Purpose <p>This paper devotes to propose a dynamic mechanics model to analyze the random response properties of functionally graded graphene platelet reinforced composite (FG-GPLRC) coupled plate structures excited by stationary/non-stationary random loads.</p> Methods <p>The effective material attributes of such composite can be calculated by the Halpin-Tsai micromechanical method and the law of mixture. The artificial spring method is applied to overcome the simulation problems of boundary conditions and coupled interface constraint of coupled plates. The first order shear deformation theory (FSDT) and variation principle are adopted for producing the random vibration differential equations of FG-GPLRC coupled plates. With the consideration of the base random acceleration excitation, the random response results for FG-GPLRC coupled plates are obtained by solving the dynamic analysis model using the spectro-geometric method (SGM) and pseudo-excitation method (PEM).</p> Results <p>Through a quantity of computational cases, the convergence and correctness of the dynamic model proposed in predicting the free vibration and random vibration solutions of FG-GPLRC coupled plates are fully confirmed. Several parametric studies on the random vibration are performed to reveal the intrinsic relationships between crucial parameters (namely, weight fraction and width-thickness ratio of GPL material) of FG-GPLRC coupled plates and stationary/non-stationary random responses.</p>