Revisiting the Jones eigenproblem in fluid-structure interaction. (English) Zbl 1482.65208
This paper studies, theoretically and computationally, the Jones eigenvalue problem in Lipschitz domains. In the context of the previous result that rules out any Jones mode in most \(C^\infty\) domains and the intuition that the boundary condition may require the domain to possess significant geometric symmetries, the authors show that Jones modes do exist in a broad class of domains, i.e. Lipschitz domains. Exact Jones eigenmodes on rectangles are given. A conforming discretization of the continuous eigenvalue problem via Lagrange finite elements is proposed, analyzed, and implemented.
Reviewer: Yanlai Chen (North Dartmouth)
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Software:
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