# Applied Mathematics Colloquium: Dr. Justin Webster

## UMBC

Friday, December 1, 2017

2:00 PM - 3:00 PM

2:00 PM - 3:00 PM

Mathematics/Psychology : 103

**Title:**

*The Flutter of a Cantilevered Structure in an Axial Flow***Speaker:**Dr. Justin Webster, UMBC

**Abstract:**Flutter is a bounded response, self-excitation instability of an elastic structure in a surrounding fluid flow. Here, we describe the difficult problems in modeling the axial flow flutter phenomenon for a cantilevered beam, when the structure’s trailing edge is free and the flow is along the principal axis.

Much can be said at the qualitative level about flag, flap, and
wing flutter; these phenomena are obviously of great interest in engineering.
However, mathematically, there is a lack of PDE and dynamical systems analysis
of these compelling models. Beyond the obvious applications in aerospace, the
flutter phenomenon arises in: the biomedical realm and in sustainable energies.
Indeed, the cantilever configuration is central to

*piezoelectric energy harvesting*, whereby energy is extracted from an ambient flow through sustained aeroelastic oscillations.In this talk, we begin by discussing recent results for simpler mathematical models of panel flutter, where the entire structural boundary is restricted. We then discuss the ways in which analysis breaks down when the trailing edge is free. We review two classes of pertinent beam models (including very recent nonlinear, nonlocal inextensible models). The analytical challenges in the analysis can be viewed as reflections of the difficulty in modeling the physics of the problem. Very results will be discussed that address well-posedness and in/stability of various cantilevered dynamics, along with recent numerical simulations.