Dynamic response of large finite and non-symmetrical twodimensional periodic structures
Résumé
The study of two-dimensional periodic media (periodic along two directions), generally focuses on dispersion curves. For structures of reasonable sizes, for example with a few hundred substructures, it is also possible to calculate their response to external excitations by classical or improved finite element using model reductions such as the Craig-Bampton method. In this work, we determine their response for a large number of substructures. We base ourselves on the Wave Finite Element (WFE) method and extend it to the 2D case, by determining, on a single substructure, the propagation constants and wave modes along a direction for given propagation constants in the transverse direction. When the structure is symmetrical, a very efficient method has been developed using FFT calculations. Here, we extend it to the case of non-symmetrical structures, that is to say whose geometry and composition of a substructure can be arbitrary. Different examples are given for symmetrical and non-symmetrical structures with a large number of substructures.
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