Interdisciplinary Foundations of Flutter: Insights from the Aeroelastic Triangle
Aeroelastic characteristics are defined by the interaction between structural dynamics and the incremental aerodynamics developed by the deformed surfaces. A standard depiction of this interaction is the aeroelasticity triangle. This one is from the classic text ‘Aeroelasticity’ by Bishplinghoff, Ashley, and Halfmann, universally called ‘BAH’:
A gratifying result for us Flutter enthusiasts is that Flutter appears front and center, involving all three elements. You can imagine flutter folks saying, ‘pity the poor analyst whose dominion only encompasses one or two of these disciplines!’ Of course the triangle puts the flutter engineer at the center—we made it! You could just as easily invent a diagram that puts us on the outside, and any other discipline you like in the middle.
But the diagram does indicate you need these three items working together for the dynamic instability of flutter:
- Elastic structure that deforms under load
- Aerodynamics that are affected by that deformation
- Weight to provide dynamics through mechanical vibrations
An interesting aside is that you don’t need weights to calculate static structural deformation under aerodynamic load, only stiffness and aerodynamics. Most aerostructure tools (including Nastran) take advantage of this simplification to formulate their static aeroelastic solutions.
You might be wondering: Which types of configurations are most likely to encounter flutter? Well, you need a structure that deforms under load in such a way that significant incremental aerodynamic forces result. For significant forces, you generally need a lifting surface, since fuselage and other non-lifting surfaces generally have low lift curve slopes by comparison. And you need the structure to deform in a way that develops this load. That leads to a few high-impact configurations:
Swept-back wings. Wings under load bend in the direction of their ‘elastic axis’, which is generally in a spanwise direction. For swept-back wings, this bending also results in an aerodynamic torsion load because of the difference between the bending direction and the airflow direction. This couples structures and aerodynamics in a significant way and is the most classic flutter example. Swept-forward wings are more stable in flutter for an equal and opposite reason.
Control surfaces. Maybe your bending-torsion coupling isn’t powerful enough to flutter? Add a trailing edge control surface like an elevator, rudder, or aileron. Tailor-made for the job, control surfaces convert physical rotation into aerodynamic force, and inertial coupling between the lifting surface (wing/stabilizer/whatever) does the rest. This should be the poster child for Flutter, probably 90% of a Flutter analyst’s work involves trailing-edge control surfaces.
Body effects. For most historical airplanes, fuselage effects were considered unimportant. So much so that an airplane’s wing and tail flutter effects were often calculated independently. But even then, this wasn’t quite true. Aft fuselage torsion and side bending contribute to vertical fin/rudder flutter for even those classic configurations. And from there we have more esoteric effects:
- Slender fuselages that allow coupling between wing and tail modes
- Short stubby fuselages that allow coupling between wing bending and the airplane’s short-period mode, so-called ‘body freedom flutter’
- Unique configurations like twin-boom airplanes. These fuselage modes are coupled with wing torsion and bring a new dimension to flutter characteristics
Gyroscopic precession. In the 1930s, mathematicians and aeronautical engineers found a unique issue. Propeller/engine/mount installations are subject to precession, just like a spinning top. I loved watching my toy tops in precession when I was a kid, it was such an interesting motion. If a propeller is spinning at the end of the ‘top’, the resulting unsteady aerodynamics are destabilizing. In the 1930s, this was a mathematical special case and not a practical issue. That was because the rotating inertia of the current engines was nowhere near enough to make the coupling dangerous. It took until the 1960s for turbopropeller installations to provide enough inertia to cause actual flutter in airplane flight envelopes. And so ‘whirl flutter’ was born.
Next up in our Flutter series, we’ll look at some specific examples of these different types of Flutter.
Connect with TLG’s Director of Engineering, FAA Flight Analyst DER, and FAA Flutter DER, Robert Lind.
Check out our last article on Flutter: Understanding Flutter: The Feedback Loop Behind Aerodynamic Stability in Aircraft
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