A Physical Explanation of Coupled-Mode Flutter Using Forced-Response Networks

Modern flutter solvers act as black boxes, providing little understanding of how a wing's aeroelastic design influences its stability. This paper presents a physical explanation of coupled-mode flutter in which the wing's natural modes form a hierarchical network connected by aerodynamic forces. Within this "forced-response network", each natural mode behaves as a mass–spring–damper system whose "effective natural frequency" varies with the freestream dynamic pressure due to aerodynamic stiffness. Using URANS calculations of the NASA Common Research Model, an energy analysis shows flutter occurs when one of these effective natural frequencies becomes equal to the flutter frequency, causing that natural mode to resonate. The resonance is shown to propagate through the network's connections, resulting in changes to all other natural modes that ultimately re-stabilize the wing and produce a hump mode. This explanation allows the influence of each aspect of the wing's aeroelastic design on stability to be physically understood and quantified. It is shown that this enables flutter in a representative modern airliner to be distilled to only a few parameters that may be targeted in aerodynamic or structural design. The utility of the analysis is demonstrated by explaining the effects of changing the natural frequencies, freestream Mach number, and static deformation.