This paper deals with the use of periodic cores in 3D printed bio-based sandwich beams to attenuate vibrations through band-gaps as well as investigating, by numerical approach, their material and structural characteristics. Harmonic analyses using the finite element method were performed on three 3D printed beams. One of them is solid while the two others are sandwich beams with different periodic core configurations. All three structures were primarily made from the same PLA/Flax short fiber composite filament using the fused deposition modelling (FDM) process, with the addition of viscoelastic elements inside the periodic cores of the sandwich beams. The two cores differ solely in the ratio of materials within their cells. Comparative analysis of the results for the solid and one of the sandwich structures has revealed several band-gaps where vibrations were significantly attenuated. Repeating the same analysis on the two sandwich beams with differing material ratios has demonstrated multiple changes in the band-gap characteristics, thus proving that they depend on at least one core parameter. This research could possibly help pave the way for more in-depth investigations into making use of band-gaps to attenuate vibrations.