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A comparison of one- and two-sided Krylov-Arnoldi projection methods for fully coupled, damped structural-acoustic analysis. (English) Zbl 1360.70032

Summary: The two-sided second-order Arnoldi algorithm is used to generate a reduced order model of two test cases of fully coupled, acoustic interior cavities, backed by flexible structural systems with damping. The reduced order model is obtained by applying a Galerkin-Petrov projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving the low frequency moments of the coupled system. The basis vectors for projection are computed efficiently using a two-sided second-order Arnoldi algorithm, which generates an orthogonal basis for the second-order Krylov subspace containing moments of the original higher dimensional system. The first model is an ABAQUS benchmark problem: a 2D, point loaded, water filled cavity. The second model is a cylindrical air-filled cavity, with clamped ends and a load normal to its curved surface. The computational efficiency, error and convergence are analyzed, and the two-sided second-order Arnoldi method shows better efficiency and performance than the one-sided Arnoldi technique, whilst also preserving the second-order structure of the original problem.

MSC:

70J50 Systems arising from the discretization of structural vibration problems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
74S05 Finite element methods applied to problems in solid mechanics
76M10 Finite element methods applied to problems in fluid mechanics

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References:

[1] DOI: 10.1016/0022-460X(71)90408-1 · doi:10.1016/0022-460X(71)90408-1
[2] DOI: 10.1016/S0022-460X(73)80243-3 · doi:10.1016/S0022-460X(73)80243-3
[3] DOI: 10.1007/BF03041465 · Zbl 1099.74538 · doi:10.1007/BF03041465
[4] DOI: 10.1007/s00158-010-0588-5 · Zbl 1274.74450 · doi:10.1007/s00158-010-0588-5
[5] DOI: 10.1016/j.apm.2009.02.016 · Zbl 1205.74037 · doi:10.1016/j.apm.2009.02.016
[6] DOI: 10.1007/3-540-27909-1_7 · doi:10.1007/3-540-27909-1_7
[7] DOI: 10.1017/S0962492902000120 · Zbl 1046.65021 · doi:10.1017/S0962492902000120
[8] DOI: 10.2514/3.20636 · doi:10.2514/3.20636
[9] DOI: 10.1137/040605552 · Zbl 1078.65058 · doi:10.1137/040605552
[10] DOI: 10.1137/S0895479803438523 · Zbl 1080.65024 · doi:10.1137/S0895479803438523
[11] DOI: 10.1007/11558958_41 · doi:10.1007/11558958_41
[12] DOI: 10.1088/0960-1317/15/3/002 · doi:10.1088/0960-1317/15/3/002
[13] DOI: 10.1016/S0003-682X(98)00070-X · doi:10.1016/S0003-682X(98)00070-X
[14] DOI: 10.1121/1.428624 · doi:10.1121/1.428624
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