Elastic stabilization of an intrinsically unstable hyperbolic flow–structure interaction on the 3D half-space
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Date
2023-03-13
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Citation of Original Publication
Balakrishna, Abhishek, Irena Lasiecka, and Justin T. Webster. “Elastic Stabilization of an Intrinsically Unstable Hyperbolic Flow–Structure Interaction on the 3D Half-Space.” Mathematical Models and Methods in Applied Sciences, March 13, 2023. https://doi.org/10.1142/S0218202523500124.
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Preprint of an article published in Mathematical Models and Methods in Applied SciencesVol. 33, No. 03, pp. 505-545. https://doi.org/10.1142/S0218202523500124 © 2023 World Scientific Publishing Co Pte Ltd. https://www.worldscientific.com/doi/epdf/10.1142/S0218202523500124
Subjects
Abstract
The strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wave-type equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airfoils, etc.) in engineering applications. Empirical observations indicate that the subsonic wave-plate system converges to equilibria. Classical approaches which decouple the plate and wave dynamics have fallen short. Here, we operate on the model as it appears in the engineering literature with no regularization and achieve stabilization by microlocalizing the Neumann boundary data for the wave equation (given through the plate dynamics). We observe a compensation by the plate dynamics precisely where the regularity of the 3D Neumann wave is compromised (in the characteristic sector).