# Modeling aerodynamic nonlinearities for two aeroelastic configurations: Delta wing and flapping flag

Journal Article

The flutter and limit cycle oscillation(LCO) behavior of two aeroelastic configurations, a delta wing model and a flapping flag model, are studied theoretically and the results are compared to experiment. The theoretical model uses a nonlinear aerodynamic model and a nonlinear structural model. The aerodynamic model is based on an unsteady vortex lattice theory. The exact normal flow boundary condition are satisfied on the solid boundary and a force-free wake condition is imposed. Two nonlinear structural models are used in the aeroelastic modeling. The delta wing is modeled using the nonlinear plate theory of von Karman. The nonlinearity in this model is due to the coupling between the in-plane and out-of-plane deflections of the wing. The flapping flag structural model uses a nonlinear beam theory which includes large curvature effects and uses an inextensible inplane assumption. The delta wing model is studied for three angles of attack, 0,2 and 4 degrees. The flutter speed for each angle of attack is found accurately. For the two degree angle of attack case, two types of LCO are predicted, a small amplitude, modulated LCO below the flutter speed predicted by the linear aerodynamic model and the nonlinear structural model, and a large amplitude LCO at a flow velocity above this flutter speed. The flutter speed is also predicted accurately for the flapping flag model. The flapping flag aeroelastic model which includes both a nonlinear aerodynamic theory and nonlinear structural theory predicts a small amplitude LCO at a speed slightly below that of the flutter speed predicted by the aeroelastic theory which does not use the nonlinear aerodynamic model. © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

### Duke Authors

### Cited Authors

- Attar, PJ; Dowell, EH; Tang, D

### Published Date

- 2003

### Published In

- 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference