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

In this work we analyze the case of a vibrating beam, simply supported or clamped at both ends, under the effect of a high supersonic airflow along its axial direction. A complete aerodynamic model of the 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 state solutions of a fluttering beam without aerodynamic damping have been studied. This paper focuses particularly on the effects of these nonlinear aerodynamic forces on three frequencies, which are useful in 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. Special attention has been given to the influence on the solution of the vibrating undamped beam with minimum modal amplitude, whose frequency is the most important among the three mentioned above; in fact, in the neighborhood of this particular solution, there exists the flutter state of the vibrating damped beam in 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 been