DOI QR코드

DOI QR Code

Combination resonance analysis of FG porous cylindrical shell under two-term excitation

  • Ahmadi, Habib (Faculty of Mechanical Engineering, Shahrood University of Technology) ;
  • Foroutan, Kamran (Faculty of Mechanical Engineering, Shahrood University of Technology)
  • Received : 2019.02.23
  • Accepted : 2019.06.10
  • 발행 : 2019.07.25

초록

This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-$K{\acute{a}}rm{\acute{a}}n$ equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

키워드

참고문헌

  1. Abdelhak, Z., Hadji, L., Daouadji, T.H. and Adda, B. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., Int. J., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
  2. 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
  3. Adim, B. and Daouadji, T.H. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., Int. J., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223
  4. Adim, B., Daouadji, T.H. and Abbes, B. (2016a), "Buckling analysis of anti-symmetric cross-ply laminated composite plates under different boundary conditions", Int. Appl. Mech., 52(6), 661-676. https://doi.org/10.1007/s10778-016-0787-x
  5. Adim, B., Daouadji, T.H., Abbes, B. and Rabahi, A. (2016b), "Buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory", Mech. Indus., 17(5), 512. https://doi.org/10.1051/meca/2015112
  6. Adim, B., Daouadji, T.H. and Rabahi, A. (2016c), "A simple higher order shear deformation theory for mechanical behavior of laminated composite plates", Int. J. Adv. Struct. Eng. (IJASE), 8(2), 103-117. https://doi.org/10.1007/s40091-016-0109-x
  7. Adim, B., Daouadji, T.H., Rabia, B. and Hadji, L. (2016d), "An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions", Earthq. Struct., Int. J., 11(1), 63-82. https://doi.org/10.12989/eas.2016.11.1.063
  8. Adim, B., Daouadji, T.H., Rabahi, A. and Abdelouahed, T. (2016e), "An Efficient and Simple Higher Order of Shear Deformation Theory for Static and Free Vibration of Laminated Composite Plates", Int. J. Compos. Mater. Matrices, 2(1).
  9. 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
  10. Ahmadi, H. and Foroutan, K. (2019), "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
  11. 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. Nonlin. Mech., 46(1), 170-179. https://doi.org/10.1016/j.ijnonlinmec.2010.08.006
  12. Belica, T. and Magnucki, K. (2006), "Dynamic stability of a porous cylindrical shell", Appl. Math. Mech., 207-208.
  13. Belica, T., Malinowski, M. and Magnucki, K. (2011), "Dynamic stability of an isotropic metal foam cylindrical shell subjected to external pressure and axial compression", J. Appl. Mech., 78(4), 041003. https://doi.org/10.1115/1.4003768
  14. Benferhat, R., Daouadji, T.H. and Mansour, M.S. (2016a), "Free vibration analysis of FG plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory", Comptes Rendus Mecanique, 344(9), 631-641. https://doi.org/10.1016/j.crme.2016.03.002
  15. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016b), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., Int. J., 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429
  16. Benferhat, R., Hassaine, D., Hadji, L. and Said, M. (2016c), "Static analysis of the fgm plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  17. 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
  18. 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
  19. Breslavsky, I.D. and Amabili, M. (2018), "Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation", Nonlin. Dyn., 1-10.
  20. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, USA.
  21. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052
  22. Daneshjou, K., Ramezani, H. and Talebitooti, R. (2011), "Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials", Appl. Math. Mech., 32, 701-718. https://doi.org/10.1007/s10483-011-1450-9
  23. Daouadji, T.H. and Adim, B. (2016a), "An analytical approach for buckling of functionally graded plates", Adv. Mater. Res., Int. J., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141
  24. Daouadji, T.H. and Adim, B. (2016b), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., Int. J., 5(1), 1-9. https://doi.org/10.12989/amr.2016.5.1.001
  25. Daouadji, T.H., Adim, B. and Benferhat, R. (2016a), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., Int. J., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035
  26. Daouadji, T.H., Benferhat, R. and Adim, B. (2016b), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Mater. Res., Int. J., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107
  27. Djoudi, M.S. and Bahai, H. (2003), "A shallow shell finite element for the linear and non-linear analysis of cylindrical shells", Eng. Struct., 25, 769-778. https://doi.org/10.1016/S0141-0296(03)00002-6
  28. 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. Part B-Eng., 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009
  29. 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
  30. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., Int. J., 20(1), 205-225. http://dx.doi.org/10.12989/scs.2016.20.1.205
  31. Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., Int. J., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999
  32. 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
  33. Ghadiri, M. and SafarPour, H. (2017), "Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment", J. Therm. Stresses, 40(1), 55-71. https://doi.org/10.1080/01495739.2016.1229145
  34. Ghiasian, S.E., Kiani, Y. and Eslami, M.R. (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
  35. Guan, X., Sok, K., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019), "A general vibration analysis of functionally graded porous structure elements of revolution with general elastic restraints", Compos. Struct., 209, 277-299. https://doi.org/10.1016/j.compstruct.2018.10.103
  36. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018), "Thermal buckling of smart porous functionally graded nanobeam rested on kerr foundation", Steel Compos. Struct., Int. J., 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349
  37. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  38. 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
  39. 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. Part B-Eng., 164, 249-264. https://doi.org/10.1016/j.compositesb.2018.11.046
  40. 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
  41. Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., Int. J., 6(4), 319-333. https://doi.org/10.12989/scs.2006.6.4.319
  42. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., Int. J., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415
  43. Mojahedin, A., Joubaneh, E.F. and Jabbari, M. (2014), "Thermal and mechanical stability of a circular porous plate with piezoelectric actuators", Acta Mech., 225(12), 3437-3452. https://doi.org/10.1007/s00707-014-1153-x
  44. 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
  45. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61, 111-129. https://doi.org/10.1016/S0003-682X(99)00063-8
  46. 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
  47. 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
  48. Rossikhin, Y.A. and Shitikova, M.V. (2015), "Nonlinear dynamic response of a fractionally damped cylindrical shell with a three-to-one internal resonance", Appl. Math. Comput., 257, 498-525. https://doi.org/10.1016/j.amc.2015.01.018
  49. Sewall, J.L. and Naumann, E.C. (1968), "An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners", NASA Technical Note D-4705.
  50. Shen, H.-S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025
  51. Sheng, G.G. and Wang, X. (2018a), "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
  52. Sheng, G.G. and Wang, X. (2018b), "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
  53. Tesar, A. (1985), "Nonlinear three-dimensional resonance analysis of shells", Comput. Struct., 21, 797-805. https://doi.org/10.1016/0045-7949(85)90156-7
  54. Volmir, A.S. (1972), Non-linear dynamics of plates and shells, Science Edition M, USSR.
  55. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Tech., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003
  56. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  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, L., Song, Z. and Liew, K. (2017), "Modeling aerothermoelastic properties and active flutter control of nanocomposite cylindrical shells in supersonic airflow under thermal environments", Comput. Methods Appl. Mech. Eng., 325, 416-433. https://doi.org/10.1016/j.cma.2017.07.014
  59. 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
  60. Zhao, J., Wang, Q., Deng, X., Choe, K., Xie, F. and Shuai, C. (2019a), "A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams", Compos. Part B-Eng., 165, 155-166. https://doi.org/10.1016/j.compositesb.2018.11.080
  61. Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R. and Shuai, C. (2019b), "Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions", Compos. Part B-Eng., 168, 106-120. https://doi.org/10.1016/j.compositesb.2018.12.044
  62. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019c), "A unified solution for the vibration analysis of functionally graded porous (FGP) shallow shells with general boundary conditions", Compos. Part B-Eng., 156, 406-424. https://doi.org/10.1016/j.compositesb.2018.08.115
  63. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019d), "Dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints", Compos. Part B-Eng., 159, 20-43. https://doi.org/10.1016/j.compositesb.2018.08.114
  64. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019e), "Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method", Compos. Part B-Eng., 157, 219-238. https://doi.org/10.1016/j.compositesb.2018.08.087

피인용 문헌

  1. Asymmetric Large Deformation Superharmonic and Subharmonic Resonances of Spiral Stiffened Imperfect FG Cylindrical Shells Resting on Generalized Nonlinear Viscoelastic Foundations vol.12, pp.5, 2019, https://doi.org/10.1142/s1758825120500520
  2. Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition vol.40, pp.4, 2019, https://doi.org/10.12989/scs.2021.40.4.555