Dynamic model of large amplitude non-linear oscillations arising in the structural engineering: Analytical solutions

A mathematical model describing the process of large amplitude vibration of a uniform cantilever beam arising in the structural engineering is proposed. Six different analytical methods are applied to solve the dynamic model of the large amplitude non-linear oscillation equation. Periodic solutions are analytically verified, and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. Comparison of the present solutions is made with the exact solution and excellent agreement is noted.