High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method

• Main Authors: Chowdhury, Md. Sazzad Hossien, Hosen, Md. Alal, Ahmad, Kartini, Ali, Mohammad Yeakub, Ismail, Ahmad Faris
• Format: Article
• Language: English; English
• Published: Elsevier 2017
• Subjects: T Technology (General); TJ Mechanical engineering and machinery; TS Manufactures
• Online Access: http://irep.iium.edu.my/60636/1/025-2017%20Results%20in%20Physics.pdf; http://irep.iium.edu.my/60636/7/60636_High-order%20approximate%20solutions_scopus.pdf; http://irep.iium.edu.my/60636/; https://reader.elsevier.com/reader/sd/9E8D7837D218F55EEDF1C617D12D6E92E4BF3F5A852991314EA5E78FA2CBBCFB89A62D630BFBD70D723A46FB9C0BCC55

In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability.