"I don't think flutter characteristics change significantly with TAS/Altitude to warrant a different

"I don't think flutter characteristics change significantly with TAS/Altitude to warrant a different Vne" .. It depends on the type of aircraft and how its certificated. for most light GA its essentially not an issue. BUT even a light GA aircraft that is Turbo-normalized that equation changes. For example a SR-22t can operate up to FL250. It has a fixed VNE (205KIAS) up to 17500 and a linearly decreasing one that is reduced to 175KIAS at FL250. This isnt a direct result of structural loads but is a result of reduced flutter/aeroelastic margin due to higher TAS at a given indicated airspeed in the flight levels.
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