Size-dependent vibration analysis of three-layered fluid-infiltrated porous curved microbeams, which are integrated with nanocomposite face sheets, is provided in this work. The effect of the fluids within the pores of the core is taken into consideration and the core’s thermomechanical properties vary across the thickness based on three different patterns. Also, the face sheets are made from epoxy, which are reinforced by graphene platelets as lightweight and high-stiffness reinforcements. Graphene platelets dispersion patterns are also considered, which obey three different functions, namely parabolic, linear, and uniform. Moreover, effective thermomechanical properties of the face sheets are determined with the aid of ERM and Halpin–Tsai micromechanical models. The microstructure is under thermal load and it is rested on Pasternak elastic foundation. In the polar coordinate system, the strains are determined for deep curved beams that lead to more accurate results. Based on a refined higher-order shear deformation theory, which includes four variables and considers the thickness stretching effect, and employing the modified couple stress theory for accounting the size effect, the differential motion equations are derived and via an analytical method, they are solved. A verification study is conducted by neglecting some parameters and after that, the results are presented and discussed in detail. It is seen that the porous core and nanocomposite face sheets material properties have significant effects on the vibrational response of the under consideration model. Up to now, no similar work in the available literature has been found, therefore, the results of this study can be considered as a benchmark for future ones. The outcomes of this study may help to design more efficient structures with the desired properties.
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