Differential Equations Seminar: Katelynn Huneycutt
Abstract: Aeroelastic flutter is a sustained, usually periodic, response of a structure to a fluid flow, occurring when a fluid destabilizes the structures natural modes. Here, we study the onset of instability of a one-dimensional beam immersed in an axial fluid flow. Our configurations of interest are clamped, hinged, and cantilever beams. After setting up the functional analytic framework for the dynamics, we conduct multi-faceted numerical stability analysis using a finite difference approach and a spectral approximation popular in the engineering literature. We demonstrate the consistency of the predictions for the onset of flutter, and, time permitting, examine the qualitative properties of the post-flutter dynamics.