Time-Domain Simulations of Linear and Nonlinear 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. 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.

Numerical model for the simulation of fixed wings aeroelastic response

“…8 (V ∞ = 100 m/s), this common frequency dominates the motion of all modes and the response is clearly unstable. The general form of the curves seems to be in agreement with similar simulations (Preidikman and Mook, 2000), but because the structures are completely different it is impossible to have a quantitative comparison.…”

“…As the dependence of the time interval for the numerical stability is a characteristic of the predictor-corrector methods (Hughes, 1987), one of the options to improve the presented numerical model is the automation of the time interval choice, or the use of a different numerical method to integrate the equation of motion. It is important to point that predictor-corrector methods were also employed by Strganac and Mook (1990) and Preidikman and Mook (2000) in similar aeroelastic models, but no mention was made about problems with numerical instability. …”

“…The dynamic characterization of the structure is done by the finite element method (Zienkiewics, 1986) and the unsteady aerodynamic loads are predicted using the vortex lattice method (Katz and Plotkin, 1991). More details about the present model can be found in Benini (2002) and similar models were presented by Strganac and Mook (1990) and Preidikman and Mook (2000).…”

Nonlinear-Aerodynamics/Nonlinear-Structure Interaction Methodology for a High-Altitude Long-Endurance Wing

“…The UVLM [12][13][14] employed here solves for incompressible unsteady aerodynamics over a flexible thin wing with its shed free wake in the time domain. The thin-wing surface is represented by a sheet of distributed vorticities for which the strengths together with those of the wake sheet vorticities are solved simultaneously at each time step.…”

Various Structural Approaches to Analyze an Aircraft with High Aspect Ratio Wings

“…Mook et al [19][20][21] indicated that the aerodynamic nonlinearities alone could be responsible for limit cycle oscillations. Patil et al [22] used geometrically exact structural analysis and finite state unsteady aerodynamic with stall.…”