A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator

The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method have been introduced to derive the approximate periods of strongly nonlinear Duffing-harmonic oscillator. The comparison of two methods is made to demonstrate that the rational harmonic balance method (RHBM) gives almost similar results to next higher-order approximation results of harmonic balance method (HBM). It is highly remarkable that the solution procedure in both methods are simple and takes less computational effort for determining approximate periods and shows a good agreement compared with the exact ones