Loret, François (2004) Time-harmonic or resonant states decomposition for the simulation of the time-dependent solution of a sea-keeping problem. PhD thesis Mathématiques appliquées, ENSTA / UMA - Laboratoire de Mathématiques Appliquées, ENSTA 2004ECAP0948 p.168.
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Abstract
This thesis is organised in two parts and presents two methods for representing the transient solution of a sea-keeping problem based on time-harmonic solutions.
The first part deals with the study of a the Singularity Expansion Method applied to the sea-keeping problem of a thin elastic plate. This method can be seen as an analytic extension of the Laplace transform and consists of representing the time-dependent solution as a discrete superposition of damped oscillating modes. The question we try to “answer numerically” is the following: is this representation an accurate way to obtain the long time behaviour of the solution in the hydrodynamic case?
The second part concerns the decomposition of a time-dependent wave on a continuous family of timeharmonic ones: the so-called Generalized Eigenfunction Expansions. We give a rigourous justification of this decomposition in the case of the linear scattering problem and we illustrate our results with the sea-keeping problem of a rigid floating body.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Hazard, Christophe |
| Date: | 15 September 2004 |
| Board of examiners: | Burq, Nicolas and Bachelot, Alain and Destuynder, Philippe and Meylan, Michael and Clouteau, Didier |
| Ecole Doctorale: | ED 287 SCIENCES POUR L'INGENIEUR |
| Discipline: | Mathématiques appliquées |
| Collection (Fonds): | ENSTA |
| Institution: | ENSTA |
| Department: | ENSTA / UMA - Laboratoire de Mathématiques Appliquées |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Laplace transform, transformée de Laplace, Resonance, Résonance, Meromorphic family of operators, Famille méromorphe d’opérateurs, Spectral theory, Théorie spectrale, Scattering theory, Théorie du scattering, Generalized eigenfunctions, Fonctions propres généralisées, Limiting absorption, Absorption limite |
| ID Code: | 2503 |
| Deposited By: | Julien Karachehayas |
| Deposited On: | 06 June 2007 |
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