Purpose <p>A graphene platelets (GPLs)-reinforced aluminum matrix core, sandwiched between porous functionally graded material (FGM) face sheets is an innovative composite material presented in this paper. Consequently, the present study establishes as a result a theoretical analytical model that can be used to analyze its mechanical behavior, by evaluating the static bending and free vibration responses of the composite beam and assessing the influence of critical parameters, including porosity coefficient, porosity and GPLs distribution patterns, volume fraction index of FGM, GPLs weight fraction, and boundary conditions.</p> Methods <p>The equations of motion are formulated using Hamilton's principle within an innovative polynomial higher-order quasi-3D beam theory. This theory accounts for nonlinear transverse shear deformations and stresses, satisfying traction-free boundary conditions on the beam surfaces without requiring a shear correction factor. It also incorporates normal deformations, including thickness stretching effects. Analytical solutions are derived for the governing equations to investigate the static bending under simply supported conditions. However, the free vibration behavior are analyzed under various boundary conditions. Numerical examples are used to thoroughly explore the impact of the key parameters.</p> Conclusions <p>The proposed quasi-3D beam theory effectively predicts the static bending and free vibration behavior of the sandwich beams. The results provide valuable insights into the mechanical performance of the proposed composite structure, offering guidance for designing and optimizing such beams under varying conditions.</p>