Free vibration and buckling of functionally graded carbon nanotubes / graphene platelets Timoshenko sandwich beam resting on variable elastic foundation

Sandwich structures made of composites are widely applicable in different industries, including aerospace and power plants. The combination of a porous sandwich with functionally graded materials makes structures more resistant to analyze buckling and vibration behaviors. According to its high surface area and high strength, adding graphene platelets to the composite increases the final mechanical properties of composites. In the present paper, the effect of volume fraction distribution of fibers, numbers, and angles of layers in composites will be investigated. Additionally, the different porosity coefficients and distribution along the beam length will consider and the best porosity distributions will identify. Pasternak elastic foundation is considered during the beam length as linearly and parabolically. The equations of motion for the Timoshenko sandwich beam are solved by the differential quadrature method (DQM). The influences of adding graphene platelets with three various patterns on critical buckling load and natural frequency of composite beam will investigate. Also, the buckling and vibration behaviors of pure composites, perfect composite and FGM (Functionally Graded Material) composites will compare. Moreover, the critical buckling load will obtain by the Mori-Tanaka model.