Uncertainty quantification of an airfoil control surface flutter system

Aeroelastic instability and nonlinear dynamics of a wing control surface have been investigated with parametric uncertainties. The aeroelastic system has a combined nonlinearity of cubic soft spring and free-play. The system shows subcritical Hopf bifurcation in which a small amplitude Limit Cycle Oscillation (LCO) jumps to an infinitely large amplitude LCO. The subcritical behavior is due to the soft spring and the amplitude of the smaller LCO is controlled by the free-play. A fifth order stiffness is used to make the large LCO amplitude finite. Such systems when modeled with parametric uncertainty shows discontinuities in the response surface along the random domain. It is difficult to model the discontinuities in the response surface accurately using conventional spectral approaches and it results in erroneous response statistics. An intelligent interpolation called integrated interpolation scheme earlier proposed by the authors using a combination of linear and proximal interpolation has been used in the present work. The scheme uses equi-probable nodes as there is equal probability of the random variable lying between any of the node intervals. The deterministic runs are made only at these node points, thus giving considerable computational advantage over standard Monte Carlo Simulations (MCS). The interpolation algorithm is applied to the response surface to capture the sharp discontinuities. Response statistics have also been compared with that of a reference Monte Carlo Simulations (MCS). As the scheme is non-intrusive it can be applied to any dimension of random domain. © 2013 Taylor & Francis Group, London.