Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core

  • Kamran Foroutan (Sino-Canada Research Centre of Nonlinear Dynamics and Noise Control of Xiamen University of Technology and the University of Regina, Xiamen University of Technology) ;
  • Liming Dai (Sino-Canada Research Centre of Nonlinear Dynamics and Noise Control of Xiamen University of Technology and the University of Regina, Xiamen University of Technology)
  • Received : 2022.11.12
  • Accepted : 2023.08.01
  • Published : 2023.08.10
⟨ Previous Next ⟩

Abstract

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

Keywords

Acknowledgement

The authors greatly appreciate the supports of the Natural Sciences and Engineering Research Council of Canada (NSERC), Xiamen University of Technology and the University of Regina to the present research.

References

  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(3-5), 957-968. https://doi.org/10.1016/j.jsv.2007.03.009.
  2. Ahmadi, H. and Foroutan, K. (2019a), "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.
  3. 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.
  4. Ahmadi, H. and Foroutan, K. (2019c), "Nonlinear vibration of stiffened multilayer FG cylindrical shells with spiral stiffeners rested on damping and elastic foundation in thermal environment", Thin. Wall. Struct., 145, 106388. https://doi.org/10.1016/j.tws.2019.106388.
  5. Ahmadi, H. (2019), "Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation", Eng. Comput., 35(4), 1491-1505. https://doi.org/10.1007/s00366-018-0679-2.
  6. Alijani, F., Amabili, M., Karagiozis, K. and Bakhtiari-Nejad, F. (2011b), "Nonlinear vibrations of functionally graded doubly curved shallow shells", J. Sound Vib., 330(7), 1432-1454. https://doi.org/10.1016/j.jsv.2010.10.003.
  7. Alijani, F., Amabili, M. and Bakhtiari-Nejad, F. (2011a), "On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells", Int. J. Non Linear Mech., 46(1), 170-179. https://doi.org/10.1016/j.ijnonlinmec.2010.08.006.
  8. Bich, D.H., Duc, N.D. and Quan, T.Q. (2014), "Nonlinear vibration of imperfect eccentrically stiffened functionally graded double curved shallow shells resting on elastic foundation using the first order shear deformation theory", Int. J. Mech. Sci., 80, 16-28. https://doi.org/10.1016/j.ijmecsci.2013.12.009.
  9. Bich, D.H., Van Dung, D. and Nam, V.H. (2013), "Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells", Compos. Struct., 96, 384-395. https://doi.org/10.1016/j.compstruct.2012.10.009.
  10. Brush, D.D. and Almroth B.O. (1975), Buckling of bars, plates and shells, Mc. Graw-Hill.
  11. Loghman, A., Faegh, R.K. and Arefi, M. (2018), "Two dimensional time-dependent creep analysis of a thick-walled FG cylinder based on first order shear deformation theory", Steel Compos. Struct., 26(5), 533-547. https://doi.org/10.12989/scs.2018.26.5.533.
  12. Chan, D.Q., Thanh, N.V., Khoa, N.D. and Duc, N.D. (2020), "Nonlinear dynamic analysis of piezoelectric functionally graded porous truncated conical panel in thermal environments", Thin Wall. Struct., 154, 106837. https://doi.org/10.1016/j.tws.2020.106837.
  13. Chorfi, S.M. and Houmat, A. (2010), "Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form", Compos. Struct., 92(10), 2573-2581. https://doi.org/10.1016/j.compstruct.2010.02.001.
  14. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  15. Cong, P.H. and Duc, N.D. (2021), "Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments", Thin Wall. Struct., 163, 107748. https://doi.org/10.1016/j.tws.2021.107748.
  16. Dai, L. (2008), Nonlinear dynamics of piecewise constant systems and implementation of piecewise constant arguments, World Scientific Publishing Co., New Jersey.
  17. Dong, Y.H., Li, Y.H., Chen, D. and Yang, J. (2018), "Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion", Compos. B. Eng., 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009.
  18. Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment", Eur. J. Mech. A Solids, 75, 355-366. https://doi.org/10.1016/j.euromechsol.2019.01.024.
  19. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017.
  20. Duc, N.D. (2014) Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi.
  21. Duc, N.D. and Cong, P.H. (2014), "Nonlinear postbuckling of an eccentrically stiffened thin FGM plate resting on elastic foundations in thermal environments", Thin Wall. Struct., 75, 103-112. https://doi.org/10.1016/j.tws.2013.10.015.
  22. Du, C. and Li, Y. (2014), "Nonlinear internal resonance of functionally graded cylindrical shells using the Hamiltonian dynamics", Acta Mech. Solida Sin., 27(6), 635-647. https://doi.org/10.1016/S0894-9166(15)60008-8.
  23. Duc, N.D., Quang, V.D. and Anh, V.T.T. (2017), "The nonlinear dynamic and vibration of the S-FGM shallow spherical shells resting on an elastic foundations including temperature effects", Int. J. Mech. Sci., 123, 54-63. https://doi.org/10.1016/j.ijmecsci.2017.01.043.
  24. Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mech., 4(4), 245-259. https://doi.org/10.22055/JACM.2018.23219.1151.
  25. Duc, N.D., Seung-Eock, K., Khoa, N.D. and Chan, D.Q. (2021), "Nonlinear buckling and post-buckling analysis of shear deformable stiffened truncated conical sandwich shells with functionally graded face sheets and a functionally graded porous core", J. Sandw. Struct. Mater., 23(7), 2700-2735. https://doi.org/10.1177/1099636220906821
  26. Foroutan, K. and Ahmadi, H. (2020), "Simultaneous resonances of SSMFG cylindrical shells resting on viscoelastic foundations", Steel Compos. Struct., 37(1), 51-73. https://doi.org/10.12989/scs.2020.37.1.051.
  27. Foroutan, K. and Dai, L. (2022a), "Nonlinear dynamic responses of porous FG sandwich cylindrical shells with a viscoelastic core resting on a nonlinear viscoelastic foundation", Mech. Adv. Mater. Struct., 1-20. https://doi.org/10.1080/15376494.2022.2070803.
  28. Foroutan, K. and Dai, L. (2022), "Subharmonic and superharmonic resonances of five-layered porous functionally graded sandwich cylindrical shells with two-layered viscoelastic cores", J. Vib. Control, 10775463221122091. https://doi.org/10.1177/10775463221122091.
  29. Gao, K., Gao, W., Wu, B., Wu, D. and Song, C. (2018), "Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales", Thin Wall. Struct., 125, 281-293. https://doi.org/10.1016/j.tws.2017.12.039.
  30. Nguyen, K., Thai, H.T. and Vo, T. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091.
  31. Jrad, H., Mars, J., Wali, M. and Dammak, F. (2019), "Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells", Eng. Comput., 35(3), 833-847. https://doi.org/10.1007/s00366-018-0633-3.
  32. Karimiasl, M., Ebrahimi, F. and Akgoz, B. (2019), "Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading", Compos. Struct., 223, 110988. https://doi.org/10.1016/j.compstruct.2019.110988.
  33. 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.
  34. Li, H., Pang, F., Chen, H. and Du, Y. (2019), "Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method", Compos. B. Eng., 164, 249-264. https://doi.org/10.1016/j.compositesb.2018.11.046.
  35. 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.
  36. Matsunaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2D higher-order deformation theory", Compos. Struct., 84(2), 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006.
  37. Nayfeh, A.H. and Mook, D.T. (2008), Nonlinear Oscillations, John Wiley & Sons.
  38. Quan, T.Q. and Duc, N.D. (2022), "Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading", Thin Wall. Struct., 170, 108606. https://doi.org/10.1016/j.tws.2021.108606
  39. Quan, T.Q. and Duc, N.D. (2016), "Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double-curved shallow shells resting on elastic foundations in thermal environments", J. Therm. Stresses, 39(4), 437-459. https://doi.org/10.1080/01495739.2016.1158601.
  40. Reddy JN. (2004), Mechanics of laminated composite plates and shells: Theory and Analysis, Boca Raton: CRC Press.
  41. Rodrigues, L., Goncalves, P.B. and Silva, F.M. (2017), "Internal resonances in a transversally excited imperfect circular cylindrical shell", Procedia Eng., 199, 838-843. https://doi.org/10.1016/j.proeng.2017.09.010.
  42. Sahan, M.F. (2015), "Transient analysis of cross-ply laminated shells using FSDT: Alternative formulation", Steel Compos. Struct., 18(4), 889-907. https://doi.org/10.12989/scs.2015.18.4.889.
  43. Sheng, G.G. and Wang, X. (2018), "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.
  44. 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. B. Eng., 116, 170-185. https://doi.org/10.1016/j.compositesb.2017.02.006.
  45. Sofiyev, A.H. (2016), "Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation", Compos. B. Eng., 98, 141-150. https://doi.org/10.1016/j.compositesb.2016.05.018.
  46. Song, Z.G., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments", Int. J. Mech. Sci., 115, 339-347. https://doi.org/10.1016/j.ijmecsci.2016.06.020.
  47. Thomas, B. and Roy, T. (2016), "Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures", Acta Mech., 227(2), 581-599. https://doi.org/10.1007/s00707-015-1479-z.
  48. Trinh, M.C. and Jun, H. (2021), "Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling", Eng. Comput., 1-39. https://doi.org/10.1007/s00366-021-01544-y.
  49. Trinh, M.C., Duc, N.D. and Kim, S.E. (2019), "Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature", Aerosp. Sci. Technol., 87, 119-132. https://doi.org/10.1016/j.ast.2019.02.010.
  50. Van Long, N., Thinh, T.I., Bich, D.H. and Tu, T.M. (2022), "Nonlinear dynamic responses of sandwich-FGM doubly curved shallow shells subjected to underwater explosions using first-order shear deformation theory", Ocean Eng., 260, 111886. https://doi.org/10.1016/j.oceaneng.2022.111886.
  51. Wang, A., Chen, H., Hao, Y. and Zhang, W. (2018), "Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets", Results Phys., 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062.
  52. Wang, Q., Cui, X., Qin, B. and Liang, Q. (2017), "Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions", Compos. Struct., 182, 364-379. https://doi.org/10.1016/j.compstruct.2017.09.043.
  53. Wang, Y.Q., Liang, L. and Guo, X.H. (2013), "Internal resonance of axially moving laminated circular cylindrical shells", J. Sound Vib., 332(24), 6434-6450. https://doi.org/10.1016/j.jsv.2013.07.007.
  54. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003.
  55. Xu, K., Yuan, Y. and Li, M. (2019), "Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets", Steel Compos. Struct., 32(5), 633-642. https://doi.org/10.12989/scs.2019.32.5.633.
  56. Yeh, J.Y. (2011), "Parametric resonance of axisymmetric sandwich annular plate with ER core layer and constraining layer", Smart Struct. Syst., 8(5), 487-499. https://doi.org/10.12989/sss.2011.8.5.487.
  57. Zare Jouneghani, F., Dimitri, R., Bacciocchi, M. and Tornabene, F. (2017), "Free vibration analysis of functionally graded porous doubly-curved shells based on the first-order shear deformation theory", Appl. Sci., 7(12), 1252. https://doi.org/10.3390/app7121252.
  58. 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.
  59. Baseri, V., Jafari, G.S. and Kolahchi, R. (2016), "Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory", Steel Compos. Struct., 21(4), 883-919. https://doi.org/10.12989/scs.2016.21.4.883.
  60. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019), "Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method", Compos. B. Eng., 157, 219-238. https://doi.org/10.1016/j.compositesb.2018.08.087.