Indicial functions and flutter derivatives: A generalized approach to the motion-related wind loads

This paper presents a general time-domain description of the loads acting on a moving cylindrical body immersed in a two-dimensional low-speed flow, aiming to consistently extend the framework of thin airfoil theory to mildly bluff sections, such as those usually employed for decks of modern long-span bridges. In order to systematically accommodate typical features of bluff-body aerodynamics, the classical Theodorsen and Wagner results are reorganized within a unified dimensionless approach, and generalized preserving their main formal structure. Accordingly, circulatory and non-circulatory contributions are separately described and superimposed, and generalized downwash-related terms are introduced. The strong duality between time-domain and frequency-domain representations is focused, and direct relationships between proper Wagner-like indicial functions and Theodorsen-like circulatory functions are deduced. Thereby, following the Scanlan formulation for bridge deck sections, flutter derivatives are represented by superimposing circulatory and non-circulatory effects, resulting in a frequency-domain description fully consistent with the Theodorsen's theory. The model is based on few parameters that can be estimated by simplified strategies and, when applicable, by asymptotic relationships. An identification procedure involving few experiments or numerical simulations is proposed and numerically implemented. Simulation results obtained in the case of a flat thin plate and of a closed box section, similar to the cross-section of the Great Belt East Bridge, are successfully compared with theoretical and/or numerical solutions, highlighting effectiveness and soundness of the presented identification strategy.