vestroni (Università di Roma "La Sapienza", Italy)
- 5 lectures on: Fundamentals of experimental vibration methods for the mechanical characterization of structures. Introduction to structural identification based on dynamic data; osservability and identifiability. Use of modal updating for damage detection in structures. Introduction to inverse problems for coupled electro-mechanical systems.