Dynamic stall utter analysis with uncertainties using Multi-Element Probabilistic Collocation

TLDR: In this paper, the effect of uncertainty present in external torque on the bifurcation behavior of a dynamic stall utter problem is analyzed using the Multi-Element Probabilistic Collocation method.

Abstract: In this paper the eect of uncertainty present in external torque on the bifurcation behavior of a dynamic stall utter problem is analyzed using the Multi-Element Probabilistic Collocation method. A Multi-Element Probabilistic Collocation approach is followed since the bifurcation in the response causes oscillations for the ordinary Probabilistic Collocation method. Two elements are used, with one element covering the damped response and the other the period-one oscillations. This is only possible if the elements are separated near the bifurcation point, of which the location is in general not known in advance. A search algorithm is used to nd a coarse estimate of the bifurcation point to divide the domain into two elements. The stochastic bifurcation plot and the probability distribution of the bifurcation point show a large variation in the output due to the uncertain external torque.