Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift
A theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constr...
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| Language: | English |
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Saratov State University
2019-08-01
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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/2019/08/305-316krylova_et_al.pdf |
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| author | E. Yu. Krylova Irina V. Papkova Tatyana V. Yakovleva Vadim A. Krysko |
| author_facet | E. Yu. Krylova Irina V. Papkova Tatyana V. Yakovleva Vadim A. Krysko |
| author_sort | E. Yu. Krylova |
| collection | DOAJ |
| description | A theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constrained particle rotation (pseudocontinuum). It is assumed that the displacement and rotation fields are not independent. An additional independent material length parameter associated with the symmetric tensor of the rotation gradient is introduced into consideration. The equations of motion of the shell element, boundary and initial conditions are obtained from the variational principle of Ostrogradskii–Hamilton on the basis of kinematic hypotheses of the third approximation (Peleha–Sheremetyev–Reddy), allowing to take into account not only the rotation, but also the curvature of the normal after deformation. It is assumed that the cylindrical shell con-
sists of n families of edges, each of which is characterized by an inclination angle with respect to the positive direction of the axis directed along the length of the shell and the distance between neighboring edges. The shell material is isotropic, elastic, and obeys Hooke’s law. A dissipative mechanical system is considered. As a special case, the system of equations of motion for Kirchhoff–Love’s micro-polar reticulated shell is presented. The theory constructed in this paper can be used, among other things, for studying the behavior of CNTs under the action of static and dynamic loads. |
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| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-13T14:02:04Z |
| publishDate | 2019-08-01 |
| publisher | Saratov State University |
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| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-efea834a16b847e899a45691c54f5c8f2022-12-21T23:42:43ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052019-08-0119330531610.18500/1816-9791-2019-19-3-305-316Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account ShiftE. Yu. Krylova0Irina V. Papkova1Tatyana V. Yakovleva2Vadim A. Krysko3Saratov State University, Russia, Saratov, Astrakhanskaya 83Saratov State Technical University named after Gagarin Y.A., Saratov State Technical University named after Gagarin Y.A., 77, Politechnicheskaya st., 410054, Saratov, RussiaSaratov State Technical University named after Gagarin Y.A., Saratov State Technical University named after Gagarin Y.A., 77, Politechnicheskaya st., 410054, Saratov, RussiaSaratov State Technical University named after Gagarin Y.A., Saratov State Technical University named after Gagarin Y.A., 77, Politechnicheskaya st., 410054, Saratov, RussiaA theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constrained particle rotation (pseudocontinuum). It is assumed that the displacement and rotation fields are not independent. An additional independent material length parameter associated with the symmetric tensor of the rotation gradient is introduced into consideration. The equations of motion of the shell element, boundary and initial conditions are obtained from the variational principle of Ostrogradskii–Hamilton on the basis of kinematic hypotheses of the third approximation (Peleha–Sheremetyev–Reddy), allowing to take into account not only the rotation, but also the curvature of the normal after deformation. It is assumed that the cylindrical shell con- sists of n families of edges, each of which is characterized by an inclination angle with respect to the positive direction of the axis directed along the length of the shell and the distance between neighboring edges. The shell material is isotropic, elastic, and obeys Hooke’s law. A dissipative mechanical system is considered. As a special case, the system of equations of motion for Kirchhoff–Love’s micro-polar reticulated shell is presented. The theory constructed in this paper can be used, among other things, for studying the behavior of CNTs under the action of static and dynamic loads.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/2019/08/305-316krylova_et_al.pdfcylindrical shellCNTmicropolar theoryCosserat pseudocontinuumPeleha– Sheremetyev–Reddy modelnet structurestatics and dynamicsmodel Tymoshenkothe Kirchhoff–Love model |
| spellingShingle | E. Yu. Krylova Irina V. Papkova Tatyana V. Yakovleva Vadim A. Krysko Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика cylindrical shell CNT micropolar theory Cosserat pseudocontinuum Peleha– Sheremetyev–Reddy model net structure statics and dynamics model Tymoshenko the Kirchhoff–Love model |
| title | Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift |
| title_full | Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift |
| title_fullStr | Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift |
| title_full_unstemmed | Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift |
| title_short | Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift |
| title_sort | theory of vibrations of carbon nanotubes like flexible micropolar mesh cylindrical shells taking into account shift |
| topic | cylindrical shell CNT micropolar theory Cosserat pseudocontinuum Peleha– Sheremetyev–Reddy model net structure statics and dynamics model Tymoshenko the Kirchhoff–Love model |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/2019/08/305-316krylova_et_al.pdf |
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