We investigated the dynamic properties of a two-section composite chain of beads under vertical vibration.By analyzing the chain's motion,including phase-shift,mean dilation,center-of-mass displacement,and energy,we found that with different bead arrangements,the chain behaved in different ways.We believe that interaction existing at the interface between bead sections provides the underlying cause.This interaction causes different energy in different arrangements,which leads to different dynamic characteristics.
We report the formation and transportation of granular heaps in vertically vibrated containers with two types of periodic corrugated bottoms: one with a periodic array of ten identical plexiglas rectangles mounted (named the periodic container), and the other with a single-step (named the single-step con-tainer). For the periodic container, when the excitation was weaker, several small heaps formed, and the number of them was the same as that of the rectangles on the bottom. As the excitation increased, the system presented three types of states: single well-defined heap, weaker wave, and stronger wave. Some local convections were observed in the interior of heap. For the single-step container, we ob-served the transportation of a heap toward step. We propose that the compressive force from the am-bient gas plays a crucial role in the movement of the heap.
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.
