Investigation of Band Structures for Different Lattice Types in Sierpinski Phononic Fractal Crystals with Local ResonanceInvestigation of Band Structures for Different Lattice Types in Sierpinski Phononic Fractal Crystals with Local Resonance

Resumo

This article presents an analysis of the band properties and forced response in phononic crystals that use fractal structures, focusing on square and triangular Brillouin lattices. Initially, we describe the construction of phononic crystals based on fractals, using fractal patterns such as the Sierpinski set or quasi-Sierpinski. Thesefractal structures allow the creation of complex and branched arrangements at different scales, resulting in different properties. Different types of Brillouin networks will be used to analyze and verify the influences on the band structures of phononic crystals. Furthermore, we examine the forced response of phononic crystals, analyzing how these structures react when subjected to external excitations. Using the finite element method, we obtained
the forced responses, revealing the resonance modes and attenuation characteristics at different frequencies. This study highlights the importance of fractal structures in manipulating the acoustic properties of phononic crystals. The analysis of the band structures and forced response offers valuable insights for the development of phononic devices with applications in acoustic insulation, frequency selective transmission and other related areas. These results contribute to the understanding and advancement of fractal phononic crystals, paving the way for future research and promising technological applications, both in terms of frequency and attenuation, depending on the complexity and hierarchy of the fractal structures used.