https://hal-upec-upem.archives-ouvertes.fr/hal-00692835Batou, AnasAnasBatouMSME - Laboratoire de Modélisation et Simulation Multi Echelle - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche ScientifiqueSoize, ChristianChristianSoizeMSME - Laboratoire de Modélisation et Simulation Multi Echelle - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche ScientifiqueStochastic reduced-order model in low frequency dynamics in presence of numerous local elastic modesHAL CCSD2010uncertainty quantificationlocal modesspatial filteringreduced order modelROMnonparametric probabilistic methodstructural dynamics[SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph][MATH.MATH-PR] Mathematics [math]/Probability [math.PR][MATH.MATH-ST] Mathematics [math]/Statistics [math.ST][SPI.MECA.VIBR] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph]Soize, ChristianUniversity of Southampton2012-05-01 15:14:452022-01-15 04:04:352012-05-02 13:07:30enConference papersapplication/pdf1This paper concerns the non usual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. The "global elastic modes" and the "local elastic modes" are calculated separately using a new formulation solving two generalized eigenvalue problems. The union of these two families constitutes a basis of the admissible space. Then, the reduced-order model is constructed by projection of the dynamical equation on the global elastic modes. The apparent damping generated in this reduced-order model by the power flow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach. The theory is presented and is validated through an application.