Gust Response Computations with Control Surface Freeplay Using Random Input Describing Functions

An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An efficient method to compute the total gust+LCO response is developed using random input describing functions (RIDF), in a manner analogous to harmonic input describing functions for LCO calculation. Results are obtained for an airfoil with trailing edge flap freeplay and linear potential flow aerodynamics at various gust strengths, freeplay sizes, and flow velocities. Both stable and unstable responses are detected. It is found that LCO coexists with gust response for weak gust/large freeplay combinations, and it is quenched for sufficiently strong gust/small freeplay. Time marching results are provided to validate the RIDF method and confirm the findings. The present work appears to be the first use of RIDF in aeroelasticity although it is well known to nonlinear control systems analysts. Notably the RIDF method in its present form is also applicable when steady flow aerodynamic nonlinearities are included.