High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
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 algebr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Elsevier
2017
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ 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 |
| Summary: | 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. |
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