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A generalized eigenvalue solution to the flutter stability problem with true damping: The p-L method

Quero-Martin, David and Vuillemin, Pierre and Poussot-Vassal, Charles (2021) A generalized eigenvalue solution to the flutter stability problem with true damping: The p-L method. Journal of Fluids and Structures, 103 (103266). Elsevier. doi: 10.1016/j.jfluidstructs.2021.103266. ISSN 0889-9746.

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Official URL: https://www.sciencedirect.com/science/article/abs/pii/S0889974621000499


An alternative solution to the flutter equation with a true damping representation is presented. The p-L method transforms the nonlinear eigenvalue problem into a linear generalized eigenvalue formulation by interpolating the nonlinear aerodynamic term with help of the Loewner and shifted-Loewner matrices, avoiding any kind of approximation. Subsequently an equivalent generalized state-space formulation in the time-domain is obtained, which stability can be determined by solving a standard generalized eigenvalue problem. The proposed method is shown to describe the aerodynamic term throughout the complex plane by analytic continuation of the interpolating rational functions over the imaginary axis, whereas expansions based on polynomial basis functions have a limited validity for excursions outside it. Further, the p-L method matches the generalized aeroelastic analysis method (GAAM) framework representing true damping but requiring only samples of the aerodynamic term along the imaginary axis, avoiding additional computations for non-zero damping. Unlike methods which solve the nonlinear eigenvalue problem whereby some roots of the flutter equation may be missed, the p-L method is able to find all roots at once. The method is applied to well-known flutter benchmark cases from the literature, namely, several two-dimensional flutter cases and the AGARD 445.6 wing aeroelastic benchmark case.

Item URL in elib:https://elib.dlr.de/141599/
Document Type:Article
Title:A generalized eigenvalue solution to the flutter stability problem with true damping: The p-L method
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Date:March 2021
Journal or Publication Title:Journal of Fluids and Structures
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Keywords:aeroelasticity, fluid–structure interaction, flutter solver, analytic continuation, Loewner framework
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Efficient Vehicle
DLR - Research area:Aeronautics
DLR - Program:L EV - Efficient Vehicle
DLR - Research theme (Project):L - Virtual Aircraft and  Validation
Location: Göttingen
Institutes and Institutions:Institute of Aeroelasticity > Aeroelastic Simulation
Deposited By: Quero-Martin, David
Deposited On:26 Aug 2021 16:29
Last Modified:24 May 2022 23:47

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