Analytical Approximate Solutions for the Helmholtz- Duffing Oscillator

In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM is applied. Investigating analytically for such kinds of nonlinear algebraic equations is a tremendously difficult task and cumbersome especially for large oscillation. In this study, the offered technique eradicates this aforementioned limitation and avoids numerical complexity. Using iterative homotopy perturbation method, only two or three iteration produces desired results even for large oscillation. It is remarkably important that a second-order approximate solution gives excellent agreement compared to exact ones.