École Nationale Supérieure de
Techniques Avancées

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.