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Assessing the dynamic performance of multilayer plates subjected to impulsive loading is of interest for identifying configurations that either absorb energy or transmit the energy in the transverse directions, thereby mitigating the through-thickness energy propagation. A reduced-order modeling approach is presented in this paper for rapidly evaluating the structural dynamic performance of various multilayer plate designs. The new approach is based on the reverberation matrix method (RMM) with the theory of generalized rays for fast analysis of the structural dynamic characteristics of multilayer plates. In the RMM model, the waves radiated from the dynamic load are reflected and refracted at each interface between layers, and the waves within each layer are transmitted with a phase lag. These two phenomena are represented by the global scattering matrix and the global phase matrix, respectively.

The goal of this work is to develop an efficient numerical modeling method for the vibration of hybrid electric vehicle (HEV) battery packs to support probabilistic forced response simulations and fatigue life predictions. There are two important sources of variations in HEV battery packs that affect their structural dynamic response. One source is the uncertain level of pre-stress due to bolts or welds used for joining cells within a pack. The other source is small structural variations among the cells of a battery pack. The structural dynamics of HEV battery packs are known to feature very high modal density in many frequency bands. That is because packs are composed of nominally identical cells. The high modal density combined with small, random structural variations among the cells can lead to drastic variations in the dynamic response compared with those of the ideal nominal system.