Thermo-mechanical vibration of FG curved nanobeam containing porosities and reinforced by graphene platelets

Recently, the graphene platelets (GPLs) are extensively used as reinforcements to enhance the strength of porous materials. However, most studies are focused on the straight GPLs-reinforced structures under macro-scale. In this paper, the thermo-mechanical vibration of a curved functionally graded (FG) porous nanobeam reinforced with GPLs is studied via the curved refined shear deformation beam theory associated with nonlocal strain gradient size scale effect. Four different porosity distribution patterns are employed to account for the graded distribution of porosity, and the GPLs are assumed to be dispersed evenly over the porous nanobeam. The effective mechanical properties of the curved nanobeam with different FG porosity patterns are evaluated by virtue of the Halpin–Tsai micromechanical-based model. The effects of GPL weight fraction, temperature variation, opening angle, porosity distribution pattern and coefficient, as well as size-scale parameters on the vibrational performance of the GPLs-reinforced curved FG porous nanobeam with different boundary conditions are investigated. It is demonstrated that the fundamental frequency enhances with the increase of the GPL weight fraction, while increasing the porosity coefficient does not always decrease the vibrational frequency, which is related to the porosity distribution pattern and boundary condition. Moreover, the thermal environment and size-scale characteristics also have significant influences on the vibration of GPLs-reinforced porous nanobeam.