The theoretical modeling of a functionally graded (FG) graphene nanoplatelet (GPL)-reinforced assembled beam–plate structure resting on elastic supports is presented for the first time, and its free vibration analysis is performed. Herein, the assembled structure is modeled according to the Kirchhoff plate theory and the Rayleigh beam theory. The graphene nanoplatelets (GPLs) gradiently distribute in the beam’s radial direction and in the plate’s thickness direction, respectively. By adopting the rule of mixture and the Halpin–Tsai model, the effective material properties can be obtained. By employing the Lagrange’s equation and considering the effects of Coriolis force and centrifugal force, the coupled governing equations of the assembled structure are determined. Furthermore, the assumed modes method and substructure modal synthesis method are applied to obtain the frequencies of the assembled beam–plate structure. A comprehensive numerical investigation is carried out to discuss the influence of the structural and material parameters on the vibration behavior of the beam–plate structure.

首次提出了基于弹性支撑的功能梯度（FG）石墨烯纳米片（GPL）增强组装梁板结构的理论建模，并进行了自由振动分析。在此，组装结构根据基尔霍夫板理论和瑞利梁理论建模。石墨烯纳米片 (GPL) 分别在光束的径向和板的厚度方向上梯度分布。通过采用混合规则和Halpin-Tsai模型，可以获得有效的材料特性。利用拉格朗日方程，考虑科里奥利力和离心力的影响，确定了装配结构的耦合控制方程。此外，应用假设模态法和子结构模态合成法来获得组装梁板结构的频率。进行了全面的数值研究，以讨论结构和材料参数对梁板结构振动行为的影响。