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

1 Carnegie Mellon University, 5000 Forbes Avenue Pittsburgh, PA 15213, USA
2 University of Maryland, Baltimore County, 1000 Hilltop Cir, Baltimore, MD, 21250, USA
3 College of Charleston, 66 George St, Charleston, SC 29424, USA

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.
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Keywords extensible beam; nonlinear elasticity; flutter; stability; attractors; modal analysis

Citation: Jason Howell, Katelynn Huneycutt, Justin T. Webster, Spencer Wilder. A thorough look at the (in)stability of piston-theoretic beams. Mathematics in Engineering, 2019, 1(3): 614-647. doi: 10.3934/mine.2019.3.614


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