Abstract
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The goal of the paper is threefold: (i) to provide an accurate review of recent resultson existence, uniqueness, and stability of weak solutions, (ii) to present a construction of finite dimensional, attracting setscorresponding to the structural dynamics and discuss convergence of trajectories, and (iii) to state several open questions associated with the topic. This second task is based on a decoupling technique which reduces the analysis of the full flow-structure system to aPDE system with delay.
Highlights
Flow-structure models have attracted considerable attention in the past mathematical literature, see, e.g., [2, 3, 4, 9, 10, 11, 17, 22, 23, 36, 59, 72] and the references therein
3.2.3 Discussion of Well-posedness Results for the Subsonic Case taken with the KuttaJoukowsky Flow Conditions
Some aspects of both the subsonic and supersonic analyses discussed in the previous theorems appear in the analysis of the case of subsonic flows with the K-J flow condition
Summary
Flow-structure models have attracted considerable attention in the past mathematical literature, see, e.g., [2, 3, 4, 9, 10, 11, 17, 22, 23, 36, 59, 72] and the references therein. The study of linear models wherein the two dimensional dynamics are reduced (typical section) to a one dimensional structure (beam, or panel with constant width which is infinitely extended in one direction) with Kutta-Joukowsky flow boundary conditions have enjoyed renewed interest, and have been extensively pursued in [3, 65, 66]. This line of work has focused on spectral properties of the system, with particular emphasis on identifying aeroelastic eigenmodes corresponding to the associated Possio integral equation
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