Uncertainty quantification of limit-cycle oscillations

Different computational methodologies have been developed to quantify the uncertain response of a relatively simple aeroelastic system in limit-cycle oscillation, subject to parametric variability. The aeroelastic system is that of a rigid airfoil, supported by pitch and plunge structural coupling, with nonlinearities in the component in pitch. The nonlinearities are adjusted to permit the formation of a either a subcritical or supercritical branch of limit-cycle oscillations. Uncertainties are specified in the cubic coefficient of the torsional spring and in the initial pitch angle of the airfoil. Stochastic projections of the time-domain and cyclic equations governing system response are carried out, leading to both intrusive and non-intrusive computational formulations. Non-intrusive formulations are examined using stochastic projections derived from Wiener expansions involving Haar wavelet and B-spline bases, while Wiener–Hermite expansions of the cyclic equations are employed intrusively and non-intrusively. Application of the B-spline stochastic projection is extended to the treatment of aerodynamic nonlinearities, as modeled through the discrete Euler equations. The methodologies are compared in terms of computational cost, convergence properties, ease of implementation, and potential for application to complex aeroelastic systems.