Free vibrations of functionally gradient CNT-infused cylindrical shells
Heading:
| 1Avramov, KV, 1Chernobryvko, MV, 1Uspensky, BV 1A. N. Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine |
| Space Sci. & Technol. 2019, 25 ;(2):23-37 |
| https://doi.org/10.15407/knit2019.02.023 |
| Publication Language: Ukrainian |
Abstract: Currently, in the world aerospace industry, metals and their alloys are widely replaced by polymer composite materials reinforced with carbon nanotubes (CNT). This is due to the much higher durability of the nanocomposites compared to aluminum alloys under high-intensity loads. Cylindrical nanocomposite rocket body elements can be reinforced with carbon nanotubes using different distribution across the matrix thickness. Currently, there are five main types of CNT-reinforcement, which lead to the formation of a functional-graded material through the thickness of the shell. Analysis of vibrations in aerospace units’ elements must be conducted considering the possibility of a resonance between the structure and aerodynamic loads. An integral part of this analysis is the analysis of free oscillations of the shell, which is carried out to determine and prevent dangerous resonant modes.
Classical oscillation models of cylindrical shells do not allow taking into consideration material properties varying within shell thickness. This paper proposes a technique of analysis of free vibrations in functionally graded nanocomposite cylindrical shells, which can be an integral part of rocket complexes and aircraft structures. The dependencies of the vibration parameters on the type of the reinforcement, a volume fraction of carbon nanotubes in the composite, and the shell thickness are considered. The results of the analytical study are compared with numerical simulation based on the finite element method. The proposed model takes into consideration the material properties varying within shell thickness for five common cases of CNT-reinforcement. It is shown that detuning of nanocomposite shells from resonant modes can be carried out by a rational choice of the type of the CNT-reinforcement.
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| Keywords: CNT-infused composite, cylindrical shell, eigen frequencies, free vibrations, functionally gradient material, nanotube |
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.
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.
https://doi.org/10.1016/j.ijnonlinmec.2009.12.013
4. Amabili M. (2011). Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories. Composite Struct., 94, 207—220.
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.