Margaux Geuzaine PhD : Multiple Timescale Spectral Analysis of Floating Structures

Several major and strategical ongoing projects, including the E39 coastal highway project in Norway or the various versions of the Messina Straits crossing, require the construction of long span bridges. As they typically aim at the crossing of wide fjords or straits, these bridges might become more economical when relieved by one or several intermediate floating supports. Their design therefore requires considering the combined action of wind and wave loads on the structure.

When performing the dynamic analysis of such large and slightly damped floating structures, there exists two traditional methods, taking place in the time domain or in the frequency domain. However, they are both computationally intense because of the clear separation that typically exists between the natural frequencies of the structures considered and the characteristic frequencies of wind or wave loads.

Fortunately, since several decades, it is precisely by hinging on this separation of timescales that the design of bridges to the random turbulent action of wind is handled in a much more efficient way, in the frequency domain, as it allowed to derive the famous background/resonant decomposition, which provides a simple analytical expression to compute the variance of the response of structures 100 to 1000 times faster than before.

In this context, the Multiple Timescale Spectral Analysis has also recently been formulated as a generalization of this decomposition, in order to get similar approximations for any of the structural response’s statistics that are necessary to obtain an accurate probabilistic description for their extreme values. For the moment though, this method has mainly been applied to structures responding in the background and resonant regimes only, i.e. subjected to a quasi-static loading, such as wind-loaded onshore structures.

In brief, the purpose of the present thesis is thus to extend further the Multiple Timescale Spectral Analysis to deal with structures responding in the inertial regime as well, such as wave-loaded floating structures, including bridges but also wind turbines or offshore platforms.

Since the method is much faster, while providing a small and controllable discrepancy, this will be the perfect tool to analyze very rapidly numerous possible layouts and configurations. This tool should be used at the early stage of the design, in order to guide engineers with graspable information, in the form of simple analytical formulas, while a heavier time domain simulation (as performed today) would be used for the final design.

Publications

Efficient estimation of the skewness of the response of a wave-excited oscillator, 2020, November

Efficient estimation of the skewness of the response of a linear oscillator under non-Gaussian loading, 2020

Introduction à l'analyse spectrale à plusieurs échelles temporelles de ponts flottants, 2019, November 25

A framework for the efficient spectral analysis of large wind- and wave-loaded structures, 2019, September 05

Estimation of modal correlation coefficients in wind buffeting spectral analysis, 2019, June 06