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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Justin Webster
UMBC
Title: Damping and Exponential Attractors in Panel Flutter Models

Abstract: Recent studies of flutter (a self-excitation instability for a flexible structure immersed in a fluid flow) have led to interesting problems in the study of long-time behavior of nonlinear dynamical systems. The panel flutter model involves an extensible nonlinear plate (von Karman or Berger) embedded in the plane (clamped boundary conditions), coupled to a perturbed wave equation on upper half-space. In certain flow regimes (e.g., for large flow velocities) the full model can be rigorously reduced to a plate equation with a memory term, or, in an ad hoc fashion, reduced to a simple non-dissipative plate equation (so called "piston-theory").

In this talk we discuss these fluttering panel models. In the case of a piston-theoretic plate, we present recent results on the existence of smooth and finite dimensional global attractors for these flutter models in the absence of imposed damping. We utilize the recent quasi-stability theory, and discuss how it also yields fractal exponential attractors. In the case of Berger's plate model, we show that "large" frictional damping actually results in smooth exponential attractor via a novel decomposition of the nonlinear dynamics.

Recording: http://mm.math.cmu.edu/recordings/cna/justin_webster_small.mp4
Date: Tuesday, April 3, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice