Estudo sobre a propagação de ondas mecânicas no plano em cristais fonônicos bidimensionais segundo o carpete de Sierpinski

Abstract

Phononic crystals are artificial periodic structures that can be manufactured by using two or more materials with different mechanical properties. In addition, one can know the use of structures according fractal lattices have an enormous potential application, such as applications in acoustic filters, due to they present results that can not be obtained in regular crystals. The present work intends to numerically obtain the structure of mechanical wave bands and identify the frequency ranges where they are prohibited of propagating. For this, the COMSOL Multiphysics ® software was used, where bidimensional crystalline lattices with fractal geometry were modeled according to the square Sierpinski Carpet and analyzed as three first generations of this fractal. We consider two systems, one consisting of square cylinders of lead (Pb) in a matrix and epoxy; and a second system composed of square cylinders of quartz (SiO 2 ) also embedded in an epoxy matrix. By means of dispersion curves of wave mechanics on these systems, the influence of the constituent materials and generations of the fractal were analyzed and, later, comparisons were made in the effects of the generation systems and forbidden bands between the studied systems and their possible applications.