Свободные колебания функционально-градиентных наноармированных цилиндрических оболочек
Рубрика:
| Аврамов, КВ, Чернобрывко, МВ, Успенский, БВ |
| Косм. наука технол. 2019, 25 ;(2):23-37 |
| https://doi.org/10.15407/knit2019.02.023 |
| Мова публікації: Украинский |
Анотація: В настоящее время в мировом ракетостроении на смену металлам и их сплавам приходят полимерные композитные материалы, армированные углеродными нанотрубками. Это связано с тем, что в условиях высокоинтенсивных нагрузок при одинаковом весе нано-композиты значительно превосходят алюминиевые сплавы по своим прочностным механическим характеристикам. Цилиндрические нанокомпозитные корпусные элементы ракет могут быть армированы углеродными нанотрубками с различным распределением их по толщине матрицы. В настоящее время существует пять основных типов наноармирования, которые приводят к возникновению функционально-градиентного материала по толщине оболочки. При анализе колебаний элементов ракетно-космической техники необходимо рассматривать возможность резонанса между конструкцией и аэродинамическими нагрузкам. Неотъемлемым элементом этого анализа является анализ свободных колебаний оболочки, который проводится с целью определения и предотвращения опасных резонансных режимов. Классические модели колебаний цилиндрических оболочек не позволяют учитывать изменяющиеся по толщине свойства материала.
В данной работе предложен метод анализа свободных колебаний функционально-градиентных нанокомпозитных цилиндрических оболочек, которые могут быть составной частью ракетных комплексов и конструкций самолетов. Рассмотрены зависимости параметров колебаний от типа наноармирования, объемной доли нанотрубок в композите и толщины оболочки. Результаты аналитического исследования сравниваются с численным моделированием методом конечных элементов. Предложенная модель учитывает изменяющиеся по толщине свойства материала для пяти случаев наноармирования. Показано, что отстройка нанокомпозитных оболочек от резонансных режимов может осуществляться путем рационального выбора типа армирования углеродными нанотрубками.
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| Ключові слова: нанокомпозит, нанотрубка, свободные колебания, собственные частоты, функционально-градиентный материал, цилиндрическая оболочка |
References:
1. Galishin A. K. (1967). Calculation of plates and shells according to specified theories. Studies in the theory of plates and shells, V, 66—92 [in Russian].
2. Allaoui A., Bai S., Cheng H. M., Bai J. B. (2002). Mechanical and electrical properties of a MWNT/epoxy composite. Composites Sci. and Technol., 62, 1993—1998.
2. Allaoui A., Bai S., Cheng H. M., Bai J. B. (2002). Mechanical and electrical properties of a MWNT/epoxy composite. Composites Sci. and Technol., 62, 1993—1998.
https://doi.org/10.1016/S0266-3538(02)00129-X
3. Amabili M. (2010). A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. Int. J. Non-Linear Mech., 45, 409—418.
4. Amabili M. (2011). Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories. Composite Struct., 94, 207—220.
https://doi.org/10.1016/j.compstruct.2011.07.001
5. Andrews R., Jacques D., Minot M., Rantell T. (2002).Fabrication of carbon multiwall nanotube/polymer composites by shear mixing. Macromol. Mater. Eng., 287, 395—403.
5. Andrews R., Jacques D., Minot M., Rantell T. (2002).Fabrication of carbon multiwall nanotube/polymer composites by shear mixing. Macromol. Mater. Eng., 287, 395—403.
https://doi.org/10.1002/1439-2054(20020601)287:6<395::AID-MAME395>3.0.CO;2-S
6. Asadi H. (2017). Numerical simulation of the fluid-solid interaction for CNT reinforced functionally graded cylindrical shells in thermal environments. Acta Astronautica, 138, 214—224.
6. Asadi H. (2017). Numerical simulation of the fluid-solid interaction for CNT reinforced functionally graded cylindrical shells in thermal environments. Acta Astronautica, 138, 214—224.
https://doi.org/10.1016/j.actaastro.2017.05.039
7. Ci L., Bai J. B. (2006). The reinforcement role of carbon nanotubes in epoxy composites with different matrix stiffness. Composites Sci. and Technol., 66, 599—603.
7. Ci L., Bai J. B. (2006). The reinforcement role of carbon nanotubes in epoxy composites with different matrix stiffness. Composites Sci. and Technol., 66, 599—603.
https://doi.org/10.1016/j.compscitech.2005.05.020
8. Duc N. D., Cong P. H., Tuan N. D., Tran P., Thanh N. V. (2017). Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations. Thin-Walled Struct., 115, 300—310.
8. Duc N. D., Cong P. H., Tuan N. D., Tran P., Thanh N. V. (2017). Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations. Thin-Walled Struct., 115, 300—310.
https://doi.org/10.1016/j.tws.2017.02.016
9. Frikha A., Zghal S., Dammak F. (2014). Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. Computer Meth. Appl. Mech. and Eng., 358, 569—584.
10. Gao K., Gao W., Chen D., Yang J. (2018). Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation. Composite Struct., 204, 831—846.
9. Frikha A., Zghal S., Dammak F. (2014). Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. Computer Meth. Appl. Mech. and Eng., 358, 569—584.
10. Gao K., Gao W., Chen D., Yang J. (2018). Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation. Composite Struct., 204, 831—846.
https://doi.org/10.1016/j.compstruct.2018.08.013
11. García-Macías E., Rodríguez-Tembleque L., Sáez A. (2018). Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Composite Struct., 186, Р. 123—138.
11. García-Macías E., Rodríguez-Tembleque L., Sáez A. (2018). Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Composite Struct., 186, Р. 123—138.
https://doi.org/10.1016/j.compstruct.2017.11.076
12. Gholami R., Ansari R. (2018). Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Eng. Struct., 156, 197—209.
12. Gholami R., Ansari R. (2018). Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Eng. Struct., 156, 197—209.
https://doi.org/10.1016/j.engstruct.2017.11.019
13. Hu H., Onyebueke L., Abatan A. (2010). Characterizing and Modeling Mechanical Properties of Nanocomposites. Review and Evaluation. J. Miner. & Mater. Character. & Eng., 9 (4), 275—319.
13. Hu H., Onyebueke L., Abatan A. (2010). Characterizing and Modeling Mechanical Properties of Nanocomposites. Review and Evaluation. J. Miner. & Mater. Character. & Eng., 9 (4), 275—319.
https://doi.org/10.4236/jmmce.2010.94022
14. Kaser Y. D., Rossana T. F. (2012). Free vibration of FGCNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation. Composites Part B: Eng., 62, 231—241.
15. Kanagaraj S., Varanda F. R., Zhil’tsova T. V., Oliveira M., Simoes A. O. (2007). Mechanical properties of high density polyethylene/carbon nanotube composites. Composites Sci. and Technol., 67, 3071—3077.
14. Kaser Y. D., Rossana T. F. (2012). Free vibration of FGCNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation. Composites Part B: Eng., 62, 231—241.
15. Kanagaraj S., Varanda F. R., Zhil’tsova T. V., Oliveira M., Simoes A. O. (2007). Mechanical properties of high density polyethylene/carbon nanotube composites. Composites Sci. and Technol., 67, 3071—3077.
https://doi.org/10.1016/j.compscitech.2007.04.024
16. Khdeir A. A., Reddy J. N., Frederick D. (1989). A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories. J. Eng. Sci., 27 (N 11), 1337—1351.
16. Khdeir A. A., Reddy J. N., Frederick D. (1989). A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories. J. Eng. Sci., 27 (N 11), 1337—1351.
https://doi.org/10.1016/0020-7225(89)90058-X
17. Lei Z. X., Liew K. M., Yu J. L. (2013). Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Composite Struct., 106, 128—138.
17. Lei Z. X., Liew K. M., Yu J. L. (2013). Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Composite Struct., 106, 128—138.
https://doi.org/10.1016/j.compstruct.2013.06.003
18. Lei Z. X., Zhang L. W., Liew K. M (2015). . Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates. Int. J. Mech. Sci.s, 99, 208—217.
18. Lei Z. X., Zhang L. W., Liew K. M (2015). . Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates. Int. J. Mech. Sci.s, 99, 208—217.
https://doi.org/10.1016/j.ijmecsci.2015.05.014
19. Leissa A. W., Nordgren R. P. (1974). Vibration of Shells. J. Appl. Mech., 41 (N 2), 544—562.
19. Leissa A. W., Nordgren R. P. (1974). Vibration of Shells. J. Appl. Mech., 41 (N 2), 544—562.
https://doi.org/10.1115/1.3423343
20. Liew K. M., Lei Z. X., Yu J. L., Zhang L. W. (2014). Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach. Comput. Methods Appl. Mech. Eng., 268, 1—17.
20. Liew K. M., Lei Z. X., Yu J. L., Zhang L. W. (2014). Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach. Comput. Methods Appl. Mech. Eng., 268, 1—17.
https://doi.org/10.1016/j.cma.2013.09.001
21. Liu Y. J., Chen X. L. (2003). Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mech. Mater., 35, 69—81.
21. Liu Y. J., Chen X. L. (2003). Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mech. Mater., 35, 69—81.
https://doi.org/10.1016/S0167-6636(02)00200-4
22. Mehrabadi S. J., Aragh B. S. (2014). Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes. Thin-Walled Struct., 80, Р. 130—141.
22. Mehrabadi S. J., Aragh B. S. (2014). Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes. Thin-Walled Struct., 80, Р. 130—141.
https://doi.org/10.1016/j.tws.2014.02.016
23. Mehri M., Asadi H., Wang Q. (2016). On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow. Composite Struct., 153, 938—951.
23. Mehri M., Asadi H., Wang Q. (2016). On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow. Composite Struct., 153, 938—951.
https://doi.org/10.1016/j.compstruct.2016.07.009
24. Mehri M., Asadi H., Kouchakzadeh M. A. (2015). Computationally efficient model for flow-induced instability of CNT reinforced functionally graded conical curved panels subjected to axial compression. Computer Meth. Appl. Mech. and Eng., 932, 163—172.
24. Mehri M., Asadi H., Kouchakzadeh M. A. (2015). Computationally efficient model for flow-induced instability of CNT reinforced functionally graded conical curved panels subjected to axial compression. Computer Meth. Appl. Mech. and Eng., 932, 163—172.
25. Mehri M., Asadi H., Wang Q. (2016). On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow. Composite Struct., 153, 938—951.
https://doi.org/10.1016/j.compstruct.2016.07.009
26. Mehri M., Asadi H., Wang Q. (2009). Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method. Computer Meth. Appl. Mech. and Eng., 59, 1164—1176.
27. Messina A., Soldatos K. P. (1999). Ritz-type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions. J. Sound and Vibration, 227(4), 749—768.
26. Mehri M., Asadi H., Wang Q. (2009). Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method. Computer Meth. Appl. Mech. and Eng., 59, 1164—1176.
27. Messina A., Soldatos K. P. (1999). Ritz-type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions. J. Sound and Vibration, 227(4), 749—768.
https://doi.org/10.1006/jsvi.1999.2347
28. Moradi-Dastjerdi R., Foroutan M., Pourasghar A. (2013). Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Mater. and Design, 44, 256—266.
28. Moradi-Dastjerdi R., Foroutan M., Pourasghar A. (2013). Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Mater. and Design, 44, 256—266.
https://doi.org/10.1016/j.matdes.2012.07.069
29. Nejati M., Asanjarani A., Dimitri R., Tornabene F. (2011). Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes. Int. J. Mech. Sci., 95, 1221—1237.
30. Ninh D. G., Bich D. H. (2018). Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads. Aerospace Sci. and Technol., 77, 595—609.
29. Nejati M., Asanjarani A., Dimitri R., Tornabene F. (2011). Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes. Int. J. Mech. Sci., 95, 1221—1237.
30. Ninh D. G., Bich D. H. (2018). Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads. Aerospace Sci. and Technol., 77, 595—609.
https://doi.org/10.1016/j.ast.2018.04.008
31. Odegard G. M., Gates T. S., Wise K. E., Park C., Siochi E. J. (2003). Constitutive modeling of nanotube—reinforced polymer composites. Composites Sci. and Technol., 63, 1671—1687.
31. Odegard G. M., Gates T. S., Wise K. E., Park C., Siochi E. J. (2003). Constitutive modeling of nanotube—reinforced polymer composites. Composites Sci. and Technol., 63, 1671—1687.
https://doi.org/10.1016/S0266-3538(03)00063-0
32. Omidi M., Rokni H., Milani A. S., SeethalerR. J., Arasteh R. (2010). Prediction of the mechanical characteristics of multi-walled carbon nanotube/epoxy composites using a new form of the rule of mixtures. Carbon, 48, 3218—3228.
32. Omidi M., Rokni H., Milani A. S., SeethalerR. J., Arasteh R. (2010). Prediction of the mechanical characteristics of multi-walled carbon nanotube/epoxy composites using a new form of the rule of mixtures. Carbon, 48, 3218—3228.
https://doi.org/10.1016/j.carbon.2010.05.007
33. Reddy J. N. (1984). A simple higher-order theory for laminated composite plates. ASME J. Appl.Mech., 51, 745—752.
33. Reddy J. N. (1984). A simple higher-order theory for laminated composite plates. ASME J. Appl.Mech., 51, 745—752.
https://doi.org/10.1115/1.3167719
34. Reddy J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids and Struct., 20(9/10), 881—896.
34. Reddy J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids and Struct., 20(9/10), 881—896.
https://doi.org/10.1016/0020-7683(84)90056-8
35. Richard P., Prasse T., Cavaille J. Y., Chazeau L., Gauthier C., Duchet V. (2003). Reinforcement of rubbery epoxy by carbon nanofibres. Mater. Sci. and Eng., 352, 344—348.
35. Richard P., Prasse T., Cavaille J. Y., Chazeau L., Gauthier C., Duchet V. (2003). Reinforcement of rubbery epoxy by carbon nanofibres. Mater. Sci. and Eng., 352, 344—348.
https://doi.org/10.1016/S0921-5093(02)00895-X
36. Seidel G. D., Lagoudas D. C. (2006). Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mech. Mater., 38, 884—907.
36. Seidel G. D., Lagoudas D. C. (2006). Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mech. Mater., 38, 884—907.
https://doi.org/10.1016/j.mechmat.2005.06.029
37. Shen H. S. (2009). Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Struct., 91, 9—19.
37. Shen H. S. (2009). Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Struct., 91, 9—19.
https://doi.org/10.1016/j.compstruct.2009.04.026
38. Shen H. S., Xiang Y. (2012). Nonlinear vibration of nanotubereinforced composite cylindrical shells in thermal environments.Comput. Meth. Appl. Mech. Eng., 57, 196—205.
38. Shen H. S., Xiang Y. (2012). Nonlinear vibration of nanotubereinforced composite cylindrical shells in thermal environments.Comput. Meth. Appl. Mech. Eng., 57, 196—205.
https://doi.org/10.1016/j.cma.2011.11.025
39. Sobhaniaragh V., Batra R. C., Mansur W. J. Peters F. C. (2017). Thermal response of ceramic matrix nanocomposite cylindrical shells using Eshelby-Mori-Tanaka homogenization scheme. Composites Part B. Eng., 118.
39. Sobhaniaragh V., Batra R. C., Mansur W. J. Peters F. C. (2017). Thermal response of ceramic matrix nanocomposite cylindrical shells using Eshelby-Mori-Tanaka homogenization scheme. Composites Part B. Eng., 118.
40. Song Z. G., Zhang L. W., Liew K. M. (2014). Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments. Int. J. Mech. Sci., 264, 289—302.
41. Timarci T., Soldatos K. P. (1995). Comparative dynamic studies for symmetric cross — ply circular cylindrical shells on the basis of a unified shear deformable shell theory.J. Sound and Vibration, 187(4), 609—624.
41. Timarci T., Soldatos K. P. (1995). Comparative dynamic studies for symmetric cross — ply circular cylindrical shells on the basis of a unified shear deformable shell theory.J. Sound and Vibration, 187(4), 609—624.
https://doi.org/10.1006/jsvi.1995.0548
42. Wang A., Chen H., Hao Y., Zhang W. (2018). Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Results in Phys., 9, 550—559.
42. Wang A., Chen H., Hao Y., Zhang W. (2018). Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Results in Phys., 9, 550—559.
https://doi.org/10.1016/j.rinp.2018.02.062
43. Wang Q., Cui X., Qin B., Liang Q. (2003).Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions.Composite Struct., 132, 60—82.
44. Wang Q., Qin B., Shi D., Liang Q. (2015). A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution. Composite Struct., 28, 2574—2591.
45. Zhang L. W., Lei Z. X., Liew K. M., Yu J. L. (2014). Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Composite Struct., 111, 205—212.
43. Wang Q., Cui X., Qin B., Liang Q. (2003).Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions.Composite Struct., 132, 60—82.
44. Wang Q., Qin B., Shi D., Liang Q. (2015). A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution. Composite Struct., 28, 2574—2591.
45. Zhang L. W., Lei Z. X., Liew K. M., Yu J. L. (2014). Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Composite Struct., 111, 205—212.