  We consider a cantilevered (clamped-free) beam in an axial potential flow.
Certain flow velocities may bring about a bounded-response instability in the
structure, termed {\em flutter}. As a preliminary analysis, we employ the
theory of {\em large deflections} and utilize a piston-theoretic approximation
of the flow for appropriate parameters, yielding a nonlinear
(Berger/Woinowsky-Krieger) beam equation with a non-dissipative RHS. As we
obtain this structural model via a simplification, we arrive at a nonstandard
nonlinear boundary condition that necessitates careful well-posedness analysis.
We account for rotational inertia effects in the beam and discuss technical
issues that necessitate this feature.
  We demonstrate nonlinear semigroup well-posedness of the model with the
rotational inertia terms. For the case with no rotational inertia, we utilize a
Galerkin approach to establish existence of weak, possibly non-unique,
solutions. For the former, inertial model, we prove that the associated
non-gradient dynamical system has a compact global attractor. Finally, we study
stability regimes and {\em post-flutter} dynamics (non-stationary end
behaviors) using numerical methods for models with, and without, the rotational
inertia terms.
