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

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-beta 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.