A simple harmonic balance method for solving strongly nonlinear oscillators

In this paper, a simple harmonic balance method (HBM) is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact). The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.