Solution of free non-linear vibration of beams

In this paper, we have considered the nonlinear governing equation of tapered beams, attempt has been made to analyze the nonlinear behavior of tapered beams analytically. The nonlinear governing equation is solved by employing the variational approach method (VAM) and Improved AmplitudeFormulation (IAFF). Despite the increasing expenses of building structures to maintain their linear behavior, nonlinearity has been inevitable and therefore, nonlinear analysis has been of great importance to the scientists in the field. The major concern is to assess excellent approximations to the exact solutions for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the VAM and IAFF. The effect of vibration amplitude on the nonlinear frequency is discussed. It is predicted that there can be wide application of VAM and IAFF in engineering problems, as indicated in this paper.

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