Loret, François (2004) *Time-harmonic or resonant states decomposition for the simulation of the time-dependent solution of a sea-keeping problem* Thesis, ENSTA.

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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: | Thesis (Thesis) |
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Uncontrolled Keywords: | Limiting absorption |

Subjects: | Mathematics and Applications |

Divisions: | |

ID Code: | 2503 |

Deposited By: | Julien Karachehayas |

Deposited On: | 06 juin 2007 02:20 |

Dernière modification: | 05 juin 2013 09:13 |

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