Mathematics Colloquium
Date:Lincoln NE 68508
Affiliation: Oregon State
Local Hosts: George Avalos and Daniel Toundykov
Title: Understanding Aerodynamic Flutter from Coupled Partial Differential Equations
Additional Public Info:
<b>Abstract</b>
An evolutionary partial differential equation (PDE) describes the time evolution of a phenomenon distributed in space. In this talk we describe various aspects of a PDE analysis of a pervasive model in aeroelasticity which describes the oscillations of a thin plate immersed in a flow of gas. The model comprises a “perturbed” wave equation for the potential flow in the half space coupled with a nonlinear plate equation on a portion of the boundary. One of the primary goals in the field of aeroelasticity is the prediction and suppression of an instability known as panel flutter, wherein the structure’s natural vibrational modes couple with the aerodynamic load.
As we move through the stages of analysis for this model, we will be careful to motivate and define fundamental notions in PDE. We will also discuss some of the primary concepts in the modern study of evolution equations, including semigroups, dynamical systems, and compact global attractors. Throughout the talk results will be presented which give the existence and uniqueness of semigroup solutions for this class of nonlinear flow-plate models. We will also discuss (1) the recently proved existence of a finite dimensional, compact global attractor for the asymptotic dynamics of the structure in the absence of any mechanical damping; (2) how the presence of damping in the structure ensures that trajectories converge to stationary states (in the case of subsonic flows); and (3) the physical interpretation of both (1) and (2) in the context of flutter prediction and suppression.
Refreshments will be served in 348 Avery, 3:30-4:00 PM. The talk is free and open to the public.