Analytical study on the non-linear vibration of Euler-Bernoulli beams

In this study, He's Variational Approach Method (VAM) is used to obtain an accurate analytical solution for the nonlinear vibrations of Euler-Bernoulli beams subjected to axial loads. It is demonstrated that the method works very well for the whole range of initial amplitudes and does not need small perturbation. It is sufficiently accurate in the case of both linear and nonlinear physics and engineering problems. Finally, the accuracy of the solution obtained with the approximate VAM method is shown graphically and compared with that of the numerical solution.