Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation

.The aim of the present article is to analyze the free-vibration behavior of multi-layer composite beams reinforced with graphene platelets (GPLs) resting on a viscoelastic foundation. The material properties of GPLs are assumed to vary from layer to layer in the thickness direction. GPLs are dispersed in each layer randomly and four different distribution patterns are employed. Further, all parameter effects on these four are investigated thoroughly. Effective material properties are estimated by the Halpin-Tsai model, and higher-order shear deformation beam theory is utilized to achieve the theoretical formulation of multi-layer graphene-platelets-reinforced composite (GPLRC) beam. Meanwhile, the Navier solution has been used to derive and follow up the governing differential equation of motion and natural frequency. To find out the effect of GPLs on composite structures and effect of the different distribution pattern of GPLs on the frequency of the beam structure and the other parameters, all sections of this study and results are presented based on four GPLs distribution patterns.