The packing densification of trilobes in rectangular containers of varying aspect ratios is systematically investigated using a geometrically exact contact detection algorithm combined with the multi-sphere method. Packing structures are analyzed in terms of overall density, spatial packing density distribution, radial distribution function, and densification mechanisms. Under mechanical vibration, two preferential particle orientations are identified. At low vibration amplitudes, spatial confinement in the bottom layer restricts rearrangement of trilobes, resulting in partial vertical alignment while many particles remain parallel to the container base. At higher amplitudes, increased mobility facilitates extensive reorientation and structural reconfiguration of trilobes, allowing nearly all trilobes near the bottom aligning vertically. In rectangular containers, trilobes predominantly adopt orientations either parallel or perpendicular to the container base, forming granular beds composed of ordered clusters of distinct orientations. The crystallization process is prohibited by the joint effects of the two distinct preferential orientations and the strong interlockings between trilobed particles and a random close packing of trilobed particles is formed in the containers. Notably, the overall packing density is not determined by the degree of crystallization but by the spatial arrangements of clusters of distinct orientations which is not sensitive to the geometry of the rectangular containers; granular beds consisting of ordered clusters with relatively low nematic order parameters can achieve higher global packing densities.
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