Stochastic Aeroelastic Analysis of Articulated Helicopter Rotor Using Response Surface Approximations

This paper investigates the effect of uncertainties in the cross sectional stiffnesses (flap, lag, and torsion) on vibratory hub loads of a four bladed articulated helicopter rotor. Using the aeroelastic analysis, response surface approximations are constructed for vibratory hub loads with respect to the cross sectional stiffnesses. The second order polynomial response surfaces are constructed using the central composite design of the theory of design of experiments and are then evaluated using statistical tests. Then, randomness with a coefficient of variation (c.o.v) of 10% is introduced into the cross sectional stiffnesses and the impact of this randomness on the vibratory hub loads is studied. It is found that the Gaussian random variables for the input cross sectional properties lead to non - Gaussian behaviour in the probability distribution functions of the vibratory hub loads. The use of response surface method allows the use of a large number of samples (100,000 in this paper) for the stochastic analysis which is necessary for reliability based design and robust optimization.