Analytical solution for Euler Bernoulli beam with moderately large deflection and variable thickness

In this paper the vibrations of a nonlinear Euler-Bernoulli beam with variable thickness under axial load are studied analytically using the perturbation technique. In order to predict the behavior of the non-uniform, the Euler–Bernoulli beam theory and nonlinear von-Kármán strain field are employed. The multiple timescales method is applied to obtain the analytical solution for the secondary response phenomena. A parametric study is performed and the effects of the axial load on the results are investigated.