Fig. 4.

(A) A montage of high-speed photographs showing the balls on the $z-x$ plane located on the $y=0$ surface of the box. The photographs show images over one vibration cycle (after steady state) of the box with an amplitude $a=2 \text{mm}$ at ƒ = 20 Hz and 90 Hz. Each image is labeled by a nondimensional time $\overline{t}=tf$, where the time $t=0$ at the start of the cycle. For reference, we show the height of the stationary assembly by a black solid line and the height of the assembly during steady-state vibration by a solid red line. The increase in height $\mathrm{\Delta }H$ of the assembly is indicated in the 90 Hz case. (B) Sketch illustrating the mechanism of the formation of the gap between the walls of the box due to the fluidization of the balls for vibration at ƒ = 90 Hz. We illustrate both the transient state (prior to the assembly attaining a steady state) and the associated flow of the balls over the top surface of the assembly resulting in the increase in height $\mathrm{\Delta }H$ as well as the steady state where the gap alternate sides. The markings (I) and (II) correlate with the 90 Hz images in (A).