Dan Borglund

The mu-k method for robust flutter solutions

A straightforward frequency-domain method for robust flutter analysis is presented. First, a versatile uncertainty description for the unsteady aerodynamic forces is derived by assigning uncertainty to the frequency-domain pressure coefficients. The uncertainty description applies to any frequency-domain aerodynamic method, benefits from the same level of geometric detail as the underlying aerodynamic model, exploits the modal formulation of the flutter equation, and is computed by simple postprocessing of standard aerodynamic data. Next, structured singular value analysis is applied to derive an explicit criterion for robust flutter stability based on the flutter equation and a parametric uncertainty description. The resulting procedure for computation of a worst-case flutter boundary resembles a p-k or g-method flutter analysis, produces match-point flutter solutions and allows for detailed aerodynamic uncertainty descriptions. Finally, the proposed method is successfully applied to a wind-tunnel model in low-speed airflow.

Robust aeroelastic stability analysis considering frequency-domain aerodynamic uncertainty

The problem of modeling frequency-domain aerodynamic uncertainty for a slender wing structure is investigated. Based on an unsteady lifting-line theory used for the generalized aerodynamic forces, a quite versatile uncertainty description with a clear physical interpretation is proposed. The uncertainty description is easily put in a form suitable for application of the mu framework in robust linear control. Because only frequency response matrices are required for the mu computations, the proposed uncertainty description can be used for robust stability and performance analysis without rational function approximations of the aerodynamic transfer function matrices. The usefulness of the uncertainty description and the methods available for robust aeroelastic stability analysis is demonstrated by performing aeroelastic wind-tunnel experiments.

Efficient Computation of Robust Flutter Boundaries Using the mu-k Method

A simple and efficient algorithm for robust flutter analysis is presented. First, a general linear fractional transformation formulation of the mu-k method is provided, making it straightforward to pose the uncertain flutter equation in a form suitable for structured singular value analysis. The new formulation establishes a close connection between mu-k flutter analysis and traditional frequency-domain flutter analysis, which is used to formulate an efficient algorithm for computation of robust flutter boundaries. The proposed method is successfully applied to an F-16 sample test case with uncertain external stores aerodynamics, showing that standard tools for structural dynamics and unsteady aerodynamics can be used to perform robust flutter analysis with only modest additional modeling.

Upper Bound Flutter Speed Estimation Using the mu-k Method

The use of upper-bound μ-k estimation method in the development of robust flutter analysis and flutter testing, was described. Since only the frequency-domain aerodynamic forces are required to compute μ(k), established aerodynamic methods can be used for the robust flutter analysis. A robust flutter analysis considering wing-tip aerodynamic uncertainty was developed in MATLAB® for a wind-tunnel model in low-speed airflow. The results show that the extended procedure for robust flutter analysis was successfully applied to a wind-tunnel model in low-speed airflow.

Assessment of Uncertain External Store Aerodynamics Using mu-p Flutter Analysis

F LUTTER testing is rarely performed on full-scale aircraft, due to the high risk for structural damage and failure. Instead, flutter boundaries are computed based on a numerical model of the aircraft, and flight testing under less critical conditions can be performed to collect data for validation of the numerical model. Clearly, problems arise when the flight-test data show deviation from the numerically predicted data. Deviations are likely to occur for any aircraft configuration, because model imperfections and simplifications always lead to some uncertainty in the numerical model, and the question arises as to the impact that these uncertainties have on the predicted flutter boundaries. Inmost cases, some parts of the numerical model, such as themass properties of different components, are well known, whereas other elements, such as the aerodynamic loads in some region of a wing with complex geometry, are known to be subject to uncertainty. Earlier studies [1–3] have shown how aerodynamic uncertainties can be introduced in the numerical model based on physical reasoning and known modeling difficulties. The same technique for modeling of aerodynamic uncertainty will be applied in this study, but it will also be shown how data points collected at subcritical conditions can be used to establish an uncertaintymodel that is capable of producing reliable flutter boundaries. In the present study, a wind-tunnel model was specifically designed to demonstrate and evaluate uncertainty modeling approaches. A fairly simple wing geometry and structure is chosen to minimize the errors introduced by modeling simplifications. An external store in the form of a wing-tip missile is used to increase the model complexity gradually, and the impact on the flutter behavior is investigated both numerically and experimentally. In cases in which the numerical predictions deviate from the experimental results, an uncertainty description is developed and -p flutter analysis and model validation [4] are applied to compute bounds on the flutter speed.

Solution of the Flutter Eigenvalue Problem with Mixed Structural/Aerodynamic Uncertainty

The solution of the flutter eigenvalue problem with mixed structural/aerodynamic uncertainty was examined. A delta-wing wind-tunnel model was used as a test case. The model had a simple structural design and was made of glass-fiber and carbon-fiber composite materials. It had a semispan of 0.88 m and mean chord of 0.70m and was mounted vertically in the low-speed wind tunnel L2000. The numerical analysis was based on a NASTRAN model with shell elements for the wing, mass elements for the missile, and aerodynamic panels for doublet-lattice aerodynamic loads. The relatively stiff missile was modeled as a rigid body attached to the wing tip. The nominal eigenvalue was always an interior point of the corresponding eigenvalue set. A parameter sweep taking only aerodynamic uncertainty into account was performed by solving the eigenvalue problem for a set of parameter values. The eigenvalue sets based on one patch and seven patches, respectively, showed only slight difference.

Robust Flutter Analysis Considering Mode Shape Variations

A study was conducted to perform robust flutter analysis, considering mode shape variation problems. The study demonstrated that the assumption of a fixed modal base can lead to incorrect flutter ...

Robust Wing Flutter Suppression Considering Aerodynamic Uncertainty

Ar obust aeroservoelastic stability analysis considering frequency-domain aerodynamic uncertainty is utilized fo rr obust control law design for flutter suppression of a flexible wing. The problem of stabilizing the wing in flutter using a minimum amount of control power is posed. For this purpose, numerical optimization is used to minimize the norm of a simple low-order controller subject to constraints on robust closed-loop stability. Robust stability is enforced in the optimization problem by posing constraints on the upper bounds on structured singular values and eigenvalues obtained from a linear stability analysis. The resulting controller is synthesized using gain scheduling, and robust wing flutter suppression is demonstrated in wind-tunnel testing.

Aeroservoelastic design optimization with experimental verification

A demonstration of integrated design optimization of an aeroservoelastic system was presented. It was shown that the simultaneous design of structural and control system required a two-step proce ...