An analytical approximate technique to investigate a finite extensibility nonlinear oscillator

Abstract

In this paper, an analytical approximate technique based on modified harmonic balance method is presented to study about the dynamics of a finite extensibility nonlinear oscillator described by Febbo (2011) and Beléndez et al. (2012). Generally, a second-order approximation is only considered in this paper. In the proposed method, the approximate period of oscillations and the corresponding periodic solutions are determined, which are valid for both range of amplitudes 0 < A ≤ 0.9 and 0.9 < A < 1 of oscillation. The approximate periods obtained in this paper are compared with numerical result (considered to be exact) and other existing results. Firstly, the results are obtained for the amplitude 0 < A ≤ 0.9 and show that the present method gives high accuracy than other existing results. Moreover, the results are also obtained for the rest of the amplitude 0.9 < A < 1. The relative error measure in this paper is 0.03% for A = 0.9 while the relative errors obtained by Febbo (2011) and Beléndez et al. (2012), were 3.53% and 0.60% respectively. On the other hand, Belendez et al. (2012) did not obtain approximate period for 0.9 < A < 1. In this article, the approximate periods have been determined in the range of value 0.9 < A < 1 and they have provided better results than the existing result of Febbo (2011).