Abstract
A new iterative method for the prediction of dynamic characteristics of coupled vibro-acoustic systems is presented in this study. The proposed method extracts the eigenvectors in a specified frequency band and it is similar in concept to the well-known eigenvalue solvers, such as the Lanczos method. At each iteration step a reduction subspace is built and the problem is projected onto this subspace which is built up from a combination of the so-called correction vectors and the uncoupled modes. The correction vectors are used to correct the starting uncoupled modes of the coupled physics. In the iterations, the uncoupled modes, correction vectors and frequencies are updated. Correction vectors are found by the use of an iterative solution method. Namely, the conjugate gradient method is used along with spectral expansion properties of the matrices to end up with an extremely efficient preconditioner. However, to save some computational cost, an iteration limit is used for the iterative solution process. These vectors are shown to enrich the reduction space in an iterative sense. Concerning the developed method, some test applications are provided.
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- 1.
This representation has an advantage for the forthcoming computations where the factorization of K s is often available from the structural eigenvalue solver.
- 2.
Note that strictly speaking, the CG is applicable only to symmetric definite systems, but in practice it is found that it can also be applied on symmetric non-definite problems as found here.
- 3.
In theory, orthogonalization in the CG is required only with respect to the two previous directions. However, in practice, one often uses orthogonalization with respect to all previous search directions due to the loss of orthogonality arising from finite precision arithmetic. Full orthogonalization is used in the present work.
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© 2012 The Society for Experimental Mechanics, Inc.
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Tabak, U., Rixen, D.J. (2012). A Spectrally Preconditioned Iterative Reduced Correction Algorithm for Vibro-acoustic Problems. In: Allemang, R., De Clerck, J., Niezrecki, C., Blough, J. (eds) Topics in Modal Analysis II, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2419-2_3
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DOI: https://doi.org/10.1007/978-1-4614-2419-2_3
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