Journal
COMPTES RENDUS MECANIQUE
Volume 347, Issue 5, Pages 445-454Publisher
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/j.crme.2019.01.005
Keywords
Linear and nonlinear parametric dynamics; Proper Generalized Decomposition; Harmonic analysis; Modal analysis; Low frequency domain
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Funding
- Spanish Ministry of Economy and Competitiveness [DPI2017-85139-C2-1-R, DPI2015-72365-EXP]
- Regional Government of Aragon
- European Social Fund [T24 17R]
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant [675919]
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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. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS.
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