Steel and Composite Structures

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Nonlinear dynamic analysis of spiral stiffened cylindrical shells rested on elastic foundation

  • Foroutan, Kamran (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Shaterzadeh, Alireza (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Ahmadi, Habib (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
  • Received : 2019.01.07
  • Accepted : 2019.07.30
  • Published : 2019.08.25
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Abstract

In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

Keywords

References

  1. Bich, D.H., Van Dung, D. and Nam, V.H. (2012), "Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels", Compos. Struct., 94(8), 2465-2473. https://doi.org/10.1016/j.compstruct.2012.03.012
  2. Bich, D.H., Van Dung, D., Nam, V.H. and Phuong, N.T. (2013), "Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression", Int. J. Mech. Sci., 74, 190-200. https://doi.org/10.1016/j.ijmecsci.2013.06.002
  3. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, NY, USA.
  4. Chen, M., Xie, K., Jia, W. and Xu, K. (2015), "Free and forced vibration of ring-stiffened conical-cylindrical shells with arbitrary boundary conditions", Ocean Eng., 108, 241-256. https://doi.org/10.1016/j.oceaneng.2015.07.065
  5. Choe, K., Tang, J., Shui, C., Wang, A. and Wang, Q. (2018a), "Free vibration analysis of coupled functionally graded (fg) doubly-curved revolution shell structures with general boundary conditions", Compos. Struct., 194, 413-432. https://doi.org/10.1016/j.compstruct.2018.04.035
  6. Choe, K., Wang, Q. and Tang, J. (2018b), "Vibration analysis for coupled composite laminated axis-symmetric doubly-curved revolution shell structures by unified jacobi-ritz method", Compos. Struct., 194, 136-157. https://doi.org/10.1016/j.compstruct.2018.03.095
  7. Darabi, M., Darvizeh, M. and Darvizeh, A. (2008), "Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading", Compos. Struct., 83(2), 201-211. https://doi.org/10.1016/j.compstruct.2007.04.014
  8. Dey, T. and Ramachandra, L. (2017), "Non-linear vibration analysis of laminated composite circular cylindrical shells", Compos. Struct., 163, 89-100. https://doi.org/10.1016/j.compstruct.2016.12.018
  9. Duc, N.D. and Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened s-fgm circular cylindrical shells surrounded on elastic foundations", Aer. Sci. Technol., 40, 115-127. https://doi.org/10.1016/j.tws.2017.04.013
  10. Duc, N.D., Nguyen, P.D. and Khoa, N.D. (2017), "Nonlinear dynamic analysis and vibration of eccentrically stiffened s-fgm elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin Wall. Struct., 117, 178-189. https://doi.org/10.1016/j.tws.2017.04.013
  11. Dung, D. and Nam, V.H. (2014), "Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium", Eur. J. Mech. A-Solid., 46, 42-53. https://doi.org/10.1016/j.euromechsol.2014.02.008
  12. Foroutan, M., Moradi-Dastjerdi, R. and Sotoodeh-Bahreini, R. (2012), "Static analysis of fgm cylinders by a mesh-free method", Steel Compos. Struct., Int. J., 12(1), 1-11. https://doi.org/10.12989/scs.2012.12.1.001
  13. Ghiasian, S., Kiani, Y. and Eslami, M. (2013), "Dynamic buckling of suddenly heated or compressed fgm beams resting on nonlinear elastic foundation", Compos. Struct., 106, 225-234. https://doi.org/10.1016/j.compstruct.2013.06.001
  14. He, X., Li, L., Kitipornchai, S., Wang, C. and Zhu, H. (2012), "Bi-stable analyses of laminated fgm shells", Int. J. Struct. Stab. Dyn., 12(2), 311-335. https://doi.org/10.1142/S0219455412500058
  15. Javed, S., Viswanathan, K.K. and Aziz, Z.A. (2016), "Free vibration analysis of composite cylindrical shells with non-uniform thickness walls", Steel Compos. Struct., Int. J., 20(5), 1087-1102. https://doi.org/10.12989/scs.2016.20.5.1087
  16. Khayat, M., Dehghan, S.M., Najafgholipour, M.A. and Baghlani, A. (2018), "Free vibration analysis of functionally graded cylindrical shells with different shell theories using semi-analytical method", Steel Compos. Struct., Int. J., 28(6), 735-748. https://doi.org/10.12989/scs.2018.28.6.735
  17. Kiani, Y., Dimitri, R. and Tornabene, F. (2018a), "Free vibration study of composite conical panels reinforced with FG-CNTs", Eng. Struct., 172, 472-482. https://doi.org/10.1016/j.engstruct.2018.06.006
  18. Kiani, Y., Dimitri, R. and Tornabene, F. (2018b), "Free vibration of fg-cnt reinforced composite skew cylindrical shells using the chebyshev-ritz formulation", Compos. Part B-Eng., 147, 169-177. https://doi.org/10.1016/j.compositesb.2018.04.028
  19. Lee, H. and Kwak, M.K. (2015), "Free vibration analysis of a circular cylindrical shell using the rayleigh-ritz method and comparison of different shell theories", J. Sound Vib., 353, 344-377. https://doi.org/10.1016/j.jsv.2015.05.028
  20. Malikan, M., Dimitri, R. and Tornabene, F. (2018), "Effect of sinusoidal corrugated geometries on the vibrational response of viscoelastic nanoplates", Appl. Sci., 8(9), 1432. https://doi.org/10.3390/app8091432
  21. Mochida, Y., Ilanko, S., Duke, M. and Narita, Y. (2012), "Free vibration analysis of doubly curved shallow shells using the superposition-galerkin method", J. Sound Vib., 331(6), 1413-1425. https://doi.org/10.1016/j.jsv.2011.10.031
  22. Mohammadi, M., Arefi, M., Dimitri, R. and Tornabene, F. (2019), "Higher-order thermo-elastic analysis of FG-CNTRC cylindrical vessels surrounded by a Pasternak foundation", Nanomaterials, 9(1), 79. https://doi.org/10.3390/nano9010079
  23. Nayfeh, A.H. and Mook, D.T. (2008), Nonlinear Oscillations, John Wiley & Sons.
  24. Nejati, M., Dimitri, R., Tornabene, F. and Hossein Yas, M. (2017), "Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by functionally graded wavy carbon nanotubes with temperature-dependent properties", Appl. Sci., 7(12), 1223. https://doi.org/10.3390/app7121223
  25. Paliwal, D., Pandey, R.K. and Nath, T. (1996), "Free vibrations of circular cylindrical shell on winkler and pasternak foundations", Int. J. Pres. Ves. Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
  26. Pellicano, F. (2007), "Vibrations of circular cylindrical shells: Theory and experiments", J. Sound Vib., 303(1-2), 154-170. https://doi.org/10.1016/j.jsv.2007.01.022
  27. Qin, Z., Chu, F. and Zu, J. (2017), "Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study", Int. J. Mech. Sci., 133, 91-99. https://doi.org/10.1016/j.ijmecsci.2017.08.012
  28. Qin, Z., Yang, Z., Zu, J. and Chu, F. (2018), "Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates", Int. J. Mech. Sci., 142, 127-139. https://doi.org/10.1016/j.ijmecsci.2018.04.044
  29. Safaei, B., Moradi-Dastjerdi, R. and Chu, F. (2018), "Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations", Compos. Struct., 192, 28-37. https://doi.org/10.1016/j.compstruct.2018.02.022
  30. Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2019), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B-Eng., 161, 44-54. https://doi.org/10.1016/j.compositesb.2018.10.049
  31. Sewall, J.L. and Naumann, E.C. (1968), "An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners", NASA TN D-4705.
  32. Sewall, J.L. Clary, R.R. and Leadbetter, S.A. (1964), "An Experimental and Analytical Vibration Study of a Ring-stiffened Cylindrical Shell Structure with Various Support Conditions", NASA TN D-2398.
  33. Shaterzadeh, A. and Foroutan, K. (2016), "Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation", Struct. Eng. Mech., Int. J., 60(4), 615-631. https://doi.org/10.12989/sem.2016.60.4.615
  34. Shen, H.-S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments", Compos. Part B-Eng., 136, 177-186. https://doi.org/10.1016/j.compositesb.2017.10.032
  35. Sheng, G. and Wang, X. (2008), "Thermomechanical vibration analysis of a functionally graded shell with flowing fluid", Eur. J. Mech. A-Solid., 27(6), 1075-1087. https://doi.org/10.1016/j.euromechsol.2008.02.003
  36. Sofiyev, A. (2005), "The stability of compositionally graded ceramic-metal cylindrical shells under aperiodic axial impulsive loading", Compos. Struct., 69(2), 247-257. https://doi.org/10.1016/j.compstruct.2004.07.004
  37. Sofiyev, A. (2009), "The vibration and stability behavior of freely supported fgm conical shells subjected to external pressure", Compos. Struct., 89(3), 356-366. https://doi.org/10.1016/j.compstruct.2008.08.010
  38. Sofiyev, A., Karaca, Z. and Zerin, Z. (2017), "Non-linear vibration of composite orthotropic cylindrical shells on the non-linear elastic foundations within the shear deformation theory", Compos. Struct., 159, 53-62. https://doi.org/10.1016/j.compstruct.2016.09.048
  39. Soong, T.C. (1969), "Buckling of cylindrical shells with eccentric spiral-type stiffeners", AIAA. J, 7(1) 65-72. https://doi.org/10.2514/3.5036
  40. Torkamani, S., Navazi, H., Jafari, A. and Bagheri, M. (2009), "Structural similitude in free vibration of orthogonally stiffened cylindrical shells", Thin Wall. Struct., 47(11), 1316-1330. https://doi.org/10.1016/j.tws.2009.03.013
  41. Vasiliev, V.V. and Morozov, E.V. (2018), Advanced Mechanics of Composite Materials and Structures, Elsevier.
  42. Volmir, A.S. (1972), Non-linear Dynamics of Plates and Shells, Science Edition M, USSR.
  43. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aer. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003
  44. Yas, M.H. and Garmsiri, K. (2010), "Three-dimensional free vibration analysis of cylindrical shells with continuous grading reinforcement", Steel Compos. Struct., Int. J., 10(4), 349-360. https://doi.org/10.12989/scs.2010.10.4.349
  45. Zghal, S., Frikha, A. and Dammak, F. (2018), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures", Appl. Math. Model., 53, 132-155. https://doi.org/10.1016/j.apm.2017.08.021

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