Features of complex vibrations of flexible micropolar mesh panels
In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel...
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| Format: | Article |
| Language: | English |
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Saratov State University
2021-03-01
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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/2021/02/mmi_2021_1_48-59.pdf |
| _version_ | 1829492632733089792 |
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| author | Krylova, Ekaterina Yu. Papkova, Irina V. Saltykova, Olga A. Krysko, Vadim A. |
| author_facet | Krylova, Ekaterina Yu. Papkova, Irina V. Saltykova, Olga A. Krysko, Vadim A. |
| author_sort | Krylova, Ekaterina Yu. |
| collection | DOAJ |
| description | In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent. An additional independent material parameter of length associated with a symmetric tensor by a rotation gradient is introduced into consideration. The equations of motion of a panel element, the boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Kirchhoff – Love’s kinematic hypotheses. It is assumed that the cylindrical panel consists of n families of edges of the same material, each of which is characterized by an inclination angle relative to the positive direction of the axis directed along the length of the panel and the distance between adjacent edges. The material is isotropic, elastic and obeys Hooke’s law. To homogenize the rib system over the panel surface, the G. I. Pshenichnov continuous model is used. The dissipative mechanical system is considered. The differential problem in partial derivatives is reduced to an ordinary differential problem with respect to spatial coordinates by the Bubnov – Galerkin method in higher approximations. The Cauchy problem is solved by the Runge – Kutta method of the 4th order of accuracy. Using the establishment method, a study of grid geometry influence and taking account of micropolar theory on the behavior of a grid plate consisting of two families of mutually perpendicular edges was conducted. |
| first_indexed | 2024-12-16T06:18:38Z |
| format | Article |
| id | doaj.art-f78f6f7d617145e6889f21714f290ae9 |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-16T06:18:38Z |
| publishDate | 2021-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-f78f6f7d617145e6889f21714f290ae92022-12-21T22:41:12ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052021-03-01211485910.18500/1816-9791-2021-21-1-48-59Features of complex vibrations of flexible micropolar mesh panelsKrylova, Ekaterina Yu.0Papkova, Irina V.1Saltykova, Olga A.2Krysko, Vadim A.3Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State Technical University, Russia, 410054, Saratov, Politekhnicheskaya st., 77Saratov State Technical University, Russia, 410054, Saratov, Politekhnicheskaya st., 77Saratov State Technical University, Russia, 410054, Saratov, Politekhnicheskaya st., 77In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent. An additional independent material parameter of length associated with a symmetric tensor by a rotation gradient is introduced into consideration. The equations of motion of a panel element, the boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Kirchhoff – Love’s kinematic hypotheses. It is assumed that the cylindrical panel consists of n families of edges of the same material, each of which is characterized by an inclination angle relative to the positive direction of the axis directed along the length of the panel and the distance between adjacent edges. The material is isotropic, elastic and obeys Hooke’s law. To homogenize the rib system over the panel surface, the G. I. Pshenichnov continuous model is used. The dissipative mechanical system is considered. The differential problem in partial derivatives is reduced to an ordinary differential problem with respect to spatial coordinates by the Bubnov – Galerkin method in higher approximations. The Cauchy problem is solved by the Runge – Kutta method of the 4th order of accuracy. Using the establishment method, a study of grid geometry influence and taking account of micropolar theory on the behavior of a grid plate consisting of two families of mutually perpendicular edges was conducted.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_48-59.pdfcylindrical panelmicropolar theorymesh structurekirchgoff – love modelbubnov – galerkin methodestablishment methodg. i. pshenichnov continuous model |
| spellingShingle | Krylova, Ekaterina Yu. Papkova, Irina V. Saltykova, Olga A. Krysko, Vadim A. Features of complex vibrations of flexible micropolar mesh panels Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика cylindrical panel micropolar theory mesh structure kirchgoff – love model bubnov – galerkin method establishment method g. i. pshenichnov continuous model |
| title | Features of complex vibrations of flexible micropolar mesh panels |
| title_full | Features of complex vibrations of flexible micropolar mesh panels |
| title_fullStr | Features of complex vibrations of flexible micropolar mesh panels |
| title_full_unstemmed | Features of complex vibrations of flexible micropolar mesh panels |
| title_short | Features of complex vibrations of flexible micropolar mesh panels |
| title_sort | features of complex vibrations of flexible micropolar mesh panels |
| topic | cylindrical panel micropolar theory mesh structure kirchgoff – love model bubnov – galerkin method establishment method g. i. pshenichnov continuous model |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_48-59.pdf |
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