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Mohammad Reza Assari Ali Kavoosi Nejad Shahryar Amirshirzad

Abstract

Functionally graded materials (FGMs) are materials that show different properties in different areas due to the gradual change of chemical composition, distribution, and orientation, or the size of the reinforcing phase in one or more dimensions. In this paper, the free vibrations of a thin cylindrical shell made of FGM is investigated. In order to investigate this problem, the first-order shear theory is used, by using relations related to the propagation of waves and fluid-structure interaction. Also, due to the rotational iner tia of first-order shear deformation and the fluid velocity potential, dynamic equation of functionally graded cylinder shell, containing current is obtained. Convergence of the solutions obtained from this method in different modes of boundary conditions as well as different geometric characteristics for the submerged cylinder and results of other studies and articles is showed. Also the effects of different parameters on the FGM cylindrical shell frequencies for the classical boundary conditions (compositions of simple, clamped, and free boundary conditions) are investigated against the ratio of length to the radius and the ratio of thickness to radius for different values of exponential power (exponential order) of FGM material. The results show that if the more density of the fluid in which the cylinder is submerged is lower, then the frequency values will be higher. Also, by examining the different fluid velocities, it can be seen that the effect of thickness change so that increas ing thickness causes the increase of effect of speed on the natural frequency reduction, especially in higher modes.

Article Details

Keywords

Functionally graded materials;, Natural frequencies of cylindrical shell;, First-order shear deformation theory;, Fluid-structure interaction;, Nonlinear vibrations;, Propagation method.

References
1. Abolghasemi, S., Eipakchi, H.R. and Shariati, M. Analytical solution for buckling of rectangular plates subjected to non-uniform in-plane loading based on first-order shear deformation theory, Modares Mechanical Engineering, 14 (2015), 37–46.
2. Benchouaf, L. and Boutyour, E.l. Nonlinear vibrations of buckled plates by an asymptotic numerical method, Comptes Rendus M´ecanique, 344 (2016), 151–166.
3. Benferhat, R., Hassaine Daouadji, T. and Said Mansoura, M. Free vibration analysis of FG plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory, Comptes Rendus M´ecanique, 344 (2016), 631–641.
4. Cherradi, D., Delfosse, B. and Kaw asaki, A. La Revue de Metallurgie, CIT, 34 (1996), 185–196.
5. Ebrahimi, F., Ghasemi, F. and Salari, E. Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica, 51 (2016), 223–249.
6. Ergin, A. and Urlu B. Linear vibration analysis of cantilever plates partially Submerged in fluid, J. Fluid Struct. 17 (2003), 927–939.
7. Farahani, H., Azarafza, R. and Barati, F. Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory, Comptes Rendus M´ecaniqu, 342 (2014), 501–512.
8. Ghasemi, M.A., Yazdani, M. and Soltan Abadi, E. Buckling behavior investigation of grid stiffened composite conical shells under axial loading, Modares Mechanical Engineering, 14 (2015), 170–176.
9. Guo, X.Y. and Zhang, W. Nonlinear vibrations of a reinforced composite plate with carbon nanotubes, Compos. Struct. 135 (2016), 96–108.
10. Haddara, M.R. and Cao, S. A study of the dynamic response of submerged Rectangular flat plates, Mar. Struct. 9 (1996), 913–933.
11. Cahn, R.W., Haasen, P. and Kramer, E.J. Materials science and technology:A Comprehensive catchment, Materials Science and Technology, VCH, 1996.
12. Hosseini-Hashemi, Sh., Fadaee M. and Atashipour S.R. Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure, Compos. Struct. 93 (2011), 722–735.
13. Hosseini-Hashemi, Sh., Rokni-Damavandi-Taher, H., Akhavan, H. and Omidi, M. Free vibration of functionally graded rectangular plates use first-order shear deformation plate theory, Appl. Math. Model. 34 (2010), 1276–1291.
14. Igbal, Z., Naeem, M.N. and Sultana, N. Vibration characteristics of FGM circular cylindrical shells using wave propagation approach, Acta Mech. (2009), 237–248.
15. Jeong, K.H., Yoo, G.H. and Lee, S.C. Hydroelastic vibration of two identical rectangular plates, J. Sound Vib. 272 (2003), 539–555.
16. Khorshidi, K. Effect of Hydrostatic pressure on vibrating rectangular plates coupled with fluid, Sci. IRAN. 17 (2010), 415–429.
17. Khorshidi, K. and Farhadi, S. Free vibration analysis of laminated composite rectangular plate in contact with bounded fluid, Compos. Struct. 104 (2013) 176–186.
18. Kwak, M.K. Hydroelastic vibration of rectangular plates, J. Appl. Mech. Mar. 63 (1996), 110–115.
19. Leissa, A.W. Vibration of shells, NASA SP-288, Reprinted by Acoustical Society of America, America institute of Physics, (1993).
20. Liang, C.C., Liao, C.C., Tai, Y.S. and Lai, W.H. The free vibration analysis of Submerged cantilever plates, Ocean Eng. 28 (2001), 1225–1245.
21. Mirzaei, M. and Kiani, Y. Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation, Compos. Struct. 180 (2017), 606–616.
22. Morse M. and Ingard, K.U. Theoretical Acoustics, Am. J. Phys. 38 (1970), 666–667.
23. Robinson, N.J. and Palmer, S.C. A modal analysis of a rectangular plate floating On an incompressible liquid, J. Sound Vib. 142 (1990), 435–460.
24. Shah, G., Mahmood, T., Naeem, M.N. and Arshad, S.H. Vibration characteristics of fluid-filled cylindrical shells based on elastic foundations, Acta Mech. 216 (2011), 17–28.
25. Shen, H.S. and Chen, T.Y. Buckling and postbuckling behavior of cylindrical shells under combined external pressure and axial compression, Thin-Walled Struct. 12 (1991), 321–334.
26. Shen, H.S., Xiang, Y. and Lin, F. Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments, Compos. Struct. 170 (2017), 80–90.
27. Shen, H.S., Xiang, Y. and Lin, F. Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments, Comput. Methods Appl. Mech. Eneg. 319 (2017), 175–193.
28. Shen, H.S., Xiang, Y. and Lin, F. Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates rest ing on elastic foundations, Thin-Walled Struct. 118 (2017), 229–237.
29. Shen, H.S., Xiang, Y., Lin, F. and D. Hui, Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments, Composites, 119 (2017), 67–78.
30. Song, M., Kitipornchai, S. and Yang, J. Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos. Struct. 159 (2017), 579–588.
31. Talha, M. and Singh, B.N. Static response and free vibration analysis of FGM Plates using higher order shear deformation theory, Appl. Math. Model. 34 (2009), 3991–4011.
32. Yadykin, Y., Tenetov, V. and Levin, D. The added mass of flexible plate oscillating in fluid, J. Fluids Struct. 17 (2003), 115–123.
33. Yu, Y., Shen, H.S., Wang, H. and Hui, D. Postbuckling of sandwich plates with grapheme reinforced composite face sheets in thermal environments, Compos. B. Eng. 135 (2018), 72–83.
34. Zhang, X.M., Liu, G.R. and Lam K.Y. , Vibration analysis of thin cylindrical shells using wave propagation approach, J. Sound Vib. 239 (2001), 397–403.
35. Zhao, X., Lee, Y.Y. and Liew, K.M. Free vibration analysis of function ally graded plates using the element-free kp-Ritz method, J. Sound Vib. 319 (2009), 918–939.
36. Zhou, D. and Cheung, Y.K. Vibration of vertical rectangular plate in contact with water on one side, Earthq. Eng. Struct. Dyn. 29 (2000), 693–710.
37. Zhou, D. and Liu, W. Hydroelastic vibrations of flexible rectangular tanks partially filled with liquid, Int. J. Numer. Meth. Eng. 71 (2007), 149–174.
How to Cite
AssariM. R., Kavoosi NejadA., & AmirshirzadS. (2020). Nonlinear vibrations of functionally graded cylindrical shell by using numerical analysis in the wave propagation method. Iranian Journal of Numerical Analysis and Optimization, 10(2), 241-264. https://doi.org/10.22067/ijnao.v10i2.81592
Section
Research Article