Geomechanics and Engineering

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Development of orthotropic Winkler-like model for rotating cylindrical shell: Stability analysis

  • Khadimallah, Mohamed Amine (Department of Civil Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Yahya, Ahmad (Nuclear Engineering Department, King Abdulaziz University) ;
  • Elimame, Elaloui (Laboratory of Materials Applications in Environment, Water and Energy LR21ES15, Faculty of Sciences, University of Gafsa) ;
  • Tounsi, Abdelouahed (Yonsei Frontier Lab, Yonsei University)
  • Received : 2020.06.27
  • Accepted : 2021.07.29
  • Published : 2021.08.10
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Abstract

Vibration investigation of rotating functionally graded cylindrical shells with fraction laws is studied here. Shell motion equations are framed according to the orthotropic Winkler-like model. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. The influence of the polynomial, exponential and trigonometric fraction laws is investigated with simply supported condition. Also the variations have been plotted against the circumferential wave mode, length-to-radius and height-to-radius ratio. Moreover, backward and forward frequency pattern is observed increasing and decreasing for the various position of angular speed. The frequency first increases and gain maximum value for circumferential wave number. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. The frequencies of trigonometric law is less than remaining laws.

Keywords

Acknowledgement

This project was supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under research project no. 2020/01/16794.

References

  1. Ahmad, M. and Naeem, M.N. (2009), "Vibration characteristics of rotating FGM circular cylindrical shell using wave propagation method", Eur. J. Sci. Res., 36(2), 184-235.
  2. Alzabeebee, S. (2020), "Dynamic response and design of a skirted strip foundation subjected to vertical vibration", Geomech. Eng., 20(4), 2020, 345-358. https://doi.org/10.12989/gae.2020.20.4.345.
  3. Amabili, M., Pellicano, F. and Paidoussis M.P. (1998), "Nonlinear vibrations of simply Love, A.E.H. (1888), 'On the small free vibrations and deformation of thin elastic shell'", Phil. Trans. Royal Soc. London, A179, 491-549. https://doi.org/10.1098/rsta.1888.0016.
  4. Asadijafari, M.H., Zarastvand, M.R. and Talebitooti, R. (2021), "The effect of considering Pasternak elastic foundation on acoustic insulation of the finite doubly curved composite structures", Compos. Struct., 256, 113064. https://doi.org/10.1016/j.compstruct.2020.113064.
  5. Bouanati, S., Benrahou, K.H., Atmane, H.A., Yahia, S.A., Bernard, F., Tounsi, A. and Bedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085.
  6. Bouazza, M., Antar, K., Amara, K., Benyoucef, S. and Bedia, E.A. A. (2019), "Influence of temperature on the beams behavior strengthened by bonded composite plates", Geomech. Eng., 18(5), 555-566. https://doi.org/10.12989/gae.2019.18.5.555.
  7. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A. A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  8. Bryan, G.H. (1890), "On the beats in the vibration of revolving cylinder", Proc. Cambridge Philosoph. Soc., 7, 101-111.
  9. Chen, Y., Zhao, H.B. and Shea, Z.P. (1993a), "Vibrations of high speed rotating shells with calculations for cylindrical shells", J. Sound Vib., 160, 137-160. https://doi.org/10.1006/jsvi.1993.1010.
  10. Chen, Y., Zhao, H.B. and Shin, Z.P. (1993b), "Vibration of high speed rotating shells with calculation for cylindrical shells", J. Sound Vib., 160, 137. https://doi.org/10.1006/jsvi.1993.1010.
  11. Chung, H., Turula, P. Mulcahy, T.M. and Jendrzejczyk, J.A. (1981), "Analysis of cylindrical shell vibrating in a cylindrical fluid region", Nucl. Eng. Des., 63(1), 109-120. https://doi.org/10.1016/0029-5493(81)90020-0.
  12. Darvish Gohari, H., Zarastvand, M. and Talebitooti, R. (2020), "Acoustic performance prediction of a multilayered finite cylinder equipped with porous foam media", J. Sound Vib., 26(11-12), 899-912. https://doi.org/10.1177/1077546319890025.
  13. Darvishgohari, H., Zarastvand, M., Talebitooti, R. and Shahbazi, R. (2019), "Hybrid control technique for vibroacoustic performance analysis of a smart doubly curved sandwich structure considering sensor and actuator layers", J. Sandw. Struct. Mater., 1099636219896251. https://doi.org/10.1177/1099636219896251.
  14. Di Taranto, R.A. and Lessen, M. (1964), "Coriolis acceleration effect on the vibration of rotating thin-walled circular cylinder", J. Appl. Mech., 31, 700-701. https://doi.org/10.1115/1.3629733.
  15. 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.
  16. Flugge, W. (1967), Stresses in Shells, 2nd Edition, Springer-Verlag, Berlin, Germany.
  17. Forsberg, K. (1964), "Influence of boundary conditions on modal characteristics of cylindrical shells", AIAA J., 2, 182-189. https://doi.org/10.2514/3.55115.
  18. Fox, C.H.J. and Hardie, D.J.W. (1985), "Harmonic response of rotating cylindrical shell", J. Sound Vib., 101, 495-510. https://doi.org/10.1016/S0022-460X(85)80067-5.
  19. Ghosh, A., Miyamoto, Y., Reimanis, I. and Lannutti, J.J. (1997), "Functionally graded materials, manufacture, properties and applications. Ceramic Transactions", Am. Ceram. Soc., 76, 171-189.
  20. Gohari, H. D., Zarastvand, M.R., Talebitooti, R., Loghmani, A. and Omidpanah, M. (2020), "Radiated sound control from a smart cylinder subjected to piezoelectric uncertainties based on sliding mode technique using self-adjusting boundary layer", Aerosp. Sci. Tech., 106, https://doi.org/10.1016/j.ast.2020.106141.
  21. Jweeg, M.J. and Alazzawy, W.I. (2007), "A suggested analytical solution for laminated closed cylindrical shells using General Third Shell Theory (GTT)", Al-Nahrain J. Eng. Sci., 10(1), 11-26.
  22. Jweeg, M.J., Alazzawy, W.I. and Dep, M.E. (2010), "A study of free vibration and fatigue for cross-ply closed cylindrical shells using General Third shell Theory (GTT)", J. Eng., 16(6), 5170-5184.
  23. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  24. Lam K.Y. and Loy, C.T. (1994), "On vibration of thin rotating laminated composite cylindrical shells", J. Sound Vib., 116, 198. https://doi.org/10.1016/0961-9526(95)91289-S.
  25. Lam, K.Y. and Loy, C.T. (1998), "Influence of boundary conditions for a thin laminated rotating cylindrical shell", Compos. Struct., 41(3-4), 215-228. https://doi.org/10.1016/S0263-8223(98)00012-9.
  26. Lata, P. and Kaur, H. (2019), "Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain", Geomech. Eng., 19(5), 369-381. https://doi.org/10.12989/gae.2019.19.5.369.
  27. Li, H. and Lam, K.Y. (1998), "Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method", Int. J. Mech. Sci., 40(5), 443-459. https://doi.org/10.1016/S0020-7403(97)00057-X.
  28. Najafizadeh, M.M. and Isvandzibaei, M.R. (2007), "Vibration of (FGM) cylindrical shells based on higher order shear deformation plate theory with ring support", Acta Mech., 191, 75-91. http/10.1007/s00707-006-0438-0.
  29. Padovan, J. (1975), "Travelling waves vibrations and buckling of rotating anisotropic shells of revolution by finite element", Int. J. Solid Struct., 11(12), 1367-1380. https://doi.org/10.1016/0020-7683(75)90064-5.
  30. Penzes, R.L.E. and Kraus H. (1972), "Free vibrations of pre-stresses cylindrical shells having arbitrary homogeneous boundary conditions", AIAA J., 10, 1309. https://doi.org/10.2514/3.6605.
  31. Saito, T. and Endo, M. (1986), "Vibrations of finite length rotating cylindrical shell", J. Sound Vib., 107(1), 17-28. https://doi.org/10.1016/0022-460X(86)90279-8.
  32. Sewall, J.L. and Naumann, E.C. (1968), "An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners", National Aeronautic and Space Administration; for sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia, U.S.A.
  33. Sharma, P., Singh, R. and Hussain, H. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. https://doi.org/10.1177/0954406219888234.
  34. Sivadas, K.R. and Ganesan, N. (1964), "Effect of rotation on vibrations of moderately thin cylindrical shell", J. Vib. Acous., 116(1), 198-202. https://doi.org/10.1115/1.2930412.
  35. Srinivasan, A.V. and Luaterbach, G.F. (1971), "Travelling waves in rotating cylindrical shells", J. Eng. Industr., 93, 1229-1232. https://doi.org/10.1115/1.3428067.
  36. Suresh, S. and Mortensen, A. (1997), "Functionally gradient metals and metal ceramic composites, Part 2: Thermo Mechanical Behavior", Int. Mater Rev., 42(3), 85-116. https://doi.org/10.1179/imr.1997.42.3.85.
  37. Swaddiwudhipong, S., Tian, J. and Wang, C.M. (1995), "Vibration of cylindrical shells with ring supports", J. Sound Vib., 187(1), 69-93. https://doi.org/10.1006/jsvi.1995.0503.
  38. Talebitooti, R. and Zarastvand, M.R. (2018a), "The effect of nature of porous material on diffuse field acoustic transmission of the sandwich aerospace composite doubly curved shell", Aerosp. Sci. Tech., 78, 157-170. https://doi.org/10.1016/j.ast.2018.03.010.
  39. Talebitooti, R. and Zarastvand, M.R. (2018b), "Vibroacoustic behavior of orthotropic aerospace composite structure in the subsonic flow considering the Third order Shear Deformation Theory", Aerosp. Sci. Tech., 75, 227-236. https://doi.org/10.1016/j.ast.2018.01.011.
  40. Talebitooti, R., Darvish Gohari, H., Zarastvand, M. and Loghmani, A. (2019), "A robust optimum controller for suppressing radiated sound from an intelligent cylinder based on sliding mode method considering piezoelectric uncertainties", J. Intell. Mater. Syst. Struct., 30(20), 3066-3079. https://doi.org/10.1177/1045389X19873412.
  41. Talebitooti, R., Zarastvand, M.R. and Gheibi, M.R. (2016), "Acoustic transmission through laminated composite cylindrical shell employing third order shear deformation theory in the presence of subsonic flow", Compos. Struct., 157, 95-110. https://doi.org/10.1016/j.compstruct.2016.08.008.
  42. Talebitooti, R., Zarastvand, M.R. and Gohari, H.D. (2018), "The influence of boundaries on sound insulation of the multilayered aerospace poroelastic composite structure", Aerosp. Sci. Tech., 80, 452-471. https://doi.org/10.1016/j.ast.2018.07.030.
  43. Talebitooti, R., Zarastvand, M. and Darvishgohari, H. (2019), "Multi-objective optimization approach on diffuse sound transmission through poroelastic composite sandwich structure", J. Sandw. Struct. Mater., 23(4), 1221-1252. https://doi.org/10.1177/1099636219854748.
  44. Uyar, G.G. and Aksoy, C.O. (2019), "Comparative review and interpretation of the conventional and new methods in blast vibration analyses", Geomech. Eng., 18(5), 545-554. https://doi.org/10.12989/gae.2019.18.5.545.
  45. Wang S.S. and Chen, Y. (1974), "Effects of rotation on vibrations of circular cylindrical shells", J. Acous. Soc. Amer., 55, 1340-1342. https://doi.org/10.1121/1.1914708.
  46. Warburton G.B. (1965), "Vibration of thin cylindrical shells", J. Mech. Eng. Sci., 7, 1965. 399-407. https://doi.org/10.1243/JMES_JOUR-1965-007-062-02.
  47. Zarastvand, M.R., Asadijafari, M.H. and Talebitooti, R. (2021), "Improvement of the low-frequency sound insulation of the poroelastic aerospace constructions considering Pasternak elastic foundation", Aerosp. Sci. Tech., 112, 106620. https://doi.org/10.1016/j.ast.2021.106620.
  48. Zarastvand, M.R., Ghassabi, M. and Talebitooti, R. (2019), "Acoustic insulation characteristics of shell structures: A review", Arch. Comput. Meth. Eng., 1-19. https://doi.org/10.1007/s11831-019-09387-z.
  49. Zohar, A. and Aboudi, J. (1973), "The free vibrations of thin circular finite rotating cylinder", Int. J. Mech. Sci., 15, 269-278. https://doi.org/10.1016/0020-7403(73)90009-X.