The WKU Student Chapter of the Society for Industrial and Applied Mathematics will host a Virtual Q&A Session with Dr. Justin Webster, Assistant Professor in the Department of Mathematics at the University of Maryland, Baltimore County.

Dr. Webster will present Can Differential Equations Explain How the Wind Brought Down a Bridge? at 3 p.m. Friday, April 23.

Where: Zoom (Meeting ID: 476 837 1123, Passcode: 123456)

Abstract: In this talk we describe, model, and analyze the phenomenon of aeroelastic flutter---that is, the way an elastic structure may become unstable in the presence of an adjacent flow of air. Under certain circumstances, a feedback instability occurs between elastic deformations and pressure changes in the airflow, resulting in sustained oscillations. A canonical example was seen in the Tacoma Narrows suspension bridge, which collapsed in 1940 while fluttering in 40 mph winds. We note the important distinction between flutter, as we will discuss it, and the resonance phenomenon, due to the presence of a periodic external forcing.

Flutter is typically discussed in the context of aero-mechanical systems: buildings and bridges in wind, and flight systems. However, applications also arise in biology (snoring and sleep apnea), and in alternative energy technologies (piezoelectric energy harvesters). Through mathematical modeling (using differential equations) and subsequent analyses of these models, we try to capture the mechanism that gives rise to this type of instability. Additionally, when flutter occurs, we attempt to describe its qualitative features, as well as how to prevent it (or bring it about).

For this talk we assume calculus and some basic notions from physics, although some ideas from differential equations and linear algebra will be mentioned and explained.