This study investigates wave dispersion characteristics of graphene-reinforced conductive adhesive functionally graded piezoelectric sandwich panels supported by Kerr substrates. The displacement field is formulated using sinusoidal shear deformation theory, and the equations of motion are derived by combining Hamilton’s principle with nonlocal strain gradient theory. The wave dispersion relations for porous functionally graded piezoelectric sandwich panels are solved numerically. The results indicate that scale effects exert distinct influences on frequency and phase velocity. Pore volume fraction and functional gradient exponent affect frequency and phase velocity through different mechanisms. Environmental loading, electrical loading, Kerr substrate parameters, graphene density, and geometric dimensions also exhibit clear and independent effects on wave propagation frequency. These results provide theoretical support for the design and application of piezoelectric smart aggregates in damage monitoring of hydraulic concrete structures.