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Multiple scattering theory allows for the computation of states and scattering fields on a diverse variety of wave systems. Through rigorous analysis, this theory provides insights into wave phenomena such as diffraction, reflection, and transmission, contributing to a comprehensive understanding of the intricate dynamics of classical systems. Our study focuses on flexural waves in thin elastic plates, with point-like mass spring resonators serving as scatterers attached the plate’s top surface. Finite clusters of scatterers will be analysed without imposing symmetries or periodicity in the system. Despite the apparent simplicity of this model, it proves capable of unveiling and predicting many behaviours related to the latest topics on metamaterials, including phononic crystals, quasicrystals, topological insulators, rainbow trapping effects or spatio-temporal modulation. In essence, this technique offers a foundation for advancements in materials science, structural engineering and all the domains where metamaterials and phononic crystals find application.
Torrent et al. (Fri,) studied this question.