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Simply supported boundary condition for bifurcation analysis of functionally graded material: Thickness control by exponential fraction law

  • Shadi Alghaffari (Department of Port and Maritime Transportation, Faculty of Maritime Studies, King Abdul Aziz University) ;
  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Faisal Al Thobiani (Department of Marine Engineering, Faculty of Maritime Studies, King Abdul Aziz University) ;
  • Hussain Talat Sulaimani (Department of Port and Maritime Transportation, Faculty of Maritime Studies, King Abdul Aziz University)
  • 투고 : 2021.11.02
  • 심사 : 2022.11.17
  • 발행 : 2023.04.25

초록

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

키워드

과제정보

This research work was funded by Institutional Fund Projects under grant no. (IFPIP-238-980-1443). Therefore, authors gratefully acknowledge the technical and financial support from the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

참고문헌

  1. Abouelregal, A.E., Mohammed, W.W. and Mohammad-Sedighi, H. (2021), "Vibration analysis of functionally graded microbeam under initial stress via a generalized thermoelastic model with dual-phase lags", Arch. Appl. Mech., 91(5), 2127-2142. https://doi.org/10.1007/s00419-020-01873-2. 
  2. Aboueregal, A.E. and Sedighi, H.M. (2021), "The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore-Gibson-Thompson heat conduction model", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(5), 1004-1020.  https://doi.org/10.1177/1464420720985899
  3. Akbas, S.D. (2016a), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125. 
  4. Akbas, S.D. (2016b), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59(3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579. 
  5. Akbas S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X. 
  6. Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009. 
  7. Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039. 
  8. Akbas, S.D. (2018b), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219-243. https://doi.org/10.12989/anr.2018.6.3.219. 
  9. Akbas, S.D. (2018c), "Forced vibration analysis of cracked nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(8), 1-11. https://doi.org/10.1007/s40430-018-1315-1. 
  10. Akbas, S.D. (2019), "Axially forced vibration analysis of cracked a nanorod", J. Comput. Appl. Mech., 50(1), 63-68. https://doi.org/10.22059/JCAMECH.2019.281285.392. 
  11. Akbas, S.D. (2020), "Modal analysis of viscoelastic nanorods under an axially harmonic load", Adv. Nano Res., 8(4), 277-282. https://doi.org/10.12989/anr.2020.8.4.277. 
  12. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., ... and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., 7(6), 443-457. https://doi.org/10.12989/anr.2019.7.6.443. 
  13. Civalek, O . (2020), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", Int. J. Numer. Meth. Eng., 121(5), 990-1019. https://doi.org/10.1002/nme.625. 
  14. Civalek, O. and Jalaei, M.H. (2020). "Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method", Acta Mechanica, 231(6), 2565-2587. https://doi.org/10.1002/nme.6254. 
  15. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene, F. (2019), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porositydependent homogenization scheme", Adv. Nano Res., 7(2), 135-143. https://doi.org/10.12989/anr.2019.7.2.135. 
  16. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039. 
  17. Ergin, A. and Temarel, P. (2002), "Free vibration of a partially liquid-filled and submerged, horizontal cylindrical shell", J. Sound Vib., 254(5), 951-965. https://doi.org/10.1006/jsvi.2001.4139. 
  18. Greif, R and Chung, H. (1975), "Vibration of constrained cylindrical shells", Am. Inst. Aeronaut. J., 13, 1190-1198. https://doi.org/10.2514/3.6970. 
  19. Iqbal, Z., Naeem, M.N., Sultana, N., Arshad, S.H. and Shah, A.G. (2009), "Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach", Appl. Math. Mech., 30, 1393-1404. https://doi.org/10.1007/s10483-009-1105-x. 
  20. Jena, S.K., Chakraverty, S., Malikan, M. and Sedighi, H. (2020), "Implementation of Hermite-Ritz method and Navier's technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using biHelmholtz nonlocal elasticity", J. Mech. Mater. Struct., 15(3), 405-434. https://doi.org/10.2140/jomms.2020.15.405. 
  21. Koochi, A. and Goharimanesh, M. (2021), "Nonlinear oscillations of CNT nano-resonator based on nonlocal elasticity: The energy balance method", Reports Mech. Eng., 2(1), 41-50. https://doi.org/10.31181/rme200102041g. 
  22. Loy, C.T. and Lam, K.Y. (1997), "Vibration of cylindrical shells with ring supports", J. Mech. Eng., 39, 455-471. https://doi.org/10.1016/S0020-7403(96)00035-5. 
  23. Loy, C.T. Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X 
  24. Ludwig, A. and R. Krieg (1981), "An analytical Quasi-exact method for calculating eigen vibrations of thin circular cylindrical shells", J. Sound Vib., 74, 155-174. https://doi.org/10.1016/0022-460X(81)90501-0. 
  25. Lyashenko, I.A., Borysiuk, V.N. and Popov, V.L. (2020), "Dynamical model of the asymmetric actuator of directional motion based on power-law graded materials", 18(2), 245-254. https://doi.org/10.22190/FUME200129020L. 
  26. Naeem, M.N. and Sharma, C.B. (2000), "Prediction of naturalfrequencies for thin circular cylindrical shells", Proc. Inst. Mech., 214(10), 1313-1328. https://doi.org/10.1243/0954406001523290. 
  27. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv. Nano Res., 7(4), 265-275. https://doi.org/10.12989/anr.2019.7.4.265. 
  28. Sarkheil, S., Foumani, M.S. and Navazi. H.M (2016), "Free vibration of bi-material cylindrical shells", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230, 2637-2649. https://doi.org/10.1177/0954406215602037 
  29. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Sizedependent vibration analysis of laminated composite plates", Adv. Nano Res., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337. 
  30. Shariati, A., Jung, D.W., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Materials, 13(7), 1707. https://doi.org/10.3390/ma13071707. 
  31. Swaddiwudhipong, S., Tian, J. and Wang, C.M. (1995), "Vibrations of cylindrical shells with intermediate supports", J. Sound Vib., 187(1), 69-93. https://doi.org/10.1006/jsvi.1995.0503. 
  32. Wang, C., and Lai, J.C.S. (2000), "Prediction of natural frequencies of finite length circular cylindrical shells", Appl. Acoust., 59(4), 385-400. https://doi.org/10.1016/S0003-682X(99)00039-0. 
  33. Zhang, L., Xiang, Y. and Wei, G.W. (2006), "Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions", Int. J. Mech. Sci., 48, 1126-1138. https://doi.org/10.1016/j.ijmecsci.2006.05.005.