Oberseminar Mathematik in den Naturwissenschaften: Justin T. Webster, Mathematical Aeroelasticity: Well-posedness and Long-time Behavior of Flow-Structure Interactions
| Date: | 07/03/2020, 3:00 PM - 5:00 PM |
| Category: | Seminar, Veranstaltung |
| Organizer: | Lehrstuhl für Mathematik VI (Mathematik in den Naturwissenschaften) |
| Speaker: | Justin T. Webster |
via Zoom video conference (request the Zoom link from anja.schloemerkemper@mathematik.uni-wuerzburg.de).
Abstract:
This talk focuses on the underlying mathematics of the aeroelastic phenomenon {\em flutter}---i.e., the way that an elastic structure may become unstable in the presence of an adjacent flow of air. Under certain circumstances, a feedback occurs between elastic deformations and pressure dynamics in the airflow, resulting in sustained oscillations. A canonical example was seen in the Tacoma Narrows bridge (Washington, USA), which collapsed in 1940 while fluttering in 65 kph winds. 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).
We will look at a variety of flow-structure interaction models which are partial differential equation systems coupled via an interface. After a brief discussion of relevant modeling, we will examine well-posedness and long-time behavior properties of PDE solutions for three different physical configurations that can exhibit aeroelastic flutter: (1) projectile paneling, (2) a bridge deck, (3) an elastic energy harvester. From a rigorous point of view, we attempt to capture the mechanism that gives rise to the flutter instability. Additionally, when flutter occurs, we attempt to describe its qualitative features through a dynamical systems approach, as well as how to prevent it or bring it about (stability).
