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 aerodynamic 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 herein exploited, as in the author’s previous
papers, where beam flutter models with linear aerodynamic analysis were used. The
good agreement between the results obtained by the three methods corroborates their
effectiveness.
More sophisticated models have been herein set up, considering that a more
accurate analysis is necessary than in previous cases, where the aerodynamic
numerical model was limited to within the framework of the quasisteady linearized
piston theory, both for the coupling component between odd and even order
vibrating modes, and for the aerodynamic damping component.
The results obtained enable us to assess quantitatively the influence of these
nonlinear aerodynamic forces on the postcritical beam flutter behavior, and
particularly on the undamped beam solution with minimum amplitude of the
vibration mode.
