Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields
The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the m...
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| Format: | Article |
| Language: | English |
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Saratov State University
2020-11-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/11/mmi_2020_4_468-477.pdf |
| _version_ | 1818432821437399040 |
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| author | Radaev, Yurii Nickolaevich |
| author_facet | Radaev, Yurii Nickolaevich |
| author_sort | Radaev, Yurii Nickolaevich |
| collection | DOAJ |
| description | The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides. |
| first_indexed | 2024-12-14T16:11:17Z |
| format | Article |
| id | doaj.art-2e48aeb2950944f781b35084e11f4267 |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-14T16:11:17Z |
| publishDate | 2020-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-2e48aeb2950944f781b35084e11f42672022-12-21T22:55:00ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052020-11-0120446847710.18500/1816-9791-2020-20-4-468-477Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector FieldsRadaev, Yurii Nickolaevich0Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia, 119526, Moscow, pr. Vernadskogo, 101-1The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/11/mmi_2020_4_468-477.pdfmicropolar elasticitydisplacement vectormicro-rotation vectorcoupledvector potentialvortex partscrew equationscrew fieldhelmholtz equationwaveguide |
| spellingShingle | Radaev, Yurii Nickolaevich Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика micropolar elasticity displacement vector micro-rotation vector coupled vector potential vortex part screw equation screw field helmholtz equation waveguide |
| title | Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields |
| title_full | Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields |
| title_fullStr | Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields |
| title_full_unstemmed | Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields |
| title_short | Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields |
| title_sort | representation of waves of displacements and micro rotations by systems of the screw vector fields |
| topic | micropolar elasticity displacement vector micro-rotation vector coupled vector potential vortex part screw equation screw field helmholtz equation waveguide |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/11/mmi_2020_4_468-477.pdf |
| work_keys_str_mv | AT radaevyuriinickolaevich representationofwavesofdisplacementsandmicrorotationsbysystemsofthescrewvectorfields |