Application of Recent Powerful Analytical Approaches on the Non-Linear Vibration of Cantilever Beams

This paper presents the advantages of some effective analytical approaches applied on the governing equation of transversely vibrating cantilever beams. Six studied methods are Min-Max Approach, Parameter Expansion Method, Hamiltonian Approach, Variational Iteration Method, Bubnov-Galerkin and Energy Balance Method. The powerful analytical approaches are used to obtain frequency-amplitude relationship for dynamic behavior of nonlinear vibration of cantilever beams. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the accuracy of these methods.