Abstract :
[en] This Thesis presents the development of a computationally efficient methodology for evaluating the aeroelastic response of large multi-degree-of-freedom (MDOF) structures subjected to turbulent wind excitation. In the context of civil engineering, and particularly the design of long-span bridges, the design process involves numerous iterations, with frequent updates to structural properties and loading conditions. Traditional buffeting analysis methods, while accurate, are often computationally intensive and thus unsuitable for early-stage design or extensive parametric studies. The methodology developed herein provides a practical alternative, significantly reducing computational costs while maintaining sufficient accuracy for preliminary assessments.
The proposed approach builds upon the Multiple Timescale Spectral Analysis (MTSA) framework and extends the classical background/resonant decomposition introduced by Davenport to aeroelastic systems. The method operates in the frequency domain and aims to estimate the response variances across the entire wind speed envelope. This is achieved through an analytical approximation of the system’s response Power Spectral Density (PSD), decomposed into background and resonant components. The resulting semi-analytical expressions allow the response variances to be analytically integrated with high efficiency, providing significant savings in computational time for high-dimensional structural systems.
The methodology was first validated on single-degree-of-freedom (SDOF) and two-degree-of-freedom (2DOF) models, demonstrating high accuracy and consistency with reference solutions. The MTSA approach was then generalized to MDOF systems, addressing key challenges such as modal coupling, frequency-dependent aeroelastic effects, and the use of complex modal bases. A detailed investigation was conducted on the influence of the modal basis and the formulation of the impedance matrix. The use of wind-on modal bases including left and right eigenvectors, combined with a linear gradient-based impedance formulation, was shown to yield optimal accuracy and robustness.
Two numerical tools were developed to support the implementation of the method. The first is a robust continuation algorithm designed to precompute wind-dependent modal properties, including complex mode shapes, across the design envelope. The second is a bisection-based algorithm for determining critical flutter velocities, formulated through the separation of the real and imaginary parts of the flutter condition, providing improved convergence and mode-tracking capabilities.
Overall, this Thesis contributes a complete, systematic, and computationally efficient framework for aeroelastic analysis at the early design stage. It facilitates rapid response predictions over a wide parameter space and offers significant potential for integration into modern iterative design processes, supporting both robustness and flexibility in the preliminary stages of long-span bridge design.
