Prediction of stochastic limit cycle oscillations using an adaptive Polynomial Chaos method

Abstract

In this paper a non-intrusive adaptive stochastic spectral projection method is employed to predict limit-cycle oscillations (LCO) of an elastically mounted airfoil with random structural properties. Due to the nonlinear dynamics of the aeroelastic system, the use of a local stochastic representation based on a partition of the parametric space is more appropriate than a global approximation. Here, the stochastic response of the airfoil due to several uncertain structural parameters is expanded on a multi-element generalized Polynomial Chaos basis. The parametric space is discretized and a cubature grid is prescribed on each element of the partition. A particular attention is paid to the computation of the stochastic supercritical bifurcation obtained when a hardening spring is considered as the nonlinear restoring pitching force. Numerical results show how the probability density function of the peak pitch response, computed for both supercritical and subcritical branches, is aected by independent multiple input random parameters with bounded distributions. The eciency and robustness of the multi-element approach is investigated by means of analysis of h/p convergence and comparison with Monte-Carlo simulations and various stochastic bifurcation behaviors are investigated in details.