investigated aeroelastic behaviors arising from variability in three input variables , the initial pitch angle and two stiffness coefficients

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.

[1]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[2]  Charbel Farhat,et al.  Nonlinear Flutter Analysis of an F-16 in Stabilized, Accelerated, and Increased Angle of Attack Flight Conditions , 2002 .

[3]  Chris L. Pettit,et al.  Uncertainty Quantification in Aeroelasticity: Recent Results and Research Challenges , 2004 .

[4]  Earl H. Dowell,et al.  Further Invesitgation of Modeling Limit Cycle Oscillation Behavior of the F-16 Fighter Using a Harmonic Balance Approach , 2005 .

[5]  G. Karniadakis,et al.  An adaptive multi-element generalized polynomial chaos method for stochastic differential equations , 2005 .

[6]  Jeffrey V. Zweber,et al.  Numerical Analysis of Store-Induced Limit-Cycle Oscillation , 2004 .

[7]  Chris L. Pettit,et al.  Spectral and multiresolution Wiener expansions of oscillatory stochastic processes , 2006 .

[8]  Earl H. Dowell,et al.  A Stochastic Analysis of the Limit Cycle Behavior of a Nonlinear Aeroelastic Model Using the Response Surface Method , 2005 .

[9]  D. Xiu,et al.  Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos , 2002 .

[10]  Roger G. Ghanem,et al.  An equation-free, multiscale approach to uncertainty quantification , 2005, Computing in Science & Engineering.

[12]  Philip S. Beran,et al.  Predicting Uncertainty Propagation in a Highly Nonlinear System with a Stochastic Projection Method , 2004 .

[13]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[14]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[15]  David Nixon.  Unsteady transonic aerodynamics , 1989 .

[16]  Juan J. Alonso,et al.  Application of a Non-Linear Frequency Domain Solver to the Euler and Navier-Stokes Equations , 2002 .

[17]  Philip S. Beran,et al.  A Stochastic Approach for Predicting Bifurcation of a Pitch-Plunge Airfoil , 2003 .

[18]  Philip S. Beran,et al.  A Reduced Order Cyclic Method for Computation of Limit Cycles , 2005 .

[19]  Chris L. Pettit,et al.  Effects of Uncertainty on Nonlinear Plate Aeroelastic Response , 2002 .

[20]  Chris L. Pettit,et al.  Effects of Parametric Uncertainty on Airfoil Limit Cycle Oscillation , 2003 .

[21]  Wright-Patterson Afb,et al.  Polynomial Chaos Expansion Applied to Airfoil Limit Cycle Oscillations , 2004 .

[22]  Lei-Yong Jiang,et al.  FLUTTER OF AN AIRFOIL WITH A CUBIC RESTORING FORCE , 1999 .

[23]  R. Ghanem,et al.  Multi-resolution analysis of wiener-type uncertainty propagation schemes , 2004 .

[24]  Jeffrey P. Thomas,et al.  Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique , 2002 .

[25]  Jeffrey P. Thomas,et al.  Modeling Viscous Transonic Limit Cycle Oscillation Behavior Using a Harmonic Balance Approach , 2002 .

[26]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[27]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[28]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[29]  Wright-Patterson Afb,et al.  A Direct Method for Quantifying Limit-Cycle Oscillation Response Characteristics in the Presence of Uncertainties , 2004 .

[30]  Chris L. Pettit,et al.  Wiener-Haar Expansion of Airfoil Limit Cycle Oscillations , 2005 .

[31]  Charles M. Denegri,et al.  F-16 Limit Cycle Oscillation Analysis Using Transonic Small-disturbance Theory , 2005 .

[32]  Chris L. Pettit,et al.  Convergence Studies of Wiener Expansions for Computational Nonlinear Mechanics , 2006 .

[33]  Daniel R Millman,et al.  Quantifying Initial Condition and Parametric Uncertainties in a Nonlinear Aeroelastic System With an Efficient Stochastic Algorithm , 2004 .

[34]  Robert W. Bunton,et al.  Limit Cycle Oscillation Characteristics of Fighter Aircraft , 2000 .

[35]  M. Kubicek,et al.  DERPER—an algorithm for the continuation of periodic solutions in ordinary differential equations , 1984 .

[36]  R. Ghanem,et al.  Uncertainty propagation using Wiener-Haar expansions , 2004 .

[37]  Philip S. Beran,et al.  Airfoil pitch-and-plunge bifurcation behavior with Fourier chaos expansions , 2005 .