A substructure approach for the midfrequency vibration of stochastic systems

A novel substructure coupling technique based on the proper orthogonal decomposition method is presented for the midfrequency range vibration of linear dynamical systems with parameter uncertainty. For a given frequency band, the methodology permits the derivation of an adaptive basis for each subsystem and the construction of a reduced-order model of the global structure. The formulation is directed toward the efficient probabilistic characterization of model-based predictions in the framework of a stochastic finite element method. The efficiency of the substructure method has been contrasted both from the viewpoint of adopting free-free and fixed-fixed substructure proper orthogonal modes in order to arrive at a reduced subsystem model. The distinction as well as similarity of the present methodology with the component mode synthesis is also pointed out The proper orthogonal modes are obtained from both frequency- and time-domain approaches, and their suitability is discussed in relation to the behavior of a specific system. The substructure approach elegantly integrates with a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes.