<p>Because of their remarkable mechanical and physical properties, including their high strength-to-weight ratio, tunable stiffness and strength, and negative Poisson's ratio, functionally graded graphene origami-enabled auxetic metamaterial structures have demonstrated great promise for a range of engineering applications. This is one of the first studies where the IGA method was used to analyze the free and forced vibration behaviors of FG-GOEAM non-uniform thickness microplates subjected to different types of dynamic loads and resting on a visco-elastic foundation. A genetic programming-based micromechanics model is used to calculate the GOEAM's material characteristic, such as its Young's modulus, and Poisson's ratio. The governing equations of motion are established using the higher-order shear deformation theory, modified couple stress theory, and Hamilton's principle. The impacts of GOri's folding degree, distribution, weight fraction, length-scale parameter, and micro-plate dimensions on the free vibration and transient response of non-uniform thickness FG-GOEAM micro-plate are shown by a thorough parametric research. The analysis, design, and optimization of FG-GOEAM structures in civil engineering, microelectronics, aerospace, semiconductor chips, and nuclear power applications are anticipated to benefit from these discoveries.</p>