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.
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Giacomo Quaranta 1 ; Clara Argerich Martin 2 ; Ruben Ibañez 3 ; Jean Louis Duval 1 ; Elias Cueto 4 ; Francisco Chinesta 3
@article{CRMECA_2019__347_5_445_0,
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},
}
TY - JOUR 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 %A Giacomo Quaranta %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 %V 347 %N 5 %I Elsevier %R 10.1016/j.crme.2019.01.005 %G en %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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.01.005/
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