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We consider a beam model representing the transverse deflections of a onedimensional elastic structure immersed in an axial fluid flow. The modelincludes a nonlinear elastic restoring force, with damping and non-conservativeterms provided through the flow effects. Three different configurations areconsidered: a clamped panel, a hinged panel, and a flag (a cantilever clampedat the leading edge, free at the trailing edge). After providing the functionalframework for the dynamics, recent results on well-posedness and long-timebehavior of the associated dynamical system for solutions are presented. Havingprovided this theoretical context, in-depth numerical stability analyses areprovided, focusing both at the onset of flow-induced instability (flutter), andqualitative properties of the post-flutter dynamics across configurations.Modal approximations are utilized, as well as finite difference schemes.

A Thorough Look at the (In)Stability of Piston-theoretic Beams