Les mathématiques au service du développement durable...

Dans le cadre de mon doctorat, je développe des outils qui permettront de comprendre plus facilement et de calculer plus rapidement l’influence de divers paramètres sur la résistance des structures flottantes. Ces outils aideront les ingénieurs à minimiser les matériaux requis pour assurer la résistance de ce type de structures. Cela permettrait, à terme, de réduire leur coût et donc de démocratiser l’accès à des technologies comme, par exemple, les éoliennes marines, qui sont considérés comme très prometteuses en termes de production d’énergie renouvelable mais encore trop chères pour être déployées à grande échelle ou employées dans des pays défavorisés. Afin de progresser dans ces recherches, je vais passer 6 mois à l’Université Norvégienne des Sciences et des Technologies de Trondheim car elle est à la pointe dans le domaine des plateformes flottantes. Elle collabore aussi étroitement avec des ingénieurs qui ont l’habitude de dimensionner des structures flottantes et qui pourront dès lors me fournir des cas concrets pour valider les méthodes que j’aurai développées. Une bourse du District m'a donc été octroyée par le Rotary afin d'entreprendre ce voyage. Cette présentation visait donc à présenter mes recherches de manière vulgarisée aux membres du club de Plombières-Welkenraedt (Belgique), accompagnés pour l'occasion de ceux de leur club jumelé de Noyon (France)

Multiple timescale spectral analysis of floating structures subjected to hydrodynamic loads

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Efficient estimation of the skewness of the response of a wave-excited oscillator

peer reviewedThe Multiple Timescale Spectral Analysis is a framework relying on the existence of well-separated timescales in the dynamic response of structures to generalize for higher-order statistics the famous background/resonant decomposition, widely applied by the wind engineer- ing community to compute the variance of the response of SDOF structures or of each modal response of MDOF structures. This fast spectral analysis method mainly concerns the statistics of the response of onshore structures subjected to a buffeting wind loading whose characteristic frequency is typically lower than the natural frequencies of the structures concerned. By con- trast, when dealing with wave-loaded floating offshore structures, the roles of the slow and fast timescales are likely to be interchanged and the method is extended further in this paper to com- pute rapidly the variances and the skewnesses of modal responses of such structures responding in the inertial regime as well, since these statistics are necessary to consider the influence of the non-Gaussianity of the loading

Approche Spectrale en Ingénierie du Vent

Présentation des résultats obtenus dans le cadre de ma thèse de doctorat intitulée : "Analyse spectrale à plusieurs échelles temporelles de ponts flottants". Notamment, cette présentation met en évidence l'existence d'une partie imaginaire dans le bispectre des sollicitations d'une structure et l'ajout d'une composante supplémentaire dans le coefficient de dissymétrie de la réponse d'une structure soumise à un tel chargement

Minimal requirements for the vibration-based identification of the axial force, the bending stiffness and the flexural boundary conditions in cables

peer reviewedThis paper aims at presenting the guidelines to follow in order to set up an identification procedure which is able to determine the axial force, the flexural rigidity and the rotational end stiffnesses of slender and tensioned structural elements, based on measurements of their natural frequencies and mode shapes. First of all, when such an element is slightly affected by bending stiffness effects, perturbation methods can be applied to get a composite approximation for its natural frequencies and an asymptotic expression for its mode shapes. These simple analytical formulas allow to understand the role played by each model parameter in the modal response and show that the axial force, the flexural rigidity and the rotational end stiffnesses can be correctly identified under some conditions, which are established and provided in this document. Among others, it is necessary that the identification procedure relies on the first few natural frequencies and mode shapes, which are measured near each extremity of the element, as well as some natural frequencies associated with higher modes

On the identification of the axial force and bending stiffness of stay cables anchored to flexible supports

The generic model of a cable with small bending stiffness and anchored to flexible supports in rotation and translation is considered. An asymptotic analysis of the natural frequencies of this generic model is derived and shows that, for small bending stiffness, the first few natural frequencies can be expressed as a function of the cable axial force, the small bending stiffness and a single dimensionless group collecting the information of all other problem parameters. This formulation is used to develop an identification procedure of the cable axial force. Two formulations are proposed, one numerical and one semi-analytical based on a simple linear regression model. Both methods do not attempt at separately identifying the problem parameters since the observability analysis has revealed that only the cable axial force, the bending stiffness and the dimensionless group can be identified. In particular, the second method is very simple to implement and provides estimates of the cable axial force which account for the flexibility of the support. The proposed method can therefore be seen as an extension of usual identification techniques based on linear regressions of natural frequencies vs. mode number relations, by considering at the same time the bending stiffness and the deformability of supports. Being simple and robust as shown by means of an uncertainty quantification analysis, the proposed method can be conveniently embedded in the framework of a continuous monitoring strategy

Efficient Long-Term Extreme Response Analysis of Floating Bridges Using Multiple Timescale Spectral Analysis

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