Nonlinear Flight Dynamics of Very Flexible Aircraft

Abstract

This paper focuses on the characterization of the response of a very ∞exible aircraft in ∞ight. The 6-DOF equations of motion of a reference point on the aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady flnite-state potential ∞ow aerodynamics form the basis for the aeroelastic model. The nonlinear beam structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the flnite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. The equations of motion are integrated using an implicit modifled generalized-alpha method. The method incorporates both flrst and second order nonlinear equations without the necessity of transforming the equations to flrst order and incorporates a Newton-Raphson sub-iteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted which encompass nonlinear rigid body, nonlinear rigid body coupled with linearized structural solutions, and full nonlinear rigid body and structural solutions. Simulations are presented which highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analyses in a representative High Altitude Long Endurance (HALE) vehicle. Results show signiflcant difierences in the three reference point axes (pitch, roll, and yaw) not previously captured by linearized or rigid body approaches. The simulations using both full and empty fuel states include level gliding descent, low-pass flltered square aileron input rolling/gliding descent, and low-pass square elevator input gliding descent. Results are compared for rigid body, linearized structural, and nonlinear structural response.