Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging

In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, which are compared with the previous analytical solutions and the exact solutions. Comparisons show the accuracy of the present solutions. The impact of nonlinear terms on the dynamical behavior of beams and the effect of the initial amplitude on frequencies of beams are investigated. Furthermore, the effect of the axial force and the length of beams on frequencies are studied.

Keywords:

Equivalent linearization method , Weighted averaging , Non-linear vibration , Euler-Bernoulli beam