Comptes Rendus
From linear to nonlinear PGD-based parametric structural dynamics
Comptes Rendus. Mécanique, Volume 347 (2019) no. 5, pp. 445-454.

The present paper analyzes different integration schemes of solid dynamics in the frequency domain involving the so-called Proper Generalized Decomposition – PGD. The last framework assumes for the solution a parametric dependency with respect to frequency. This procedure allowed introducing other parametric dependences related to loading, geometry, and material properties. However, in these cases, affine decompositions are required for an efficient computation of separated representations. A possibility for circumventing such difficulty consists in combining modal and harmonic analysis for defining an hybrid integration scheme. Moreover, such a procedure, as proved in the present work, can be easily generalized to address nonlinear parametric dynamics, as well as to solve problems with non-symmetric stiffness matrices, always operating in the domain of low frequencies.

Published online:
DOI: 10.1016/j.crme.2019.01.005
Keywords: Linear and nonlinear parametric dynamics, Proper Generalized Decomposition, Harmonic analysis, Modal analysis, Low frequency domain

Giacomo Quaranta 1; Clara Argerich Martin 2; Ruben Ibañez 3; Jean Louis Duval 1; Elias Cueto 4; Francisco Chinesta 3

1 ESI GROUP, 99, rue des Solets, 94513 Rungis cedex, France
2 GeM, École centrale de Nantes, 1, rue de la Noe, 44321 Nantes cedex 3, France
3 ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France
4 Aragon Institute of Engineering Research, Universidad de Zaragoza, Edificio Betancourt, Maria de Luna, s.n., 50018 Zaragoza, Spain
     author = {Giacomo Quaranta and Clara Argerich Martin and Ruben Iba\~nez and Jean Louis Duval and Elias Cueto and Francisco Chinesta},
     title = {From linear to nonlinear {PGD-based} parametric structural dynamics},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {445--454},
     publisher = {Elsevier},
     volume = {347},
     number = {5},
     year = {2019},
     doi = {10.1016/j.crme.2019.01.005},
     language = {en},
AU  - Giacomo Quaranta
AU  - Clara Argerich Martin
AU  - Ruben Ibañez
AU  - Jean Louis Duval
AU  - Elias Cueto
AU  - Francisco Chinesta
TI  - From linear to nonlinear PGD-based parametric structural dynamics
JO  - Comptes Rendus. Mécanique
PY  - 2019
SP  - 445
EP  - 454
VL  - 347
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crme.2019.01.005
LA  - en
ID  - CRMECA_2019__347_5_445_0
ER  - 
%0 Journal Article
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%A Clara Argerich Martin
%A Ruben Ibañez
%A Jean Louis Duval
%A Elias Cueto
%A Francisco Chinesta
%T From linear to nonlinear PGD-based parametric structural dynamics
%J Comptes Rendus. Mécanique
%D 2019
%P 445-454
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%N 5
%I Elsevier
%R 10.1016/j.crme.2019.01.005
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%F CRMECA_2019__347_5_445_0
Giacomo Quaranta; Clara Argerich Martin; Ruben Ibañez; Jean Louis Duval; Elias Cueto; Francisco Chinesta. From linear to nonlinear PGD-based parametric structural dynamics. Comptes Rendus. Mécanique, Volume 347 (2019) no. 5, pp. 445-454. doi : 10.1016/j.crme.2019.01.005.

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