This work studies the flutter characteristics of a metallic high-aspect ratio wing, with linearly varying chord across the semi-span, and a simulated elastic foundation at the root. The general planform of the wing is similar to the one found in a High-Altitude Long-Endurance Uninhabited Aerial Surveillance Vehicle (HALE USAV). The problem is studied using a simplified aerodynamic loading based on thin-airfoil theory, which is then combined with a Lagrangian formulation to solve the system as stationary. The wing has no control surfaces or external stores, and is modeled as a beam with known mechanical properties, being attached to a combination of torsion springs at the root to reproduce the elastic foundation. The analysis of the problem includes the development of a Matlab 14 code, which permits different root conditions to be defined, and computes the flutter speed and frequency, outputting information in the form of plots and data lists.
I. IntroductionThe study and understanding of the flutter characteristics of a wing is extremely important during the aircraft design process. This structural dynamics phenomenon is responsible for limiting the flight speed due to its unstable nature, and represents a potentially catastrophic condition if not taken properly into account. Flutter is understood as the harmonic oscillation of a structural member as a result of its interaction with the surrounding fluid stream. In the case of wing flutter, the wing is subjected to aerodynamic loads as it moves into the airstream; when the harmonic oscillations for bending and torsion are coupled with no damping, any increase in the airspeed will introduce an increase in the amplitude of these oscillations, making the structure unstable and leading to the risks which this represents. At this particular airspeed, the structure is said to reach its critical flutter speed. The flutter phenomenon related to aircraft structures has been studied for many years, for almost all different types of wing configurations and airspeed regimes such as subsonic incompressible flow (sailplanes, general aviation aircraft, etc.), transonic compressible flow (high speed turboprops, jet liners, propeller and turbo machinery blades, etc.), supersonic compressible flow with the effects of temperature (jet fighters and jet liners, missiles, etc.), and hypersonic compressible flow with heat interaction for space reentry vehicles. In the classical theoretical approach for the flutter of a cantilever wing, the wing's root boundary conditions are typically fixed constraints requiring all displacements and rotations at the boundary to be zero with no damping. These conditions make solution to the problem tractable and complete. Using this approach and a simplified aerodynamic load, the flutter of a uniform cantilever wing was studied by the author of this report in a previous work 1 (using a similar model to the one developed by Dhainaut 2 to study the aeroelastic behavior of swept wings) that was validated with results obtained by Goland 3 in his work on th...