This study investigates the equivalent damping properties of gyroid-filled polylactic acid (PLA) components manufactured by fused filament fabrication (FFF) and their implementation in simplified finite element models. Specimens with nominal gyroid infill ratios from 20% to 80% were subjected to pulse excitation using an electrodynamic vibration exciter. The test sections contained only the gyroid infill structure, without outer perimeters or top/bottom solid layers, thereby limiting the influence of external shell features on the measured response. Damping ratios were identified from free-vibration responses using the logarithmic decrement method. The damping ratio decreased from 0.0548 at 20% infill to 0.0293 at 80% infill, while the corresponding natural frequency increased from 19.22 to 68.12 Hz. The identified damping parameters were implemented in a simplified finite element model in which the actual gyroid geometry was replaced by a homogeneous equivalent medium. Mass-proportional and stiffness-proportional Rayleigh damping formulations were considered separately and reproduced the measured global dynamic response with comparable accuracy. Within the investigated specimen set, the equivalent damping characteristics varied systematically with nominal infill ratio under the investigated manufacturing and testing conditions. Since only one specimen was manufactured for each infill ratio, the reported scatter reflects measurement repeatability rather than specimen-to-specimen manufacturing variability.