Time-domain simulations of linear and nonlinear aeroelastic behavior

A method for simulating unsteady, nonlinear, subsonic aeroelastic behavior of an aircraft wing is described. The flowing air and deforming structure are treated as the elements of a single dynamic system, and all of the governing equations are integrated numerically, simultaneously, and interactively in the time domain. The authors' version of the general nonlinear, unsteady, vortex-lattice method is used to predict the aerodynamic forces; a linear finite-element model of the wing, which is derived from MSC/NASTRAN, is used to predict the deformations of the wing; and the models are coupled in such a way that the structural and aerodynamic grids can be chosen arbitrarily. The deformation of the wing is expressed as an expansion in terms of the linear free-vibration modes obtained from the finite-element model, and the time-dependent coefficients in the expansion serve as the generalized coordinates for the entire dynamic system. A predictor-corrector method is adapted to solve for the generalized coordinates and the flowfield. The results clearly show that when the speed is low, the responses to initial disturbances contain many frequencies and decay, but that the responses become more organized (energy concentrates around a few frequencies) as the speed and/or the angle of attack increases. Finally, at the onset of flutter, all of the modes, after an initial transient period, respond at the same frequency. It appears that the flutter-causing instability is a supercritical Hopf bifurcation. At and above the critical speed, the amplitudes of the responses appear to grow linearly with time initially, but then become limit cycles. The amplitudes of the limit cycles grow as the speed increases, and eventually it appears that the limit cycles experience a secondary supercritical Hopf bifurcation and become unstable; their amplitudes and phases modulate. At this point, the response can be described as motion on a torus.