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 |
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Elsevier
2017
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| Online Access: | 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 |
| _version_ | 1848785524886601728 |
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| author | Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris |
| author_facet | Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris |
| author_sort | Chowdhury, Md. Sazzad Hossien |
| building | IIUM Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T16:54:31Z |
| format | Article |
| id | iium-60636 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:54:31Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-606362018-07-10T09:37:59Z http://irep.iium.edu.my/60636/ High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris T Technology (General) TJ Mechanical engineering and machinery TS Manufactures 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. Elsevier 2017-10-08 Article PeerReviewed application/pdf en http://irep.iium.edu.my/60636/1/025-2017%20Results%20in%20Physics.pdf application/pdf en http://irep.iium.edu.my/60636/7/60636_High-order%20approximate%20solutions_scopus.pdf Chowdhury, Md. Sazzad Hossien and Hosen, Md. Alal and Ahmad, Kartini and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2017) High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method. Results in Physics, 7. pp. 3962-3967. E-ISSN 2211-3797 https://reader.elsevier.com/reader/sd/9E8D7837D218F55EEDF1C617D12D6E92E4BF3F5A852991314EA5E78FA2CBBCFB89A62D630BFBD70D723A46FB9C0BCC55 10.1016/j.rinp.2017.10.008 |
| spellingShingle | T Technology (General) TJ Mechanical engineering and machinery TS Manufactures Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title | High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title_full | High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title_fullStr | High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title_full_unstemmed | High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title_short | High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method |
| title_sort | high-order approximate solutions of strongly nonlinear cubic-quintic duffing oscillator based on the harmonic balance method |
| topic | T Technology (General) TJ Mechanical engineering and machinery TS Manufactures |
| url | 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 |