Comptes Rendus
no. 7
Model reduction, data-based and advanced discretization in computational mechanics
Advanced parametric space-frequency separated representations in structural dynamics: A harmonic–modal hybrid approach
Muhammad Haris Malik1  ; Domenico Borzacchiello2 ; Jose Vicente Aguado2 ; Francisco Chinesta3
1 Department of Mechanical Engineering, DHA Suffa University Off Khayaban-e-Tufail, Phase VII(Ext) DHA, Karachi-75500, Pakistan
2 ICI – Institut de calcul intensif & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, 44300 Nantes, France
3 PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France
Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 590-602.

This paper is concerned with the solution to structural dynamics equations. The technique here presented is closely related to Harmonic Analysis, and therefore it is only concerned with the long-term forced response. Proper Generalized Decomposition (PGD) is used to compute space-frequency separated representations by considering the frequency as an extra coordinate. This formulation constitutes an alternative to classical methods such as Modal Analysis and it is especially advantageous when parametrized structural dynamics equations are of interest. In such case, there is no need to solve the parametrized eigenvalue problem and the space-time solution can be recovered with a Fourier inverse transform. The PGD solution is valid for any forcing term that can be written as a combination of the considered frequencies. Finally, the solution is available for any value of the parameter. When the problem involves frequency-dependent parameters the proposed technique provides a specially suitable method that becomes computationally more efficient when it is combined with a modal representation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.04.005
Mots-clés : Proper Generalized Decomposition, Frequency-dependent parametric models, Harmonic analysis, Modal analysis, Dynamics

Muhammad Haris Malik 1 ; Domenico Borzacchiello 2 ; Jose Vicente Aguado 2 ; Francisco Chinesta 3

1 Department of Mechanical Engineering, DHA Suffa University Off Khayaban-e-Tufail, Phase VII(Ext) DHA, Karachi-75500, Pakistan
2 ICI – Institut de calcul intensif & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, 44300 Nantes, France
3 PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France 
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Muhammad Haris Malik; Domenico Borzacchiello; Jose Vicente Aguado; Francisco Chinesta. Advanced parametric space-frequency separated representations in structural dynamics: A harmonic–modal hybrid approach. Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 590-602. doi : 10.1016/j.crme.2018.04.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.005/

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