Large Deflection Aeroelasticity and Aeroelastic Lifting Line Theory for Examination of Aerodynamic Effects and Nonlinear Limit Cycle Oscillations

This paper investigates the effects of nonlinear large deflection bending on the aerodynamic performance and aeroelasticity of a high aspect ratio flexible wing. A nonlinear large deflection theory is developed for aeroelasticity to account for large deflection bending. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening of the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields a lower lift and higher induced drag than the linear bending theory. The nonlinear large deflection bending also can affect the structural dynamics of a high aspect ratio wing significantly. Limit cycle oscillations are a nonlinear phenomenon which arises from geometric nonlinearity and other sources of nonlinearities. Large deflection can manifest itself in limit cycle oscillations whereby linear flutter behaviors can result in an increase in the bending deflection up to a point where the geometric nonlinearity due to the large deflection begins to set in that results in limit cycle oscillations.