When a thin elastic structure is immersed in a fluid flow, certain conditions may bring about excitations in the structure. That is, dynamic fluid loading feeds back with the natural modes of the structure. In this case oscillatory behavior may persist until the flow parameters change or energy is dissipated from the system. This interactive phenomenon is referred to as flutter.
Beyond the obvious applications in aeroscience (paneling, flaps, flags, and airfoils), the flutter phenomenon arises in: (i) the biomedical realm (snoring and sleep apnea), and (ii) sustainable energies (piezoelastic energy harvesters). 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., monotone operator theory, the theory of global attractors). We will relate these results back to experimental results in engineering and recent numerical work. We will also describe very recent problems in the analysis of axial flow configurations, where a portion of the structure is unsupported (e.g., a flag).