The study presents an experimental and analytical investigation of foamed polyurethane viscoelastic materials with varying density and pore structures, focusing on their dynamic mechanical behavior relevant for vibration damping applications. Samples with distinct pore configurations (open, closed, and combined) and varying densities (165–380 kg/m3) were subjected to resonance-based dynamic tests under static loads of 2, 5, and 10 kPa. The dynamic modulus of elasticity and damping characteristics, including loss factor, fractional damping parameters, and relaxation times, were determined. Results indicated that damping properties are strongly influenced by material density and internal pore structure, with closed-pore materials exhibiting lower damping capacities compared to materials with open or combined pores. A Fractional Standard Linear Solid (FSLS) model was effectively utilized to characterize the observed nonlinear viscoelastic behaviors, successfully correlating experimental data through parameter identification methods. The findings confirm that increased density generally enhances the dynamic modulus while reducing damping capacity, whereas pore structure significantly affects the material's dynamic response. These insights validate fractional derivative models as efficient predictive tools, facilitating the optimized design of viscoelastic isolation systems for engineering structures.