Applied Mathematics Colloquium: Dr. Justin Webster

Title: Aeroelastic Flutter: The Waltz of Wave and Plate Dynamics

When a thin elastic structure is immersed in a fluid flow, certain conditions may bring about excitations in the structure. That is, the dynamic loading of the fluid feeds back with the natural oscillatory modes of the structure. In this case we have a bounded-response instability, and the oscillatory behavior may persist until the flow velocity changes or energy is dissipated from the structure. This interactive phenomenon is referred to as flutter. Beyond the obvious applications in aeroscience (projectile paneling and flaps, flags, and airfoils), the flutter phenomenon arises in: (i) the biomedical realm (in treating sleep apnea), and (ii) sustainable energies (in providing a low-cost power generating mechanisms). Modeling, predicting, and controlling flutter have been a foremost problems in engineering for nearly 70 years.

In this talk we describe the basics of modeling flutter in the simplest configuration (an aircraft panel) using differential equations and dynamical systems. After discussing the partial differential equation model, we will discuss theorems that can be proved about solutions to these equations using modern analysis (e.g., nonlinear functional analysis, semigroups, monotone operator theory, the theory of global attractors, elliptic theory). We will relate these results back to experimental results in engineering and recent numerical work. We will also describe very recent (and very open) problems in the analysis of wing and flag configurations, where a portion of the structure is unsupported.