×

Building a suited reduced modal basis for updating 3D acoustic models with the constitutive law error method. (English) Zbl 1173.76336

Summary: We have recently reported the possibility of developing an updating technique for acoustic finite element models based on the constitutive law error proposed by P. Ladevèze and co-workers in structural dynamics. Like with every updating technique, we are confronted with and interested in reducing the computational time. The main idea of this paper consists in building a reduced modal basis made of two contributions: static modes complete a truncated modal basis corresponding to the frequency range of computation. The static modes are associated to the system excitation (for instance a normal velocity boundary condition), but also to the system damping and to the reference measurements.
Updating acoustic models using the reduced modal basis shows a significant CPU-time saving with respect to the full non reduced system with an acceptable accuracy.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Balmès, E., Parametric families of reduced finite element models, theory and applications, Mech. Syst. Signal Process., 10, 4, 381-394 (1996)
[2] E. Balmès, Efficient sensitivity analysis based on finite element model reduction, in: Proc. IMAC XVII, SEM, Santa Barbara, CA, 1998.; E. Balmès, Efficient sensitivity analysis based on finite element model reduction, in: Proc. IMAC XVII, SEM, Santa Barbara, CA, 1998.
[3] A. Bobillot, E. Balmès, Solving minimum dynamic residual expansion and using results for error localisation, in: Proc. IMAC XIX, SEM, Kissimee, FL, 2001.; A. Bobillot, E. Balmès, Solving minimum dynamic residual expansion and using results for error localisation, in: Proc. IMAC XIX, SEM, Kissimee, FL, 2001.
[4] Bouazzouni, A.; Lallement, G.; Cogan, S., Selecting a Ritz basis for the reanalysis of the frequency response functions of modified structures, J. Sound Vibr., 2, 309-322 (1997)
[5] Bui, Z., Krylov subspace techniques for reduced order modelling of large-scale dynamical systems, Appl. Numer. Math., 43, 9-44 (2002)
[6] Burnett, D. S., A three-dimensional acoustic finite element based on a prolate spheroidal multipole expansion, J. Acoust. Soc. Am., 96, 2798-2816 (1994)
[7] Decouvreur, V.; Bouillard, P.; Deraemaeker, A.; Ladevèze, P., Updating 2D acoustic models with the constitutive relation error, J. Sound Vibr., 278, 4/5, 773-787 (2004)
[8] Deraemaeker, A.; Ladevèze, P.; Leconte, P., Reduced bases for model updating in structural dynamics based on constitutive relation error, CMAME, 191, 21-22 (2002) · Zbl 1131.74310
[9] Deraemaeker, A.; Ladevèze, P.; Romeuf, T., Model validation in the presence of uncertain experimental data, Engrg. Comput., 21-8, 808-833 (2004) · Zbl 1134.65304
[10] Freund, R. W., Krylov-subspace methods for reduced order modelling in circuit simulation, J. Comput. Appl. Math., 123, 395-421 (2000) · Zbl 0964.65082
[11] Ladevèze, P., A modelling error estimator for dynamic model updating, (New Advances in Adaptive Computational Methods in Mechanics (1998), Elsevier), pp. 135-151
[12] Qu, Z., Accurate methods for frequency responses and their sensitivities of proportionally damped systems, Comput. Struct., 79, 87-96 (2001)
[13] Rohl, P.; Reese, G., Salinas – an implicit finite element structural dynamics code developed for massively parallel platforms, Am. Instit. Aeronaut. Astronaut., 1651-1660 (2000)
[14] Tournour, M.; Atalla, N., Efficient evaluation of the acoustic radiation using multipole expansion, Int. J. Num. Meth. Engrg., 46, 6, 825-837 (1999) · Zbl 1041.76548
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.