A global/local approach for stochastic reduced-order modeling in low- and mid-frequency structural dynamics

International audience; The research addressed here concerns the construction of a stochastic reduced-order model for complex structure exhibiting many local and some global eigenmodes in the mid-frequency range but also in the low-frequency range. The methodology proposed here consists in splitting the admissible displacement space into two subspaces: a global displacement space and a local displacement space. The bases of these two subspaces are constructed by solving two separated eigenvalue problems for which the kinetic energy is modified in order to filter the local or global contributions for the displacements. This modification of the kinetic energy is performed by constructing adapted projection operators. Then the reduced-order model can be constructed by truncating and concatenating the global and local bases. The system-parameters uncertainties and the modeling uncertainties are taken into account using a nonparametric probabilistic approach. The global/local separation allows for constructing a probabilistic model for which the fluctuations of the global displacements and the fluctuations of the local displacements can be controlled separately. The methodology is validated through a numerical application related to the complex computational model of an automotive vehicle. Several families of projection operators are constructed and compared with respect to (1) the size the reduced-order model and (2) the effectiveness of the global/local separation.[1]C. Soize, A. Batou, Stochastic reduced-order model in low-frequency dynamics in presence of numerous local elastic modes, Journal of Applied Mechanics - Transactions of the ASME, 78(6) :061003 (2011).