Stochastic Reduced-ordermodel for Dynamical Structureswith High Modal Density in the Low-frequency Range

The problem considered here concerns the construction of a stochastic reduced-order model for dynamical structures having a high modal density in the low frequency range. The classical methods used for the low-frequency range to construct a reduced-order model are not adapted in this case. We then use a recently proposed method which consists in constructing a basis of the global displacements and a basis of the local displacements by solving two separate eigenvalue problems. We then construct a stochastic reduced-order model using the basis of the global displacements and the contribution of the local displacements is taken into account using a probabilistic approach. The theory is presented and is applied to tube bundles structures which is are quasi-periodic structures for which the dynamical response is characterized by ensemble (global) displacements and more local displacements.