<p>This study presents an integrated approach to investigate the free vibration characteristics of variable-thickness, seamless, hinge-folded trapezoidal sandwich panels with magneto-electro-elastic face sheets and a functionally graded graphene platelet-reinforced composite core. The design leverages the excellent mechanical strength, high electrical conductivity, and lightweight properties of graphene, while considering multi-field coupling effects among elastic, thermal, electrical, and magnetic fields. The incorporation of hinge mechanisms significantly enhances structural flexibility and adaptability, enabling position-specific morphing under different operational conditions, thereby optimizing stress distribution and improving reliability. An enhanced Halpin-Tsai method is employed to accurately characterize composite material properties. Nonlinear equations are derived via the first-order shear deformation theory and Hamilton’s principle, comprehensively accounting for shear deformation, rotatory inertia, and providing a rigorous theoretical basis for motion equations. Double trigonometric series approximation combined with Galerkin’s method is used to calculate the natural frequencies. Through systematic analysis, the study reveals how key geometrical parameters, material properties, and thickness variations impact the intrinsic frequency. This work not only provides insights into the theoretical aspects of advanced smart composite structures but also provides practical guidelines for optimizing design parameters related to geometry, material selection, and thickness distribution. The proposed methodology offers potential applications in aerospace, micro-electromechanical systems, and other adaptive structural systems.</p>