Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates
The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arb...
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| Format: | Article |
| Language: | English |
| Published: |
Igor Sikorsky Kyiv Polytechnic Institute
2022-12-01
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| Series: | Mechanics and Advanced Technologies |
| Subjects: | |
| Online Access: | http://journal.mmi.kpi.ua/article/view/263541 |
| _version_ | 1797838354941739008 |
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| author | Ігор Ориняк Юлія Бай Ірина Костюшко |
| author_facet | Ігор Ориняк Юлія Бай Ірина Костюшко |
| author_sort | Ігор Ориняк |
| collection | DOAJ |
| description |
The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arbitrary chosen parameters are constructed. This allows to choose any number of exact solutions, while the required number of them depends on the boundary conditions which should satisfy in considered collocation points.
The efficiency of method is demonstrated for the most unfavorable case of all sides clamped rectangular plate. Nevertheless, the accuracy is quite satisfactory for first six natural frequencies even for relatively small number of collocation boundary points, and testify about big prospects as to application for complex structures, different geometries, various boundary conditions.
Additionally two variants of the Galerkin method are realized and compared. First one, employs the exponential functions, while the second one –the very popular beam functions. The calculation results show the superiority of first variant as in technical realization as in accuracy, and in further applications in structural mechanics.
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| first_indexed | 2024-04-09T15:39:30Z |
| format | Article |
| id | doaj.art-1ec2dfdff8fa4d2ca65a2bf76191c091 |
| institution | Directory Open Access Journal |
| issn | 2521-1943 2522-4255 |
| language | English |
| last_indexed | 2024-04-09T15:39:30Z |
| publishDate | 2022-12-01 |
| publisher | Igor Sikorsky Kyiv Polytechnic Institute |
| record_format | Article |
| series | Mechanics and Advanced Technologies |
| spelling | doaj.art-1ec2dfdff8fa4d2ca65a2bf76191c0912023-04-27T11:51:41ZengIgor Sikorsky Kyiv Polytechnic InstituteMechanics and Advanced Technologies2521-19432522-42552022-12-016310.20535/2521-1943.2022.6.3.263541Applications of randomly selected sets of exact Voight's solutions for vibration of thin platesІгор Ориняк0Юлія Бай1Ірина Костюшко2Department of Applied Mathematics at National Technical University Kiev Polytechnic InstituteIgor Sikorsky Kyiv Polytechnic InstituteDepartment of Applied Mathematics at National Technical University Kiev Polytechnic Institute The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arbitrary chosen parameters are constructed. This allows to choose any number of exact solutions, while the required number of them depends on the boundary conditions which should satisfy in considered collocation points. The efficiency of method is demonstrated for the most unfavorable case of all sides clamped rectangular plate. Nevertheless, the accuracy is quite satisfactory for first six natural frequencies even for relatively small number of collocation boundary points, and testify about big prospects as to application for complex structures, different geometries, various boundary conditions. Additionally two variants of the Galerkin method are realized and compared. First one, employs the exponential functions, while the second one –the very popular beam functions. The calculation results show the superiority of first variant as in technical realization as in accuracy, and in further applications in structural mechanics. http://journal.mmi.kpi.ua/article/view/263541rectangular platefree vibrationsclamped-clamped plateGalerkin methodVoigt solution |
| spellingShingle | Ігор Ориняк Юлія Бай Ірина Костюшко Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates Mechanics and Advanced Technologies rectangular plate free vibrations clamped-clamped plate Galerkin method Voigt solution |
| title | Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates |
| title_full | Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates |
| title_fullStr | Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates |
| title_full_unstemmed | Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates |
| title_short | Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates |
| title_sort | applications of randomly selected sets of exact voight s solutions for vibration of thin plates |
| topic | rectangular plate free vibrations clamped-clamped plate Galerkin method Voigt solution |
| url | http://journal.mmi.kpi.ua/article/view/263541 |
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