Dynamic instability of a compound nanocomposite shell
Heading:
| 1Sakhno, NH, 1Avramov, KV, 1Uspensky, BV 1A. N. Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine |
| Space Sci. & Technol. 2021, 27 ;(5):060-070 |
| https://doi.org/10.15407/knit2021.05.060 |
| Publication Language: Ukrainian |
Abstract: Free oscillations and dynamic instability due to supersonic airflow pressure are investigated in a functional-gradient compound composite conical-cylindrical shell made of a carbon nanotubes-reinforced material. Nanocomposite materials with a linear distribution of the volumetric fraction of nanotubes over the thickness are considered. Extended mixture rule is used to estimate nanocomposite’s mechanical characteristics. A high-order shear deformation theory is used to represent the shell deformation. The assumed-mode technique, along with a Rayleigh-Ritz method, is applied to obtain the equations of the structure motion. To analyze the compound structure dynamics, a new system of piecewise basic functions is suggested. The pressure of a supersonic flow on the shell is obtained by using the piston theory.
An example of the dynamic analysis of a nanocomposite conical-cylindrical shell in the supersonic gas flow is considered. The results of its modal analysis using the Rayleigh-Ritz technique are close to the natural frequencies of the shell obtained by finite element analysis. In this case, finite element analysis can only be used for shells made of material with a uniform distribution of nanotubes over the thickness. The dependence of the natural frequencies of a compound shell on the ratio of the lengths of the conical and cylindrical parts is studied. The dependence of the critical pressure of a supersonic flow on the Mach numbers and the type of carbon nanotubes reinforcement is investigated. Shells with a concentration of nanotubes predominantly near the outer and inner surfaces are characterized by higher values of natural frequencies and critical pressure than the shells with a uniform distribution of nanotubes or with a predominant concentration of nanotubes inside the shell.
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| Keywords: assumed-mode method, dynamic instability, functionally graded carbon nanotubes, joined conical-cylindrical shell in supersonic flow, reinforced composite |
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https://doi.org/10.1016/j.compstruct.2013.12.035
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https://doi.org/10.1016/j.cma.2017.07.014
https://doi.org/10.1016/j.ijnonlinmec.2014.11.026
2. Asadi H. (2018). Numerical simulation of the fluid-solid interaction for CNT reinforced functionally graded cylindrical shells in thermal environments. Acta Astronaut., 138, 214-224.
https://doi.org/10.1016/j.actaastro.2017.05.039
3. Avramov K. V., Chernobryvko M. V., Kazachenko O., Batutina T. J. (2016). Dynamic instability of parabolic shells in supersonic gas stream. Meccanica, 51, 939-950.
https://doi.org/10.1007/s11012-015-0247-4
4. Avramov K V., Chernobryvko M., Uspensky B., Seitkazenova K. K., Myrzaliyev D. (2019). Self-sustained vibrations of functionally graded carbon nanotubes-reinforced composite cylindrical shells in supersonic flow. Nonlinear Dynamics, 98(3), 1853-1876.
https://doi.org/10.1007/s11071-019-05292-z
5. Caresta M., Kessissoglou N. (2010). Free vibrational characteristics of isotropic coupled cylindrical-conical shells. J. Sound and Vib., 329 (6), 733-751.
https://doi.org/10.1016/j.jsv.2009.10.003
6. Chernobryvko M. V., Avramov K. V., Romanenko V. N., Batutina T. J., Tonkonogenko A. M. (2014). Free linear vibrations of parabolic shells. Meccanica, 49 (8), 14-21.
https://doi.org/10.1007/s11012-014-0027-6
7. ChwaЕ‚ M., Muc A. (2019). Buckling and free vibrations of nanoplates-comparison of nonlocal strain and stress approaches. Appl. Sci., 9, 1409.
https://doi.org/10.3390/app9071409
8. Hoff N. J. (1951). The dynamics of the buckling of elastic columns. Proc. of the Soc. for Exper. Stress analysis, 9 (1), 68-74.
https://doi.org/10.1115/1.4010222
9. Hu W. C. L., Raney J. P. (1965). Experimental and analytical study of vibrations of joined shells. AIAA J.,5(5), 976-980.
https://doi.org/10.2514/3.4111
10. Irie T., Yamada G., Myramoto Y. (1984). Free vibration of joined conical-cylindrical shells. J. Sound and Vib., 95(1), 31-39.
https://doi.org/10.1016/0022-460X(84)90256-6
11. GarcГa-MacГas E., RodrГguez-Tembleque L., SГЎez A. (2018). Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Composite Struct., 186, 123-138.
https://doi.org/10.1016/j.compstruct.2017.11.076
12. Krumhaar Hans (1963). The accuracy of linear piston theory when applied to cylindrical shells. AIAA J., 1 (6), 1448-1449.
https://doi.org/10.2514/3.1832
13. Lashkari M., Weingarten V. I. (1973). Vibrations of segmented shells. Exp. Mech., 13(3), 120-125.
https://doi.org/10.1007/BF02323969
14. Lei Z. X., Zhang L. W., Liew K. W. (2016). Buckling analysis of CNT reinforced functionally graded laminated composite plates. Composite Struct., 152, 62-73.
https://doi.org/10.1016/j.compstruct.2016.05.047
15. Liu Y. J., Chen X. L. (2003). Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, 35, 69-81.
https://doi.org/10.1016/S0167-6636(02)00200-4
16. Mehar K., Panda S. K., Mahapatra T. R. (2017). Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure. Int. J. mech. Sci., 133, 319-329.
https://doi.org/10.1016/j.ijmecsci.2017.08.057
17. Mehri M., Asadi H., Kouchakzadeh M. A. (2017). Computationally efficient model for flow-induced instability of CNT reinforced functionally graded truncated conical curved panels subjected to axial compression. Comput. Methods Appl. Mech. Energ, 318, 957-980.
https://doi.org/10.1016/j.cma.2017.02.020
18. 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
19. Meirovitch L. (1998). Elements of vibration analysis. New York: McGraw-Hill Publishing Company, 560 p.
20. Moradi-Dastjerdi R., Foroutan M., Pourasghar A. (2013). Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Materials and Design, 44, 256-266.
https://doi.org/10.1016/j.matdes.2012.07.069
21. Odegard G. M., Gates T. S., Wise K. E., Park C., Siochi E. J. (2003). Constitutive modeling of nanotube-reinforced polymer composites. Composites Science and Technology, 63, 1671-1687.
https://doi.org/10.1016/S0266-3538(03)00063-0
22. Reddy J. N. (1984). A simple higher-order theory for laminated composite plates. ASME J. Applied Mechanics,51, 745-752.
https://doi.org/10.1115/1.3167719
23. Reddy J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids and Structures, 20(9/10), 881-896.
https://doi.org/10.1016/0020-7683(84)90056-8
24. Ritz W. (1909). Uber eine Methode zur Losung gewisser Vatiations probleme der mathematiscen Physik. J. fur die reine und angewandte Mathematik. Bd 135, Heft 1, 61 S.
https://doi.org/10.1515/crll.1909.135.1
25. Seidel G. D., Lagoudas D. C. (2006). Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mechanics of Materials, 38, 884-907.
https://doi.org/10.1016/j.mechmat.2005.06.029
26. Sivadas K. R., Ganesan N. (1990). Free vibration of cantilever conical shells with variable thickness. Comput. Struct.,36(3), 559-566.
https://doi.org/10.1016/0045-7949(90)90290-I
27. Strutt J. W. (Rayleigh) The theory of sound. 2nd edition. London and New York, McMillan and Co, (1894) V. 1, 480 p.; (1896) V. 2, 504 p.
28. 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
29. 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.
https://doi.org/10.1016/j.compstruct.2013.12.035
30. Zhang L. W., Song Z. G., Liew K. M. (2017). Modeling aerothermoelastic properties and active flutter control of nanocomposite cylindrical shells in supersonic airflow under thermal environments. Comput. Methods Appl. Mech. Eng., 325, 416-433.
https://doi.org/10.1016/j.cma.2017.07.014