Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation

Abstract

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta <TEX>$4^{th}$</TEX> technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta <TEX>$4^{th}$</TEX> leads to highly accurate solutions.