Modeling Response of Flexible High-Aspect-Ratio Wings to Wind Turbulence1

Analytical modeling of the effect of wind turbulence on flexible high-aspect-ratio aircraft wings typical of unmanned air vehicles (UAVs). The wind model is derived from the Kolmogorov power-law spectrum random field turbulence model invoking the Taylor “frozen-field” hypothesis. The aerodynamic model is based on the typical-section compressible attached-flow with Kutta–Joukowski boundary conditions. The gust loading—both lift and moment—is calculated explicitly for $M=0$ and $M=1$ as typical of subsonic and transonic flow. The gust loading intensity is shown to decrease as the speed increases, so that the turbulence effects are not significant at transonic speeds. To calculate the wing response we use the continuum two degree-of-freedom cantilever beam model of Goland and derive explicit expressions of the spectral density of both the plunge (bending) and pitch (torsion) response for $M=0$ . Numerical results are presented for two illustrative wings. Most of the turbulence energy is in the $0–10H$ range. Since flexibility and high aspect ratio push flutter modes and speeds down, turbulence can be a significant safety issue for UAVs in particular.