The mu-k Method for Robust Flutter Solutions

Abstract

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 windtunnel model in low-speed airflow.

Modeling and robust Body Freedom Flutter Analysis of flexible aircraft configurations

“…4), where it is evident how V f increases as σ s (equivalently EI) is reduced. This is due to the fact that a decrease in EI implies an analogous trend in the bending frequency, as expressed by (6). Since the torsional stiffness is kept constant in these analyses, a decrease in σ s can be then interpreted as a reduction in the ratio between the uncoupled bending and torsional natural frequencies.…”

“…This is the transfer function from the signal w to z associated to the LFT expression of the uncertain plant. Since the BFF problem is here formulated in the frequency-domain (11), once the uncertainties are introduced and the nominal dynamics is separated from the unknown terms, it is possible to build M 11 from its definition (see [6] for a comprehensive description of the algorithm). This procedure implies a gridding of the frequency range under investigation: for each frequency value ω the terms involved in the definition of M 11 are constant matrices and then the algorithm for the calculation of µ can be initialized.…”

“…The so-called flutter robust analysis [5], [6] aims to quantify the gap between the prediction of the nominal stability analysis (i.e. model without uncertainties) and the worst prediction when the whole set of uncertainty is contemplated.…”

Comparison of Aeroelastic Modeling and Robust Flutter Analysis of a Typical Section**This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 636307, project FLEXOP

“…This is the transfer function seen by the perturbation block of the uncertain plant. Borglund (2004) proposed to perform the robust flutter analysis by starting from the plant formulated in the frequency-domain (3), with M 11 manually assembled once the uncertain parameters are embedded. This procedure implies a gridding of the frequency range under investigation: for each discrete value ω in the range, the terms involved in the definition aerodynamic ∆ with the range of variation of lag roots in MS approximation related to that of Roger according to the proposed criteria of M 11 are constant matrices and then the algorithm for the calculation of µ can be initialized.…”

“…This is believed to be a powerful tool when used as a complement to the classical techniques in that it could highlight weak points of the model requiring more refinement and conversely identify parameters that can be coarsely estimated as they do not have a strong influence on the results. The most wellknown robust flutter approaches are those from Lind and Brenner (2012), Borglund (2004), Idan et al (1999), with the first even including on-line analysis during flight tests.…”