关键词： 声子晶体, 平面波展开法, 带隙, 密度比

Abstract: Starting from elastic wave equation,plane wave expansion method is used to calculate the band structure of two-dimensional(three-dimensional) phononic crystals.The dependence of the lowest bandgap on the density ratio of scatterer to host is discussed.The authors obtain the variation principle of the bandgap’s width and bandgap’s boundary with the variety of the density ratio.Numerical results show that the frequency of the bandgap’s lower boundary becomes small,while the upper boundary becomes big as the density ratio increases.So the width of the lowest bandgap increases，and energy level of the lowest bandgap is invariable.

Key words: phononic crystal, plane wave expansion method, bandgap, density ratio