Flutter Analysis Of High-Aspect-Ratio Wings

The high-altitude long-endurance uninhabited air vehicles(UAV) have widely applications and are being investigated actively. The aeroelastic problems of the UAV are significant due to its high-aspect-ratio wings.To this type of wings it has a great bending and torsion deformation under the flight loads, so the conventional method for solving linear systems in the small deformation assumption is not applicable, the large deformation caused by the structure geometry and the equilibrium must be considered in the analysis. In the flighting, the aerodynamic nonlinearities also cannot be avoided, but to UAV , the aerodynamic nonlinearities can be negligible when the speed of the plan is not very high. Therefore, quasi-steady aerodynamic theory of Grossman can meet the requirements of theoretical analysis. The main work of this paper is as follows:1. Develop an analytical model for the flutter of the high-aspect-ratio wings by using the curvature theory and Hamilton's prin ciple. The geometric nonlinear differential equation of the wing is derived, the non-dimension equation of motion is also obtained.2. Since nonlinear flutter is a self-excitated vibration, using the average method we get the first approximation solution of the system and obtain the flutter speed, which is compared to the result calculating of Routh-hurwiz rules3. To the dimensionless nonlinear equation, the normal form of the Hopf bifurcation is deduced with the Maple procedure of the Normal Form Direct Method. Let the airspeed as the bifurcation parameters, we can get its diagram of the Hopf bifurcation. Supercritical Hopf bifurcation will occur under some kind of the wings parameter. Changing some parameter, the type of flutter will be Subcritical flutter. Numerical simulations verify the analytical results.4. With the change of the relevant parameters of some kind of high-aspect wings, it makes quantitative study of the fluence of the parameters and gives the curve of the relation between the flutter speed curve and aspect ratio, bending stiffness and torsional stiffness ratio, non-coupling frequency, linear density, bending center to center distance.In this paper, further and detailed investigations are given both theoretically and numerically. Some qualitative and quantitative rules are obtained, which provide some guidance to the analysis and design for the airfoil.