Van Der Pol-Duffing oscillator under combined harmonic and random excitations
A new technique is proposed to investigate the response of Van der Pol-Duffing (V-D for short) oscillator to a combination of harmonic and random excitations in the primary resonant frequency region. The analytical approach is based on the stochastic averaging method and equivalent linearization me...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2014-08-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/3485 |
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| author | N. D. Anh V. L. Zakovorotny D. N. Hao |
| author_facet | N. D. Anh V. L. Zakovorotny D. N. Hao |
| author_sort | N. D. Anh |
| collection | DOAJ |
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A new technique is proposed to investigate the response of Van der Pol-Duffing (V-D for short) oscillator to a combination of harmonic and random excitations in the primary resonant frequency region. The analytical approach is based on the stochastic averaging method and equivalent linearization method. The stochastic averaging is applied to the original equation transformed into Cartesian coordinates. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. Numerical results show that the proposed approximate technique is an effective approach to solving the V-D equation. Although the technique has been used for the V-D equation in the paper, however, it can also be used to solve many other nonlinear oscillators.
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| format | Article |
| id | doaj-art-2d36a8c04a404f3d9b2948aba282b6ed |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2014-08-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-2d36a8c04a404f3d9b2948aba282b6ed2025-08-20T02:10:39ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822014-08-0136310.15625/0866-7136/36/3/3485Van Der Pol-Duffing oscillator under combined harmonic and random excitationsN. D. Anh0V. L. Zakovorotny1D. N. Hao2Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, VietnamDon State Technical University, Rostov-on-Don, RussiaUniversity of Information Technology, VNU-HCM, Ho Chi Minh, Vietnam A new technique is proposed to investigate the response of Van der Pol-Duffing (V-D for short) oscillator to a combination of harmonic and random excitations in the primary resonant frequency region. The analytical approach is based on the stochastic averaging method and equivalent linearization method. The stochastic averaging is applied to the original equation transformed into Cartesian coordinates. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. Numerical results show that the proposed approximate technique is an effective approach to solving the V-D equation. Although the technique has been used for the V-D equation in the paper, however, it can also be used to solve many other nonlinear oscillators. https://vjs.ac.vn/index.php/vjmech/article/view/3485Van der PolDuffingaveraging methodequivalent linearizationharmonic excitationrandom excitation |
| spellingShingle | N. D. Anh V. L. Zakovorotny D. N. Hao Van Der Pol-Duffing oscillator under combined harmonic and random excitations Vietnam Journal of Mechanics Van der Pol Duffing averaging method equivalent linearization harmonic excitation random excitation |
| title | Van Der Pol-Duffing oscillator under combined harmonic and random excitations |
| title_full | Van Der Pol-Duffing oscillator under combined harmonic and random excitations |
| title_fullStr | Van Der Pol-Duffing oscillator under combined harmonic and random excitations |
| title_full_unstemmed | Van Der Pol-Duffing oscillator under combined harmonic and random excitations |
| title_short | Van Der Pol-Duffing oscillator under combined harmonic and random excitations |
| title_sort | van der pol duffing oscillator under combined harmonic and random excitations |
| topic | Van der Pol Duffing averaging method equivalent linearization harmonic excitation random excitation |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/3485 |
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