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

Jason Howell; Katelynn Huneycutt; Justin T. Webster; Spencer Wilder; Jason Howell; Katelynn Huneycutt; Justin T. Webster; Spencer Wilder

doi:10.3934/mine.2019.3.614

Mathematics in Engineering

2019, Volume 1, Issue 3: 614-647. doi: 10.3934/mine.2019.3.614

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Research article

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

Received: 27 April 2019 Accepted: 03 July 2019 Published: 31 July 2019

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.
- 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[J]. Mathematics in Engineering, 2019, 1(3): 614-647. doi: 10.3934/mine.2019.3.614

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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.

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