中文摘要：

垂直地为 2D 的像波浪的运动基于簇模型我们以前建立了的颤动的小粒的系统(下巴 Phys Lett， 2010， 27：124501 ) ，为 3D 的簇模型的归纳小粒的系统在这份报纸被介绍。3D 簇模型建议是的金字塔的平截头体 3D 聚类小粒的系统，并且作为簇边界和簇板碰撞的结果解释波浪模式。由在一个碰撞时期分析一簇的运动，我们导出一个基本方程，它联系内部典型参数到外部开车参数。理论结果在开车参数，和 3D 分散关系作为变化复制波浪模式的行为，它同意试验性的结果。

英文摘要：

Based on the cluster model for wave-like motions of a 2D vertically vibrated granular system we established previously （Chin Phys Lett, 2010, 27： 124501）, a generalization of the cluster model for a 3D granular system is presented in this paper. The 3D cluster model proposes frustums of pyramids as clusters of the 3D granular system, and explains wave patterns as the result of the cluster- boundary and cluster-plate collisions. By analyzing the movement of one cluster in a collision period, we derive a basic equation, which relates the internal characteristic parameter to the external driving parameters. The theoretical results reproduce the behaviors of wave patterns as changes in the driving parameters, and the 3D dispersion relation, which agree with the experimental results.