Deterministic model construction for flutter characterisation of cantilever flat plates

Abstract

Assessing exactly the flutter speed and frequency is of prior importance when designing an aircraft to ensure a safe flight envelope and to this purpose, experimental and numerical tests have been developed throughout the years. To simplify the computation of the critical speed and frequency, this master thesis proposes to build a mathematical model for flutter characterisation as a function of geometrical parameters of cantilever flat plates namely the Aspect Ratio, the taper ratio and the sweep angle, on the basis of the unsteady Vortex Lattice Method (VLM). The investigation of the hump mode activation as a function of those parameters is carried out in first place to assess its conditions of appearance and it is concluded that a straight discontinuity line can be drawn on the domain to distinguish the zone where the hump is active from the zone where it is not. Then, the linear regression theory is used for building the model and three different polynomial orders are compared namely a simple first order polynomial, a seconde order polynomial with interaction terms only and a second order polynomial comprising both the direct and the interaction terms. and conclusion is made that a incomplete second order model provides results reliable up to 99%. A comparison is made with experimental results obtained in wind tunnel. To do so, an excitation system is designed so that its eigenfrequencies do not interfere with those of the tested plates. Several issues encountered due to lack of time because of the sanitary crisis prevented to perform more than two tests for which the different problems could not all be checked and solved. In the end, a proper conclusion about the practical validity of the model could not be drawn.