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| It is well known that flutter is an endemic phenomenon in aeroelasticity. It occurs in high speed
flying jets, suspension bridges, wind mills etc.
Eliminating or controlling flutter is one of the fundamental issues arising in applications. From the mathematical point of view, the problem can be modeled by an evolutionary system of coupled PDE's with an interface. It involves a perturbed wave equation coupled - in a hybrid way- with a nonlinear system of elasticity. It will be shown that the resulting evolutionary system (i) generates a nonlinear semigroup and (ii) the semigroup is strongly stabilizable in the subsonic case. As a consequence, flutter can be eliminated all together in the subsonic regimes. For supersonic velocities it will be shown that the long time behavior of structural solutions is reducible to a finite dimensional attracting set. The above results extend
the theory previously known only for the "regularized" models which account for the rotational inertia or thermal effects. The proof of this result relies on a newly developed method for studying strong stabilizability in non-dissipative evolutions with a non-compact resolvent. |
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