DOI QR코드

DOI QR Code

Simultaneous resonances of SSMFG cylindrical shells resting on viscoelastic foundations

  • Foroutan, Kamran (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Ahmadi, Habib (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
  • 투고 : 2020.01.15
  • 심사 : 2020.09.22
  • 발행 : 2020.10.10

초록

The present paper investigates the simultaneous resonance behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with internal and external functionally graded stiffeners under the two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal. The exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material layer is located between these layers. With regard to classical shells theory, von-Kármán equation, and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The simultaneous resonance is obtained using the multiple scales method. Finally, the influences of different material and geometrical parameters on the system resonances are investigated comprehensively.

키워드

참고문헌

  1. Abe, A., Kobayashi, Y. and Yamada, G. (2007), "Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance", J. Sound Vib., 304, 957-968. https://doi.org/10.1016/j.jsv.2007.03.009.
  2. Ahmadi, H. (2018), "Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-018-0679-2.
  3. Ahmadi, H. and Foroutan, K. (2019a), "Superharmonic and subharmonic resonances of spiral stiffened functionally graded cylindrical shells under harmonic excitation", Int. J. Struct. Stab. Dyn., https://doi.org/10.1142/S0219455419501141.
  4. Ahmadi, H. and Foroutan, K. (2019b), "Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales", Thin Wall. Struct., 135, 33-44. https://doi.org/10.1016/j.tws.2018.10.028.
  5. Ahmadi, H. and Foroutan, K. (2019c), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel Compos. Struct., 32(2), 253-264. https://doi.org/10.12989/scs.2019.32.2.253.
  6. Alijani, F., Amabili, M. and Bakhtiari-Nejad, F. (2011), "On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells", Int. J. Nonlinear. Mech., 46, 170-179. https://doi.org/10.1016/j.ijnonlinmec.2010.08.006.
  7. 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.
  8. Dai, H.L., Dai, T. and Zheng, H.Y. (2013), "Creep buckling and post-buckling analyses for a hybrid laminated viscoelastic FGM cylindrical shell under in-plane loading", Int. J. Mech. Mater. Des., 9(4), 309-323. https://doi.org/10.1007/s10999-013-9223-0.
  9. Dat, N.D., Quan, T.Q. and Duc, N.D. (2019), "Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells", Int. J. Mech. Mater. Des., 1-20. https://doi.org/10.1007/s10999-019-09464-y.
  10. Du, C. and Li, Y. (2013), "Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments", Compos. Struct., 102, 164-174. https://doi.org/10.1016/j.compstruct.2013.02.028.
  11. Duc, N.D., Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations", Aerosp. Sci. Technol., 40, 115-127. https://doi.org/10.1016/j.ast.2014.11.005
  12. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. http://dx.doi.org/10.12989/scs.2016.20.1.205.
  13. Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2018), "Nonlinear dynamic analysis of spiral stiffened functionally graded cylindrical shells with damping and nonlinear elastic foundation under axial compression", Struct. Eng. Mech., 66(3), 295-303. https://doi.org/10.12989/sem.2018.66.3.295.
  14. Foroutan, K. and Ahmadi, H. (2020), "Nonlinear free vibration analysis of SSMFG cylindrical shells resting on nonlinear viscoelastic foundation in thermal environment", Appl. Math. Model., 85, 294-317. https://doi.org/10.1016/j.apm.2020.04.017.
  15. Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2019), "Nonlinear dynamic analysis of spiral stiffened cylindrical shells rested on elastic foundation", Steel Compos. Struct., 32(4), 509-519. https://doi.org/10.12989/scs.2019.32.4.509.
  16. Gao, K., Gao, W., Chen, D. and Yang, J. (2018a), "Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation", Compos. Struct., 204, 831-846. https://doi.org/10.1016/j.compstruct.2018.08.013.
  17. Gao, K., Gao, W., Wu, D. and Song, C. (2017), "Nonlinear dynamic characteristics and stability of composite orthotropic plate on elastic foundation under thermal environment", Compos. Struct., 168, 619-632. https://doi.org/10.1016/j.compstruct.2017.02.054.
  18. Gao, K., Gao, W., Wu, D. and Song, C. (2018b), "Nonlinear dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by Winkler-Pasternak elastic foundation subjected to a linearly increasing load", J. Sound Vib., 415, 147-168. https://doi.org/10.1016/j.jsv.2017.11.038.
  19. Khayat, M., Dehghan, S.M., Najafgholipou,r 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., 28(6), 735-748. https://doi.org/10.12989/scs.2018.28.6.735
  20. 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., 20(5), 1087-1102. https://dx.doi.org/10.12989/scs.2016.20.5.1087.
  21. Lezgy-Nazargah, M., Shariyat, M. and Beheshti-Aval, S.B. (2011), "A refined high-order global-local theory for finite element bending and vibration analyses of the laminated composite beams", Acta Mech., 217(3-4), 219-242. https://doi.org/10.1007/s00419-012-0621-9.
  22. Li, F.M. and Yao, G. (2013), "1/3 Subharmonic resonance of a nonlinear composite laminated cylindrical shell in subsonic air flow", Compos. Struct., 100, 249-256. https://doi.org/10.1016/j.compstruct.2012.12.035.
  23. Li, X., Du, C.C. and Li, Y.H. (2018), "Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment", Appl. Math. Model., 59, 393-409. https://doi.org/10.1016/j.apm.2018.01.048.
  24. Mahmoudkhani, S., Navazi, H.M. and Haddadpour, H. (2011), "An analytical study of the non-linear vibrations of cylindrical shells", Int. J. Nonlinear. Mech., 46, 1361-1372. https://doi.org/10.1016/j.ijnonlinmec.2011.07.012.
  25. Mustafa, B.A.J. and Ali, R. (1989), "An energy method for free vibration analysis of stiffened circular cylindrical shells", Comput. Struct., 32, 355-363. https://doi.org/10.1016/0045-7949(89)90047-3.
  26. Nam, V.H., Phuong, N.T., Van Minh, K. and Hieu, P.T. (2018), "Nonlinear thermo-mechanical buckling and post-buckling of multilayer FGM cylindrical shell reinforced by spiral stiffeners surrounded by elastic foundation subjected to torsional loads", Eur. J. Mech. A-Solid., 72, 393-406. https://doi.org/10.1016/j.euromechsol.2018.06.005.
  27. Nayfeh, A.H. and Mook D.T. (1995), Nonlinear Oscilations, John Wiley and Sons.
  28. Pendhari, S.S., Kant, T., Desai, Y.M. and Subbaiah, C.V. (2012), "Static solutions for functionally graded simply supported plates", Int. J. Mech. Mater. Des., 8(1), 51-69. https://doi.org/10.1007/s10999-011-9175-1.
  29. 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.
  30. 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.
  31. Rodrigues, L., Goncalves, P.B. and Silva, F.M.A. (2017), "Internal resonances in a transversally excited imperfect circular cylindrical shell", Pro. Eng., 199, 838-843. https://doi.org/10.1016/j.proeng.2017.09.010.
  32. Sarigul, M. and Boyaci, H. (2010), "Nonlinear vibrations of axially moving beams with multiple concentrated masses Part I: primary resonance", Struct. Eng. Mech., 36(2), 149-163. https://doi.org/10.12989/sem.2010.36.2.149.
  33. Shaterzadeh, A. and Foroutan, K. (2016), "Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation", Struct. Eng. Mech., 60, 615-631. https://doi.org/10.12989/sem.2016.60.4.615.
  34. Sheng, G.G. and Wang, X. (2018a), "Nonlinear vibrations of FG cylindrical shells subjected to parametric and external excitations", Compos. Struct., 191, 78-88. https://doi.org/10.1016/j.compstruct.2018.02.018.
  35. Sheng, G.G. and Wang, X. (2018b), "The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells", Appl. Math. Model., 56, 389-403.https://doi.org/10.1016/j.apm.2017.12.021.
  36. Sofiyev, A.H. (2016), "Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation", Compos. Part B, 98, 141-50. https://doi.org/10.1016/j.compositesb.2016.05.018.
  37. Sofiyev, A.H., Avcar, M., Ozyigit, P. and Adigozel, S. (2009), "The Free Vibration of non-homogeneous truncated conical shells on a winkler foundation", Int. J. Eng. Appl. Sci., 1, 34-41.
  38. Sofiyev, A.H., Hui, D., Haciyev, V.C., Erdem, H., Yuan, G.Q., Schnack, E. and Guldal, V. (2017), "The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory", Compos. Part B, 116, 170-85. https://doi.org/10.1016/j.compositesb.2017.02.006.
  39. Van Dung, D. and Hoa, L.K. (2013), "Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure", Thin Wall. Struct., 63,117-124. https://doi.org/10.1016/j.tws.2012.09.010.
  40. Van 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.
  41. Wang, Y.Q. (2018), "Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state", Acta Astronaut., 143, 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004.
  42. Wang, Y.Q. (2014), "Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration", Nonlinear Dynam., 77(4), 1693-1707. https://doi.org/10.1007/s11071-014-1410-5.
  43. Wang, Y.Q., Huang, X.B. and Li, J. (2016), "Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process", Int. J.Mech. Sci., 110, 201-216. https://doi.org/10.1016/j.ijmecsci.2016.03.010.
  44. Wang, Y.Q., Li, H.H., Zhang, Y.F. and Zu, J.W. (2018a), "A nonlinear surface-stress-dependent model for vibration analysis of cylindrical nanoscale shells conveying fluid", Appl. Math. Model., 64, 55-70. https://doi.org/10.1016/j.apm.2018.07.016.
  45. Wang, Y.Q., Liang, L. and Guo, X.H. (2013), "Internal resonance of axially moving laminated circular cylindrical shells", J. Sound Vib., 332, 6434-6450. https://doi.org/10.1016/j.jsv.2013.07.007.
  46. Wang, Y.Q., Liu, Y.F. and Yang, T.H. (2019c), "Nonlinear Thermo-Electro-Mechanical Vibration of Functionally Graded Piezoelectric Nanoshells on Winkler-Pasternak Foundations Via Nonlocal Donnell's Nonlinear Shell Theory", Int. J. Struct. Stab. Dynam., 19(9), 1950100. https://doi.org/10.1142/S0219455419501001.
  47. Wang, Y.Q. and Liu, Y.F. (2019), "Free vibration and buckling of polymeric shells reinforced with 3D graphene foams", Results in Phys., 14, 102510. https://doi.org/10.1016/j.rinp.2019.102510.
  48. Wang, Y.Q., Ye, C. and Zu, J.W. (2018b), "Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities", Appl. Math. Mech., 39(11), 1587-1604. https://doi.org/10.1007/s10483-018-2388-6.
  49. Wang, Y.Q., Wan, Y.H. and Zu, J.W. (2019a), "Nonlinear dynamic characteristics of functionally graded sandwich thin nanoshells conveying fluid incorporating surface stress influence", Thin Wall. Struct., 135, 537-547. https://doi.org/10.1016/j.tws.2018.11.023.
  50. Wang, Y.Q., Wan, Y.H. and Zhang, Y.F. (2017), "Vibrations of longitudinally traveling functionally graded material plates with porosities", Eur. J. Mech. A-Solid., 66, 55-68. https://doi.org/10.1016/j.euromechsol.2017.06.006.
  51. Wang, Y.Q. and Yang, Z. (2017), "Nonlinear vibrations of moving functionally graded plates containing porosities and contacting with liquid: internal resonance", Nonlinear Dynam., 90(2), 1461-1480. https://doi.org/10.1007/s11071-017-3739-z.
  52. Wang, Y.Q. and Zhao, H.L. (2019), "Free vibration analysis of metal foam core sandwich beams on elastic foundation using Chebyshev collocation method", Arch. Appl. Mech., 89(11), 2335-2349. https://doi.org/10.1007/s00419-019-01579-0.
  53. Wang, Y.Q., Ye, C. and Zu, J.W. (2019b), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  54. Wang, Y.Q., Ye, Ch. and Zu, J.W. (2019d), "Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions", Int. J. Mech. Mater. Des., 15(2), 333-344. https://doi.org/10.1007/s10999-018-9415-8.
  55. Wang, Y.Q. and Zu, J.W. (2017a), "Instability of viscoelastic plates with longitudinally variable speed and immersed in ideal liquid," Int. J. Appl. Mech., 9(1), 1750005. https://doi.org/10.1142/S1758825117500053.
  56. Wang, Y.Q. and Zu, J.W. (2017b), "Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates", Smart Mater. Struct., 26(10), 105014. https://doi.org/10.1088/1361-665X/aa8429.
  57. Wang, Y.Q. and Zu, J.W. (2017c), "Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid", Compos. Struct., 164, 130-144. https://doi.org/10.1016/j.compstruct.2016.12.053.
  58. Wang, Y.Q. and Zu, J.W. (2017d), "Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment", Aerosp. Sci. Technol., 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023.
  59. Yas, M.H. and Garmsiri, K. (2010), "Three-dimensional free vibration analysis of cylindrical shells with continuous grading reinforcement", Steel Compos. Struct., 10(4), 349-360. https://doi.org/10.12989/scs.2010.10.4.349.
  60. Zhang, W., Liu, T., Xi, A. and Wang, Y.N. (2018), "Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes", J. Sound Vib., 423, 65-99. https://doi.org/10.1016/j.jsv.2018.02.049.
  61. Zarouni, E., Rad, M.J. and Tohidi, H. (2014), "Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods", Int. J. Mech. Mater. Des., 10(4), 421-438. https://doi.org/10.1007/s10999-014-9254-1 .

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