Flutter analysis of a tip-mass-wing using Rayleigh-Ritz by hierarchical polynomials

Resumo

In an attempt to reduce fuel consumption and noise, aircraft designers try to minimize structural weight
and maximize the wing aspect ratio. Both constraints lead to an increase in structural flexibility. Consequently,
aeroelastic effects, as flutter, must be researched extensively from conceptual design stages. In order to avoid
flutter, several studies have been conducted seeking to use active control techniques using piezoelectric materials.
This paper proposes to analyze the vibration frequencies and flutter velocities of a wing model described as a
clamped-free beam with bending and torsion movements with mass at its tip. A second model, the Goland wing,
whose flutter speeds are widely reported in the literature, is used to validate the results of flutter velocity obtained
for the propose model. To compare the accuracy of the results obtained and the computational cost, approximate
methods are used to obtain the discrete structural equations: Rayleigh-Ritz with hierarchical standard and Bardell

polynomials. The complete aeroelastic model is developed applying the Peters aerodynamic model, which approx-
imates the effects of the unsteady incompressible flow using a state-space approximation. Thanks to the use of

hierarchical polynomials, a low-order and computationally cheap numerical model is obtained. This model can be
used for optimization in conceptual design stages, as well for feedback control design.