An investigation of the vibration of multi-layer composite beams reinforced by graphene platelets resting on two parameter viscoelastic foundation

The current study goal is to analyze free vibration behavior of multi-layer composite beams reinforced by graphene platelets resting on viscoelastic foundation. These material properties varies layer to layer in the thickness direction. GPLs are spreaded in each layer randomly and four different distribution patterns are employed and all parameter effects on these four are investigated. Effective material properties are estimated by Halpin–Tsai model and higher order shear deformation beam theory is utilized to achieve the theoretical formulation of multi-layer GPLRC beam and Navier solution have 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 different distribution pattern of GPLs on frequency of the beam structure and the other parameters, all sections of this study and results are presented based on four GPLs distribution patterns.