Doubly-curved shells due to their extreme stiffness and small weight are innovative structures for applications in civil, biomedical, and other engineering fields. For the first time, with the aid of a time-dependent wave propagation approach, free and forced vibrations of graphene platelets-reinforced doubly curved panel is presented. 3D-flexibility theory, equilibrium condition, and space-state differential equations expressed in the Laplace and spatial domain are used to model the current work’s motion equations. Half-sine loading with a specific duration time is presented as the external mechanical loading on the current curved open-type shell structure. Due to a wide range of applications such as encountering some curved parts with external loading, it is essential to improve the mechanical properties. To improve the mechanical properties of the open-type shell structure, graphene nanoplatelet (GPL) reinforcement is presented. The machine learning model is developed using data-driven solutions and mathematical simulation (MS). Initially, the MS analyzes the composite panels analytically under different situations. The data-driven model is then trained using the Levenberg-Marquardt approach using the outputs of the MS model (410 configurations). The impact of different parameters on the composite panel's amplitude motion is then assessed using a data-driven model. The results of the current study are useful suggestions for designing composite systems such as composite panels under external shock.