Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Matrix computations (3rd ed.)
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Nonlinear aeroelasticity in rotorcraft
Mathematical and Computer Modelling: An International Journal
Benchmark problems for incompressible fluid flows with structural interactions
Computers and Structures
Numerical analysis of the Burgers' equation in the presence of uncertainty
Journal of Computational Physics
Polynomial chaos representation of spatio-temporal random fields from experimental measurements
Journal of Computational Physics
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
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A nonlinear dynamic problem of stall induced flutter oscillation subject to physical uncertainties is analyzed using arbitrary polynomial chaos. A single-degree-of-freedom stall flutter model with torsional oscillation is considered subject to nonlinear aerodynamic loads in the dynamic stall regime and nonlinear structural stiffness. The analysis of the deterministic aeroelastic response demonstrated that the problem is sensitive to variations in structural natural frequency and structural nonlinearity. The effect of uncertainties in these parameters is studied. Arbitrary polynomial chaos is employed in which appropriate expansion polynomials are constructed based on the statistical moments of the uncertain input. The arbitrary polynomial chaos results are compared with Monte Carlo simulations.