Modified harmonic balance method for solving strongly nonlinear oscillators

Abstract

In this paper, a modified harmonic balance method is applied to obtain higher-order approximate periodic solutions of strongly nonlinear oscillatory systems having a rational force. Approximate frequency and periodic solution are obtained. Frequency and solutions are analytically analyzed. Obtained results are compared with several authors and corresponding numerical results. Error analysis is carried out and found satisfactory results for the proposed method. The new technique also avoids the necessity of solving sets of equations with very complex nonlinearities numerically as in the classical harmonic balance method. Effectiveness of the method found from comparison with other articles. The method is illustrated by examples.