Stochastic reduced-order model for dynamical structures having numerous local elastic modes in the low-frequency range

We propose a method to construct 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 powerflow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach