Effects of Nonlinearity on the Flutter Speed of High Aspect Ratio Wings

In this paper the effects of geometric nonlinearity on the aeroelasticity behavior of high aspect ratio wings are investigated. These types of wings have large static deformations that change structural properties of wings and as a result the change of aeroelastic behavior. In order to account for this behavior it is necessary to use nonlinear aeroelastic analysis. In the analysis of aeroelasticity, a model for the structure. a model for aerodynamic and finally a solution method are needed. With consideration of specification of these kinds of wings, nonlinear general flexible Euler-Bernoulli beam equations are used for structural modeling and linear ONERA model is used for aerodynamic modeling. The ONERA model is constructed in terms of unsteady aerodynamic forces in the form of differential equations for each aerodynamic section element of a one-dimensional beam-like structure. A dynamic perturbation equation a bout a nonlinear static equilibrium is derived and it is used to determine the small perturbation flutter boundary. It is seen that when there are moderate displacements the flutter speed is decreased and this is the effects of nonlinearity. Also affects of quadratic and cubic terms of Euler-Bernoulli beam equations in structural properties of wing is investigated and as a result it is seen that when the displacement is moderate the cubic-nonlinear terms have significant influence.

Keywords:

Nonlinearity , Flutter speed , dynamic perturbation