This paper is concerned with analytical approximate solutions, to the nonlinear vibration of Euler-Bernoulli beams subjected to the axial loads. Hamiltonian Approach (HA) and Differential Transformation Method (DTM) are applied to solve the nonlinear differential equation cause in current problem and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. To verify the accuracy of the present approach, illustrative examples are provided and compared with Exact Solution. The procedure yields rapid convergence with respect to the exact integral solution.
Karimian, S., & Azimi, M. (2014). Periodic solution for vibration of eulerbernoulli beams subjected to axial load using dtm and ha. UPB Scientific Bulletin, Series D: Mechanical Engineering, 76(2), 69–76.