Nonlinear flight dynamics of very flexible aircraft

This paper focuses on the characterization of the response of a very flexible aircraft in flight. The six-degree-of-freedom 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 finite state potential-flow 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 finite 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 modified Newmark method. The method incorporates both first- and second-order nonlinear equations without the necessity of transforming the equations to first order and incorporates a Newton-Raphson subiteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted that encompass nonlinear rigid-body, nonlinear rigid-body coupled with linearized structural solutions, and full nonlinear rigid-body and structural solutions. Simulations are presented that highlight the importance of nonlinear structural modeling compared with rigid-body and linearized structural analyses in a representative high-altitude long-endurance vehicle. Results show significant differences 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-filtered 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.