Stochastic reduced-order model for the dynamical analysis of complex structures with a high modal density

In this research, we are interested in predicting the dynamical response of complex structures characterized by the presence of numerous local elastic modes that appear immediatly in the low-frequency range. Where the modal analysis method would classically provide a small-dimension basis constituted of global displacements for the construction of a robust and accurate reduced-order model adapted to the case of a low modal density, it is not the case considered here. Unlike global displacements, the local displacements are very sensitive to both parameters uncertainties and model uncertainties induced by modeling errors. This paper presents an original methodology which allows us to separate the admissible displacements space into the two algebraically independent subspaces of global and local displacements. This global/local separation allows a separated nonparametric probabilistic model of uncertainties to be implemented and thus allows the variabilities of the global displacements and of the local displacements to be controlled separately.