中文摘要：

相位常数面可以描述特定频率、特定结构中波的传播方向及传播区域．将相位常数面这一分析方法应用于薄板状周期栅格结构中弹性波传播特性的研究，采用集中质量法计算了周期栅格结构的相位常数面，得到了直观的三维能带结构图．相位常数面可以用二维等高线图描述，通过计算等高线上每一点的法线方向，得到了在特定通带频率下弹性波的传播方向及传播区域．这些研究对于通带频率范围内的弹性波传播特性具有重要意义．

英文摘要：

The characteristics of wave propagation in laminated grid structure are analyzed using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in this grid structure for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are also validated with the calculated harmonic responses of a finite two-dimensional grid structure with 15 × 15 unit cells.