<p>This paper investigates the nonlinear free vibration of functionally graded porous graphene platelets-reinforced composite (FGP-GPLs) plates resting on the Kerr foundation, with piezoelectric sheets integrated on the upper and lower surfaces. The material model of the composite layer incorporates three types of porosity and three distinct patterns of graphene platelets distribution. To determine the effective material properties of the composite layer, the Halpin–Tsai micromechanical model, the rule of mixture, and the closed-cell Gaussian random field scheme are employed. The numerical model of the piezoelectric smart laminated structure is developed, carefully considering the effects of the piezoelectricity and flexoelectricity, temperature, and von Kármán nonlinear assumption. This is done in conjunction with the higher-order shear deformation theory (HSDT), the modified couple stress theory (MCST), and isogeometric analysis (IGA) techniques. The nonlinear response of the numerical model is solved using a direct iterative method. The accuracy and effectiveness of the model and solution approach have been validated through comparison with results from the available literature. Lastly, a comprehensive discussion is provided on the effects of various parameters, including the distribution patterns of porosity and graphene platelets, the porosity coefficient, the weight fraction of graphene platelets, the temperature rise, the stiffness of the elastic foundation, the flexoelectric effect, and the size-dependent effect on the nonlinear free vibration of the piezoelectric functionally graded porous graphene platelets-reinforced laminated plate resting on the foundation.</p>