Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Fourier analysis and applications: filtering, numerical computation, wavelets
Fourier analysis and applications: filtering, numerical computation, wavelets
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
An Equation-Free, Multiscale Approach to Uncertainty Quantification
Computing in Science and Engineering
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
Journal of Computational Physics
Numerical analysis of the Burgers' equation in the presence of uncertainty
Journal of Computational Physics
Uncertainty investigations in nonlinear aeroelastic systems
Journal of Computational and Applied Mathematics
Structural and Multidisciplinary Optimization
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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.