基于波传播法的一维声子晶体禁带

FORBIDDEN BAND GAPS OF ONE-DIMENSIONAL PHONONIC CRYSTALS BASED ON WAVE PROPAGATION METHOD

提出用波传播法(Wave propagation method,WPM)来研究一维声子晶体的禁带特性,并将该方法与平面波展开法(Plane wave expansion,PWE)进行比较,发现PWE随着波数的增加而逐渐收敛于WPM的结果。将WPM应用于一维二元和一维四元声子晶体禁带特性的计算中,在相同计算精度下WPM的计算时间大约为PWE的1/50和1/100。当考虑到粘弹性材料的频变特性时,WPM能直接得到声子晶体的禁带特性,在相同的计算精度下WPM的计算量大约要比经过迭代改进的PWE的计算量小两个数量级。

Using the wave propagation method （WPM）, the forbidden band gaps of one-dimensional phononic crystals are studied. Results obtained using the method are evaluated against those by plane wave expansion （PWE）. It shows that the results of PWE are close to those of WPM with an increasing of the wave number of PWE. Under the condition of the same computational accuracy, the computing time of WPM is about one fiftieth of that of WPE in the research of the forbidden band gaps in one-dimensional binary phononic crystals, and one hundredth in one-dimensional quaternary phononic crystals. Considering the changing of elastic constants with fi＇equency of viscoelastic material, the forbidden band gaps can be obtained directly, and the computing time of WPM is about two orders of magnitude lower than that of PWE improved using iterative method.