Influence of the nonlinear aerodynamic force components on a vibrating beam, simply supported or clamped at both ends, exposed to a high supersonic airflow along its axial direction

Abstract

In this work we analyze the case of a vibrating beam, simply supported or clamped at both ends, underthe effect of a high supersonic airflow along its axial direction. A complete aerodynamic model ofthe piston theory, which also takes into account the nonlinear components of the distributed aerody-namic transversal force, is used. The postcritical flutter behavior and its influence on the vibration statesolutions of a fluttering beam without aerodynamic damping have been studied. This paper focusesparticularly on the effects of these nonlinear aerodynamic forces on three frequencies, which are usefulin characterizing the postcritical flutter solution set of the undamped beam in the whole frequency range:the minimum frequency, the frequency where the change of the modal shape with lower amplitude occurs,and the frequency corresponding to the solution with minimum amplitude of the vibration mode. Specialattention has been given to the influence on the solution of the vibrating undamped beam with minimummodal amplitude, whose frequency is the most important among the three mentioned above; in fact, inthe neighborhood of this particular solution, there exists the flutter state of the vibrating damped beamin limit cycle conditions.Three different schemes, two of them semianalytical (based on the classical and well known Rayleigh–Ritz and Galerkin methods) and one of them numerical (based on the finite element method), have beenherein exploited, as in the author’s previous papers, where beam flutter models with linear aerodynamicanalysis were used. The good agreement between the results obtained by the three methods corroboratestheir effectiveness.More sophisticated models have been herein set up, considering that a more accurate analysis isnecessary than in previous cases, where the aerodynamic numerical model was limited to within theframework of the quasisteady linearized piston theory, both for the coupling component between oddand even order vibrating modes, and for the aerodynamic damping component.The results obtained enable us to assess quantitatively the influence of these nonlinear aerodynamicforces on the postcritical beam flutter behavior, and particularly on the undamped beam solution withminimum amplitude of the vibration mode.