Analytical approximation of nonlinear frequency of cantilever beam vibrations

This research presents the application of modern analytical approaches for the nonlinear vibrations of cantilever beams. These methods are Homotopy Analysis Method, Parameter Expansion Method and Bubnov-Galerkin Weighted Residual Method. Powerful analytical methods are used to obtain frequency-amplitude relationship of dynamic behavior of the mentioned system. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a comparison with numerical methods is provided in order to confirm the soundness of the obtained results.