Analytical approximate solutions for the Helmholtz-Duffing oscillator

• Main Authors: Md. Alal, Hosen, Chowdhury, Md. Sazzad Hossien
• Format: Article
• Language: English
• Published: Asian Research Publishing Network (ARPN) 2015
• Subjects: QA76 Computer software
• Online Access: http://irep.iium.edu.my/47978/1/Analytical_approximate_solutions_for_the_Helmholtz-Duffing_oscillator_-.pdf; http://irep.iium.edu.my/47978/; http://www.arpnjournals.com/
• Institution: Universiti Islam Antarabangsa Malaysia

In the present paper, analytical approximate periodic solutions for the Helmholtz-Duffing oscillator are obtained. 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 amplitude. In this work, the offered technique eradicate this aforementioned limitation and to avoid 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.