The paper presents the free vibration as well as the nonlinear behaviors of a new plate structure which the authors call double-variable-edge (DVE) plates in contact with fluid under the impacts of uniform time-dependent blast load. The used material is laminated functionally graded graphene-reinforced composite (FG-GRC) described by the extended Halpin-Tsai micromechanical model. Based on the classical plates theory (CPT), the governing motion system of equation is established and then the dynamical behaviors of the system are investigated by solving the ordinary differential equations. The velocity potential function and along with Bernoulli's equation is employed to obtain the hydrodynamic pressure on the plate-fluid interface while the blast load is modeled by Friedlander's equation. The CPT shows the convenience in analyzing the dynamic characteristics of complex shape plates, the results are compared with outcomes of previous articles and the Finite Element Analysis (FEA) to confirm the accuracy and reliability of present works. Some influences of materials, geometrics, temperature environment and fluid are given through numerical and graphical results. The current outcomes have great potential for the application of aerospace, ocean, civil engineering, and military fields such as: submarines, diving equipment, UAV or space exploration equipment.