Tuning of band structures in porous phononic crystals by grading design of cells

As the results of the evolution of species, grading structures widely exist in the nature and display distinguish advantages. In this manuscript, grading concept is introduced to redesign the topological structure of pores with the aim to see the effects of grading on the band structure in porous phononic crystals. Circular pores are considered and the crossing grading is made. The wave dispersion in graded structures is investigated comparatively to the normal ones under the same porosity. The band gaps in grading structures are given, as well as the vibration modes of the unit cell corresponding to the absolute band gap (ABG) edges. The results show that the grading structure greatly decreases the critical porosity for the opening of the ABGs. Wider ABGs could be obtained at lower frequencies along with the increase of the porosity. Through controlling the topological parameters of the grading structure, the band structure could be tuned. These results will provide an important guidance in the band tuning in porous phononic crystals by grading design of cells.