Aeroelastic Stability Analysis of a Wing with a Variable Cant Angle Winglet

Abstract

Currently, multiple air vehicles employ wing shape change to enhance their performance and achieve mission adaptability in different environments inside the Earth's atmosphere. This concept has been around since the dawn of aviation. In 1903, the Wright brothers implemented wing warping to control their aircraft during flight. Subsequently, a variety of techniques and devices have used to achieve wing shape change and make the vehicles more versatile. For example, they include variable wing sweep, folding wing tips, and variable camber. However, aeroelasticity has played in important role in these developments. Thus, this work focuses on the aeroelastic analysis and understanding of the fundamental physics of the flutter mechanism of a wing equipped with a variable cant angle winglet. Two methods are applied to model the wingletted wing system. The Rayleigh Ritz method is the first technique used to model the system. This method involves the implementation of a shape function to represent the entire structure. The second method used in the analysis is the Finite Element Analysis. In this formulation, the wing structure is divided into elements and elemental functions are used for local interpolation. Strip theory is used to model the spanwise aerodynamic loading. In addition, steady, quasi-steady, and unsteady aerodynamic models are used, each with different levels of complexity. Both the structural and aerodynamic models were coupled to generate four dynamic aeroelastic equations that represent the continuous system. Those equations were used to model the system and perform a dynamic aeroelastic analysis. The results indicate that having a vehicle equipped with a variable cant angle winglet can be favorable. It can increase flutter speed and expand its flight envelope. Moreover, when the winglet length is greater than 50% the length of the wing section and the cant angle greater than 50 degrees, the second torsional mode of vibration becomes unstable. Whereas, the first mode remains marginally stable. Thus, the second mode has become the critical mode that leads to structural failure. In this case, that phenomenon is referred as mode switching.