Multiple band gaps of phononic crystals with quasi-Sierpinski carpet unit cells

Abstract

This work investigated the dispersion curves of phononic crystals with quasi-Sierpinski carpet unit cells via improved plane wave expansion method. The position vector derivative method was applied to generate Sierpinski and quasi-Sierpinski carpet unit cells. Wave dispersion mechanisms of fractal phononic crystals were investigated by calculating the vibration modes of unit cells. The results show that (quasi-)fractal phononic crystals are benefit for obtaining multiple and wider band gaps, especially for the second stage case. For quasi-Sierpinski carpet unit cells, the multiple band gap feature becomes much more obvious due to the increase of the filling fraction. Numerical analysis of a finite quasi-fractal phononic crystal indicated the potential application of phononic crystals with quasi-Sierpinski carpet unit cells.