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The integration of mechanics-based analysis and materials design procedures has become central to the development of multi-material structures with tailored mechanical and dynamic performance. In this study, the dynamic and flexural behaviour of multi-material FDM sandwich beams composed of PETG face sheets and an ABS core is experimentally investigated. Seven different infill patterns Grid, Line, Wavy, Honeycomb, Gyroid, Cubic, and Triangle were implemented in the core layer to assess their influence on damping and natural frequency behaviour. Experimental modal analysis was performed using impact testing to identify the first three vibration modes. Natural frequencies were extracted from Frequency Response Functions (FRFs), and modal damping ratios were determined using the half-power bandwidth method. The reliability of the damping results was evaluated through statistical analysis. Additionally, quasi-static three-point bending tests were conducted to assess flexural strength and load-carrying capacity. The results demonstrate that infill topology has a significant impact on both dynamic and mechanical responses. In particular, geometrically complex infill patterns exhibit enhanced stiffness, higher natural frequencies, and improved damping performance. Among the investigated designs, the Triangle infill exhibited the highest natural frequency values across the first three vibration modes (<i>f</i><sub>1</sub> ≈ 24.910 Hz, <i>f</i><sub>2</sub> ≈ 162.609 Hz, <i>f</i> ≈ 466.595 Hz), indicating its superior stiffness characteristics. In terms of damping behaviour, the Cubic infill showed the highest loss factor in the first vibration mode (0.0426), while the Line and Gyroid patterns exhibited the highest damping in the second (0.0439) and third modes (0.0354), respectively. Moreover, the force-displacement results revealed that the Triangle infill exhibited the highest load-bearing capacity, further confirming its superior structural stiffness among the investigated designs (SEA = 110.83 J/kg). These findings highlight the potential of multi-material FDM for designing polymer-based sandwich structures with tailored vibration and energy dissipation characteristics.