Howell, JasonHuneycutt, KatelynnWebster, JustinWilder, Spencer2024-06-112024-06-112019-07-31Howell, Jason, Katelynn Huneycutt, Justin T. Webster, Spencer Wilder, Jason Howell, Katelynn Huneycutt, Justin T. Webster, and Spencer Wilder. "A Thorough Look at the (in)Stability of Piston-Theoretic Beams." Mathematics in Engineering 1, no. 3 (2019): 614–47. https://doi.org/10.3934/mine.2019.3.614.https://doi.org/10.3934/mine.2019.3.614http://hdl.handle.net/11603/34608We 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.34 pagesen-USCC BY 4.0 DEED Attribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/Text