基于集中质量法的一维声子晶体弹性波带隙计算

Lumped-mass method on calculation of elastic band gaps of one-dimensional phononic crystals

通过将一维声子晶体中的原胞简化为有限多个自由度的弹簧振子结构 ,引入了一种基于集中质量法的一维声子晶体弹性波带隙计算方法 .与传统平面波展开法相比 ,该方法的计算结果与之相符合 ,而且在收敛性方面较之有很大改善 .通过使用集中质量法 ,可在得到同样计算精度的条件下 ,显著降低计算量 。

With each unit cell replaced by finite cascaded mass-spring oscillators, 1D phononic crystals (PCs) can be simplified to an infinite periodic mass-spring chain. Therefore, the elastic wave band structures of the 1D PCs can be calculated with a straightforward approach which we call lumped-mass method (LM). For comparison, the band structures of the same 1D PC calculated with this method and the well-known plane wave expansion method are both presented in this paper. The results of the two methods are in good agreement while the computation costs of LM method are much lower than that of PWE method.