Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell

In this study we have considered the governing nonlinear equation of an eccentrically reinforced cylindrical shell. A new analytical method called He\'s Variational Approach (VA) is used to obtain the natural frequency of the nonlinear equation. This analytical representation gives excellent approximations to the numerical solution for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the variation approach method. It has been proved that the variational approach is very effective, convenient and does not require any linearization or small perturbation. Additionally it has been demonstrated that the variational approach is adequately accurate to nonlinear problems in physics and engineering.