Abstract
The aeroelasticity is the science which models, analyses and describes the coupled movements between a flow and a flexible structure. The different phenomena encountered can be classified using three (at least) adimensional numbers: the Strouhal number, the Reynolds number and the reduce frequency number (which despite its name, has no dimension). For sake of clarity, let us just mention in this abstract, that the reduce frequency is the ratio between the time necessary to a flow particle for flying over a flexible structure and the fundamental period of oscillation of this structure.
In the framework of quasi-static aeroelasticity, it is always assumed that the reduce frequency is smaller than the unity. It enables one to define the flow fields (velocity, pressure) from a static position of the structure. The effect of its position with respect to the flow leads to a modification of the stiffness (added aerodynamic stiffness). Furthermore, the relative flow velocity (difference between the flow velocity and the one of the structure) leads to introduce damping due to the flow and therefore modifies the static analysis of stability into the dynamic stability study (aerodynamic damping).
Recently, engineers have upgraded this approach by introducing the added mass concept. This is a mechanical effect due to the fact that the inertia of the structure should take into account the mass of flow which is involved in a movement. This is performed using an incompressible and inviscid model which gives a retroaction effect on the structure proportionally to its velocity. The two first parts of this text are devoted to a formulation of this three effects which are necessary in the dynamic modeling of a flexible (or not) structure immersed in a flow (air or water for instance). Examples in civil engineering and aerodynamics are given in order to illustrate the theoretical formulation. Few control aspects in a dynamic behavior of the coupled fluid-structure modeling are also discussed in a section of this text.
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Destuynder, P., Fabre, C. (2021). An Introduction to Quasi-Static Aeroelasticity. In: Greiner, D., Asensio, M.I., Montenegro, R. (eds) Numerical Simulation in Physics and Engineering: Trends and Applications. SEMA SIMAI Springer Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-62543-6_1
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