Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results
The article considers the dynamics of a nonlinear mechanical system under the action of a kinematic perturbation on it. The object's vibration isolation system is described by a rigid cubic power characteristic and is based on compensation of external perturbations — the introduction of an a...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2023-09-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%963%20(187)%20(%D0%9E%D0%9D%D0%92)/15-22%20%D0%9D%D0%B5%D1%85%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%A1%D0%BC%D0%B0%D0%BB%D0%B5%D0%B2%20%D0%90.%20%D0%9D.,%20%D0%A1%D0%B5%D1%80%D1%8F%D0%BA%D0%BE%D0%B2%20%D0%9A.%20%D0%9E..pdf |
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| author | V. A. Nekhaev V. A. Nikolaev A. N. Smalev K. O. Seryakov |
| author_facet | V. A. Nekhaev V. A. Nikolaev A. N. Smalev K. O. Seryakov |
| author_sort | V. A. Nekhaev |
| collection | DOAJ |
| description | The article considers the dynamics of a nonlinear mechanical system under the action
of a kinematic perturbation on it. The object's vibration isolation system is described
by a rigid cubic power characteristic and is based on compensation of external
perturbations — the introduction of an additional elastic element with negative
stiffness into the suspension. Numerical modeling of the system is performed, the
results of which are analyzed by the method of spectral analysis, based on the
representation of the correlation function on a small time interval by a square
polynomial.
As a result of the analysis, it is found that in the pre-resonant and resonant regions,
the general solution should consist of three components: a subharmonic of the order
of 1/3, the fundamental harmonic, and the third harmonic. It is noted that only the
subharmonic of the order of 1/3 and the fundamental harmonic are important in
the resonant zone.
It is also noted that even simple nonlinear mechanical systems in the study of
dynamics should use approximate analytical and numerical methods in combination
with spectral analysis, since traditional methods of nonlinear mechanics are not
adapted to solving problems taking into account a relatively large number of
harmonic components that appear due to nonlinearity. |
| format | Article |
| id | doaj-art-7dcfcfd6527c43c5a9cf770932e39b32 |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-7dcfcfd6527c43c5a9cf770932e39b322025-02-03T06:21:13ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412023-09-013 (187)152210.25206/1813-8225-2023-187-15-22Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the resultsV. A. Nekhaev0V. A. Nikolaev1A. N. Smalev2K. O. Seryakov3Omsk State Transport UniversityOmsk State Transport UniversityOmsk State Transport UniversityOmsk State Transport UniversityThe article considers the dynamics of a nonlinear mechanical system under the action of a kinematic perturbation on it. The object's vibration isolation system is described by a rigid cubic power characteristic and is based on compensation of external perturbations — the introduction of an additional elastic element with negative stiffness into the suspension. Numerical modeling of the system is performed, the results of which are analyzed by the method of spectral analysis, based on the representation of the correlation function on a small time interval by a square polynomial. As a result of the analysis, it is found that in the pre-resonant and resonant regions, the general solution should consist of three components: a subharmonic of the order of 1/3, the fundamental harmonic, and the third harmonic. It is noted that only the subharmonic of the order of 1/3 and the fundamental harmonic are important in the resonant zone. It is also noted that even simple nonlinear mechanical systems in the study of dynamics should use approximate analytical and numerical methods in combination with spectral analysis, since traditional methods of nonlinear mechanics are not adapted to solving problems taking into account a relatively large number of harmonic components that appear due to nonlinearity.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%963%20(187)%20(%D0%9E%D0%9D%D0%92)/15-22%20%D0%9D%D0%B5%D1%85%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%A1%D0%BC%D0%B0%D0%BB%D0%B5%D0%B2%20%D0%90.%20%D0%9D.,%20%D0%A1%D0%B5%D1%80%D1%8F%D0%BA%D0%BE%D0%B2%20%D0%9A.%20%D0%9E..pdfmechanical systemrigid cubic force characteristicduffing equationapproximate analytical methodsmathematical modelingspectral density (power)subharmonicsfrequency response |
| spellingShingle | V. A. Nekhaev V. A. Nikolaev A. N. Smalev K. O. Seryakov Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results Омский научный вестник mechanical system rigid cubic force characteristic duffing equation approximate analytical methods mathematical modeling spectral density (power) subharmonics frequency response |
| title | Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| title_full | Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| title_fullStr | Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| title_full_unstemmed | Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| title_short | Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| title_sort | dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results |
| topic | mechanical system rigid cubic force characteristic duffing equation approximate analytical methods mathematical modeling spectral density (power) subharmonics frequency response |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%963%20(187)%20(%D0%9E%D0%9D%D0%92)/15-22%20%D0%9D%D0%B5%D1%85%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B5%D0%B2%20%D0%92.%20%D0%90.,%20%D0%A1%D0%BC%D0%B0%D0%BB%D0%B5%D0%B2%20%D0%90.%20%D0%9D.,%20%D0%A1%D0%B5%D1%80%D1%8F%D0%BA%D0%BE%D0%B2%20%D0%9A.%20%D0%9E..pdf |
| work_keys_str_mv | AT vanekhaev dynamicsofamechanicalsystemwithnonlinearelasticsuspensionandspectralanalysisoftheresults AT vanikolaev dynamicsofamechanicalsystemwithnonlinearelasticsuspensionandspectralanalysisoftheresults AT ansmalev dynamicsofamechanicalsystemwithnonlinearelasticsuspensionandspectralanalysisoftheresults AT koseryakov dynamicsofamechanicalsystemwithnonlinearelasticsuspensionandspectralanalysisoftheresults |