Dynamical Inverse Problems: Theory and Application (Dynamical Inverse Pr)
Venue: CISMM, Udine, Italy
|Event Date/Time: May 25, 2009||End Date/Time: May 29, 2009|
In addition to its applications, the study of inverse problems in vibration has also inherent mathematical interest, since the issues encountered have remarkable features in terms of originality and technical difficulty, when compared with the classical problems of direct vibration theory. In fact, inverse problems do not usually satisfy the Hadamard postulates of well-posedeness, also, in many cases, they are extremely non-linear, even if the direct problem is linear. In most cases, in order to overcome such obstacles, it is impossible to invoke all-purpose, ready made, theoretical procedures. Instead, it is necessary to single out a suitable approach and trade-off with the intrinsic ill-posedeness by using original ideas and an extended use of mathematical methods from various areas. Another specific and fundamental aspect of the study of inverse problems in vibration concerns the numerical treatment and the development of ad-hoc strategies for the treatment of ill-conditioned, linear and non-linear problems. Finally, when inverse techniques are applied to the study of real problems, additional obstructions arise because of the complexity of mechanical modelling, the inadequacy of the analytical models used for the interpretation of the experiments, measurement errors and incompleteness of the field data. Therefore, of particular relevance for practical applications is to assess the robustness of the algorithms to measurement errors and to the accuracy of the analytical models used to describe the physical phenomenon.
The purpose of the course is to present a state-of-the-art overview of the general 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, computational and experimental aspects relevant for engineering problems.