Prof. Dr. Thomas Schuster (Universität Oldenburg): Computation of Dispersion Curves and PDE Based Parameter Identification for Defect Detection in Composite Materials |
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| Startdatum/-zeit: | 25.04.2012 17:15 |
| Enddatum/-zeit: | 25.04.2012 |
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| Adresse: | Fachbereich Mathematik/ Informatik, Institut für Mathematik Prof. Dr. Stefan Kunis Albrechtstr. 28a 49076 Osnabrück |
| Telefon: | 0541 - 969 - 2538 |
| Telefax: | 0541 - 969 - 2770 |
| E-Mail: | stefan.kunis@uos.de |
| Homepage: | http://www.mathematik.uni-osnabrueck.de/index.php?controller=wochenprogramm&action=detail&vortrag=53 |
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| Adresse: | Institut für Mathematik Institut für Mathematik, Albrechtstr. 28a, Geb. 69/ Raum 125 49076 Osnabrück |
| Karte: | Bei Google Maps anzeigen |
| Beschreibung: | Defect detection for composite materials by autonomous systems, the so-called Structural Health Monitoring (SHM), is, on the one hand, of large economic interest since these materials are used in the construction of airplanes, and, on the other hand, the application and analysis of numerical methods for the corresponding parameter identifi cation problems represent great challenges from a mathematical point of view. SHM means the generation of guided waves in plates consisting of carbon fi bre reinforced composites, which interact with defects in the structure and are then measured at sensors. Thereby both, actors and sensors are embedded into the structure. SHM aims for giving information about the kind, the localization and the size of damages by computing material parameters that are assumed to vary spatially. Besides the anisotropy of composite materials one faces the further di fficulty that the so-called Lamb waves, which arise in thin plates, are dispersive, i.e. the group velocity depends on frequency. Thus one has to solve an inverse parameter identification for an anisotropic wave equation. The talk outlines different numerical approaches to tackle the SHM problem. We show how dispersion curves can be computed either by solving a generalized eigenvalue problem or by using the matrix pencil method. Furthermore we present two different models which solve the problem of defect detection by minimizing specific Tikhonov functionals. The talk ends with some fi rst numerical results for one of these models which interprets defects as external forces. |
| Kategorie: | Mathematisches Kolloquium |
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