Vibration analysis of functionally graded graphene oxide-reinforced composite beams using a new Ritz-solution shape function

Abstract

In this study, a new Ritz-solution shape function, in the form of a combination of polynomials and general exponential functions for various boundary conditions, is constructed from two-dimensional elasticity solutions using an inverse method. In conjunction with an improved third-order shear deformation theory, a reliable and accurate model is developed for the analysis of the mechanical behavior of composite beams. Free and forced vibrations of a functionally graded (FG) polymer nanocomposite beam reinforced with a low content of graphene oxide (GO) and excited by a moving load with a constant velocity are investigated. The weight fraction of the GOs is assumed to vary continuously and smoothly in the thickness direction. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the FG GO-reinforced composites. The governing equations of motion are derived using the Lagrange method. The Newmark-β method is adopted to solve the forced vibration problem of a beam subjected to a moving load. A parametric study is conducted to demonstrate the effects of GO distribution patterns, weight fraction, and size on the vibration response of the nanocomposite beam with various classical boundary conditions.