Large amplitude dynamics of beam subjected to a compressive axial force resting on non -linear elastic foundation

Abstract

In this paper, the large amplitude of free vibration and buckling of Euler–Bernoulli beam rests on a non-linear elastic foundation subjected to an axial force are studied. Hamilton’s principle is followed to derive governing equation of the beam response. Using an analytical method based on the Galerkin technique,the nonlinear governing equations of motion was simplified to a time-dependent Duffing equation with cubic nonlinearities and then solved using Laplace Iteration Method. Comparison between results of the present work and those available in literature review shows reasonable agreement of this method. Effects of vibration amplitude, elastic coefficients of foundation and axial force on the non-linear natural frequencies and buckling load of beams are presented. Results reveal that decreasing linear and shear parameters and increasing nonlinear parameters of foundation lead to increasing frequency ratio and buckling load ratio. Furthermore, increasing axial force decreases absolute values of both linear and nonlinear frequencies as well as natural frequency ratio.