Several industrial and fundamental studies focus on the consolidation of granular materials as this covers many technological fields. When a granular material is shaken, it densifies. The energy needed to compact or decompact a powder column is of great interest in handling, filling and transport operations. This work studies the dynamic behaviour of four industrial granular materials–wheat flour, sericite, microcrystalline cellulose and glass beads–when submitted to vertical vibration using a particle damper. The effect of the vibration wave was studied by varying two dimensionless parameters: the relative acceleration, Γ and relative frequency, Ω including the relaxation time between periods. Our results show that despite the cohesiveness of the samples, their compaction dynamics occurs in at least two-compaction steps that a succession of stretched exponentials can model, denoted herein as a generalised KWW model. Also the absence of a relaxation time between periods leads to fluidisation during the first periods of vibration.The Fluidisation phenomena–the convective movement, granular jets, bubbling and slugging–appear to enhance particle reorganisation giving rise to higher packing fractions depending on the nature of the grains and operational conditions. A classification of the observed behaviours is proposed and related to the compaction kinetics.