Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam

Abstract

Large amplitude free and forced vibration of FG beam resting on nonlinear elastic foundation containing shearing layer and cubic nonlinearity are investigated. The material properties are assumed to vary continuously according to a simple power law. The theoretical formulations and governing partial deferential equation of motion are derived based on Euler–Bernoulli beam theory and von Karman geometric nonlinearity. Adopting appropriate trial functions for various boundary conditions and employing Galerkin technique and assuming a uniformly distributed harmonic load, single nonlinear ordinary differential equation with quadratic and cubic nonlinearities is obtained. Variational Iteration Method (VIM) is used to derive closed form approximate solutions for both free and forced vibration. Comparison of the acquired results with those of existence literature revealed good agreement with a desired accuracy. The frequency response curves are presented for different coefficients of elastic foundation together with various boundary conditions and the effects of nonlinearities are discussed in detail.