  We consider a beam model representing the transverse deflections of a one
dimensional elastic structure immersed in an axial fluid flow. The model
includes a nonlinear elastic restoring force, with damping and non-conservative
terms provided through the flow effects. Three different configurations are
considered: a clamped panel, a hinged panel, and a flag (a cantilever clamped
at the leading edge, free at the trailing edge). After providing the functional
framework for the dynamics, recent results on well-posedness and long-time
behavior of the associated dynamical system for solutions are presented. Having
provided this theoretical context, in-depth numerical stability analyses are
provided, focusing both at the onset of flow-induced instability (flutter), and
qualitative properties of the post-flutter dynamics across configurations.
Modal approximations are utilized, as well as finite difference schemes.
