Band structures based phononic crystals in quasi-Sierpinski fractals with defects

This study presents a detailed analysis of the effects of geometric defects in phononic crystals, focusing on the use of a distribution of Sierpinski fractals for the strategic placement of inclusions. Using theoretical and computational approaches, we investigate the influence of these defects on the material's band structure. Phononic crystals, designed based on fractal geometry inspired by the Sierpinski pattern, are particularly sensitive to the introduction of inclusions, resulting in disorder in the periodic structure. Our study examines in detail how different defect configurations affect the formation of localized modes and the energy distribution in the material's band structure. The results obtained provide valuable insights into how the presence of geometric defects can be exploited or minimized in the design of phononic crystals for practical applications, including acoustic isolation, vibration control, and the development of advanced acoustic devices. 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.