Effect of density homogeneity on the dynamic response of powder beds

Homogeneous and inhomogeneous powder beds subjected to low-magnitude vibration are compared in terms of the dynamic response. The inhomogeneous samples were segregated into two phases: loose and dense phases, layering the two phases horizontally or vertically. An apparent mass, defined as a ratio of the base force to base acceleration, was measured. Comparison of homogeneous and segregated data demonstrated a significant density gradient dependence on the apparent mass data. First, homogeneous systems showed a resonant peak, which gave the longitudinal elastic modulus of the bed via the velocity of longitudinal stress wave propagation. Second, vertically segregated systems exhibited two significant peaks at low frequencies, corresponding to the resonance of each phase. In addition, the apparent mass values at the two peaks were related to the quantity of each phase. Third, horizontally segregated systems exhibited a resonant peak, whose frequency was approximately equal to homogeneous data, but the apparent mass value at the peak differed from homogeneous data. A model based on the fourth-power scaling law, two-phase theory and Rayleigh's energy method gave an interpretation for the insensitivity of the peak frequency to the density gradient in the vertical direction.