Time-Domain Simulations of Nonlinear, Unsteady, Aeroelastic Behavior

Abstract

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. Our version of the general nonlinear, unsteady, vortex-lattice method is used to predict the aerodynamic forces, a linear fine-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 th 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 concentrated 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.