Parametric uncertainty quantification in coalescene flutter

Matachniouk, Anton

doi:10.22215/etd/2013-06186

Cited by 2 publications

(9 citation statements)

References 69 publications

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“…The unsteady term (nondimensionalized as Z) is approximated as in Eq. (3.21), using a combination of both the basis functions in bending and in torsion to form the basis for the unsteady terms as in [50],…”

Section: Finite Dimensional Representation Of the Unsteady Aerodynamic Modelmentioning

confidence: 99%

Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis

Robinson¹

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The focus of this thesis is the aeroelastic dynamics of a rectangular cantilever wing with a NACA 0012 profile, whose base is free to rotate rigidly about a longitudinal axis. The wing is analytically modelled as part of a project to simulate the dynamics of an aeroelastic wind tunnel model.Structural geometric nonlinearities are modelled to the second order to capture the essential effects of large deformation. While the derivation closely follows common approaches from the literature on the subject of the nonlinear bending and torsion of rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics that arise from the added rigid body degree of freedom in pitch. A system of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) is derived using Hamilton's principle. These equations of motion describe the coupled axial-bending-bending-torsion-pitch motion of the system. A Galerkin projection scheme is employed to obtain a finite dimensional representation of the equations of motion, leading to a coupled system of ODEs. The resulting nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Using unsteady linear aerodynamics, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. The post-flutter behaviour is dictated by the structural geometric nonlinear terms which limit the oscillations to a limit cycle. Global sensitivity analysis is performed to study the effect of parametric uncertainty introduced by the rigid body base rotation on the flutter speed and associated frequency. It is found that the stiffness parameter has the largest influence on the variation of both the flutter speed and frequency, while the structural damping has a negligible influence.

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Section: Finite Dimensional Representation Of the Unsteady Aerodynamic Modelmentioning

confidence: 99%

Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis

Robinson¹

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“…The quasi-steady thin-airfoil theory aerodynamic model is used for the system. The equations of motion of the pitch α and plunge h motions shown below are adopted from [16,17,18,28].…”

Section: Equations Of Motionmentioning

confidence: 99%

“…( 6) is converted into the state-space form: ẋ = Ax (where x being the state-vector containing heave and pitch displacements and velocities) , the state matrix A is given by (e.g. [28]):…”

Section: Equations Of Motionmentioning

confidence: 99%

“…where n u is the index of airspeed at which experiments are conducted, and the prior pdf p(α nu p ) is estimated using the parametric uncertainty quantification method through MCS [28]. Samples of modal parameters αq = (β nu 1 , β nu 2 , ω nu 1 , ω nu 2 ) in Eq.…”

Section: Application Of Bayesian Inference In Flutter Speed Estimationmentioning

confidence: 99%

“…where the prior p(α 1 p , • • • , α nu p ) is estimated using parametric uncertainty quantification [28]. Using Eq.…”

Section: Application Of Bayesian Inference In Flutter Speed Estimationmentioning

confidence: 99%

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Probabilistic Prediction of Coalescence Flutter Using Measurements: Application to the Flutter Margin Method

Chajjed¹

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Zimmerman and Weissenburger's flutter margin method is widely used to estimate the aeroelastic coalescence flutter speed. In contrast to aeroelastic decay rates, the flutter margin exhibits monotonic decay with respect to airspeed redering it effective in extrapolating the flutter speed using flight test data conducted at pre-flutter airspeeds. This paper reports the generalization of the Bayesian formulation of the flutter margin method by Khalil et al. developed to tackle measurement and modeling uncertainties. This paper improves the predictive performance of the previous algorithm by incorporating the joint prior of aeroelastic modal frequencies and decay rates among airspeeds in order to better estimate the joint posterior of modal parameters using observational data. The modal parameter prior is constructed using the classical two-degree-of-freedom pitch-plunge aeroelastic model whose system matrices (e.g. structural stiffness and damping matrices) vary randomly. Such joint modal parameter prior enforces statistical dependence among posteriors of modal parameters and the associated flutter margins across airspeeds. Numerical studies demonstrate a considerable reduction of uncertainties on the predicted flutter speed obtained from the generalized Bayesian flutter margin method. This improved algorithm can cut cost by reducing the number of flight tests and better assess the uncertainty against aeroelastic flutter.

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Parametric uncertainty quantification in coalescene flutter

Cited by 2 publications

References 69 publications

Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis

Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis

Probabilistic Prediction of Coalescence Flutter Using Measurements: Application to the Flutter Margin Method

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