Dynamic analysis of functionally graded carbon nanotube (FGCNT) reinforced composite beam resting on viscoelastic foundation subjected to impulsive loading

In this study, dynamic analysis of functionally graded carbon nanotube reinforced composite (FGCNT) beam resting on viscoelastic foundation is investigated. Four different types of carbon nanotubes (CNTs) distribution including uniform (UD-CNT), and three types of functionally graded distribution of CNTs through the thickness of beam‌‌ are‌ considered. The Kelvin–Voigt viscoelastic model and higher-order shear deformation beam theory (HOBT) have been used. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The equations of motion are derived by using Lagrange’s equations, and solved by using finite element and Newmark methods. The effects of volume fraction and distribution of CNTs, stiffness and damping of viscoelastic foundation, slenderness ratio and different boundary conditions on transverse displacement and stresses of beam are investigated. The results show that by using viscoelastic foundation the amount of normal and shear stress have decreased considerably, and by increasing the stiffness coefficient of foundation, transverse displacement of beam reduces and the frequency of vibration increases as well, meanwhile by increasing the damping coefficient of foundation, amplitude of vibration decreases considerably. The model is verified and compared with previously published works and it shows good agreement.