A thorough look at the (in)stability of piston-theoretic beams

Abstract

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 solutions are presented. Having provided this theoretical context, in-depth numerical stability analyses follow, focusing both on 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.

Keywords

• extensible beam
• nonlinear elasticity
• flutter
• stability
• attractors
• modal analysis