Purpose <p>This study presents a comprehensive investigation into the free vibration characteristics of an advanced composite sandwich plate featuring a novel viscoelastic auxetic core and three-phase functionally graded face layers. The research aims to characterize the synergistic damping effects arising from the combination of negative Poisson's ratio (NPR) geometry and viscoelastic behavior.</p> Methods <p>The face layers consist of a three-phase functionally graded composite comprising graphene nanoplatelets (GPLs), graphite fibers, and polyimide matrix, with effective properties determined using the Halpin–Tsai micromechanical model. The auxetic core's structural properties are derived from Gibson's model, while its viscoelastic behavior is captured using the standard four-parameter Burger model. The governing equations are formulated based on Reddy's third-order shear deformation theory (TSDT) and solved using the Galerkin method.</p> Results <p>The parametric analysis shows that the viscoelastic auxetic (NPR) core significantly enhances damping performance, nearly doubling it compared to the conventional honeycomb configuration. The FG-VA distribution pattern yields the highest natural frequencies, while increased viscoelastic Burger model parameters substantially improve the plate’s loss factors. Additionally, an increase in the core-to-total thickness ratio and elastic foundation parameters also markedly increases the plate’s natural frequency.</p> Conclusion <p>The combined use of auxetic geometry and the viscoelastic Burger model, which represents the novelty of this study, results in significantly enhanced vibration damping compared to conventional sandwich lattice structures. This work establishes a foundation for designing high-performance sandwich structures with tailored dynamic properties for engineering applications.</p>