Steel and Composite Structures

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Vibration analysis of damaged core laminated curved panels with functionally graded sheets and finite length

  • Zhao, Li-Cai (Department of Civil and Construction Engineering, National Taiwan University of Science and Technology) ;
  • Chen, Shi-Shuenn (Department of Civil and Construction Engineering, National Taiwan University of Science and Technology) ;
  • Xu, Yi-Peng (China Railway 19th Bureau Co., Ltd) ;
  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • Received : 2020.02.25
  • Accepted : 2021.02.01
  • Published : 2021.03.10
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Abstract

The main objective of this paper is to study vibration of sandwich open cylindrical panel with damaged core and FG face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. It is seen that for the large amount of power-law index "P", increasing this parameter does not have significant effect on the non-dimensional natural frequency parameters of the FG sandwich curved panel. Results indicate that by increasing the value of isotropic damage parameter "D" up to the unity (fully damaged core) the frequency would tend to become zero. One can dictate the fiber variation profile through the radial direction of the sandwich panel via the amount of "P", "b" and "c" parameters. It should be noticed that with increase of volume fraction of fibers, the frequency parameter of the panels does not increase necessarily, so by considering suitable amounts of power-law index "P" and the parameters "b" and "c", one can get dynamic characteristics similar or better than the isotropic limit case for laminated FG curved panels.

Keywords

References

  1. Abrate, S. (1998), "Impact on composite structures", Cambridge UK: Cambridge University Press.
  2. Affdl Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  3. Afrookhteh, S.S., Fathi, A., Naghdipour, M. and Alizadeh Sahraei, A. (2016), "An experimental investigation of the effects of weight fractions of reinforcement and timing of hardener addition on the strain sensitivity of carbon nanotube/polymer composites:, U.P.B. Sci. Bull., Series B, 78(4), 121-130.
  4. Afrookhteh, S.S., Shakeri, M., Baniassadi, M. and Alizadeh Sahraei, A. (2018), "Microstructure Reconstruction and Characterization of the Porous GDLs for PEMFC Based on Fibers Orientation Distribution", Fuel Cells, 18(2), https://doi.org/10.1002/fuce.201700239.
  5. Anderson, T.A. (2003), "3D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60(3), 265-274. https://doi.org/10.1016/S0263-8223(03)00013-8.
  6. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659.
  7. Bacciocchi, M. and Tarantino, A.M. (2019), "Time-dependent behavior of viscoelastic three-phase composite plates reinforced by carbon nanotubes", Compos. Struct., 216, 20-31. https://doi.org/10.1016/j.compstruct.2019.02.083.
  8. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091.
  9. Bellman, R. and Casti, J. (1971), "Differential quadrature and long term integration", J. Math. Anal. Appl., 34(2), 235-238. https://doi.org/10.1016/0022-247X(71)90110-7.
  10. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. DOI: https://doi.org/10.12989/scs.2015.19.3.521.
  11. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493.
  12. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. DOI: https://doi.org/10.12989/scs.2015.19.3.679.
  13. Brischetto, S., Tornabene, F., Fantuzzi, N., Bacciocchi, M. (2015), "Refined 2D and exact 3D shell models for the free vibration analysis of single- and double-walled carbon nanotubes", Technologies, 3(4), 259-284. https://doi.org/10.3390/technologies3040259.
  14. Bui, T.Q., Khosravifard, A., Zhang, C., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041.
  15. Bui, T.Q., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T., Nguyen-Van, T.A., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  16. Bui, T.Q., Nguyen, T.N. and Nguyen-Dang, H. (2009), "A moving Kriging interpolation‐based meshless method for numerical simulation of Kirchhoff plate problems", Int. J. Numer. Meth. Eng., 77(10), 1371-1395. https://doi.org/10.1002/nme.2462.
  17. Bui, T.Q., Nguyen, N.T., Lich, L.V., Nguyen, M.N. and Truong, T.T. (2018), "Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods", Theor. Appl. Fract. Mech., 96, 642-657. https://doi.org/10.1016/j.tafmec.2017.10.005.
  18. Cai, J.B., Chen W.Q., Ye, G.R. and Ding, H.J. (2000), "On natural frequencies of a transversely isotropic cylindrical panel on a kerr foundation", J. Sound Vib., 232(5), 997-1004. https://doi.org/10.1006/jsvi.1999.2703.
  19. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251.
  20. Chen, W.Q., Bian, Z.G. and Ding, H.U., (2004), "Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells", Int. J. Mech. Sci., 46(1), 159-171. https://doi.org/10.1016/j.ijmecsci.2003.12.005.
  21. Civalek, O. (2005), "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods", Int. J. Press Vessel Pip., 82(6), 470-479. https://doi.org/10.1016/j.ijpvp.2004.12.003.
  22. Do, T.V., Bui, T.Q., Yu, T.T., Pham, D.T. and Nguyen, C.T. (2017), "Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment", J. Comput. Sci., 21, 164-181. https://doi.org/10.1016/j.jocs.2017.06.015.
  23. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", P. Roy. Soc. Lond. A Mat., 241, 376-396. https://www.jstor.org/stable/100095. https://doi.org/10.1098/rspa.1957.0133
  24. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R., (2016), "Free vibration analysis of arbitrarily shaped functionally carbon nanotube-reinforced plates", Compos. Part B, 115(1), 384-408. https://doi.org/10.1016/j.compositesb.2016.09.021.
  25. Gang, S.W., Lam, K.Y. and Reddy, J.N. (1999), "The elastic response of functionally graded cylindrical shells to low-velocity", Int. J. Impact Eng., 22(4), 397-417. https://doi.org/10.1016/S0734-743X(98)00058-X.
  26. Ghavamian, A., Rahmandoust, M. and Ochsner, A. (2012), "A numerical evaluation of the influence of defects on the elastic modulus of single and multi-walled carbon nanotubes", Comput. Mater. Sci., 62, 110-116. https://doi.org/10.1016/j.commatsci.2012.05.003.
  27. Gunawan, H., Mikami, T., Kanie, S. and Sato, M. (2006), "Free vibration characteristics of cylindrical shells partially buried in elastic foundations", J. Sound Vib., 290(3-5), 785-793. https://doi.org/10.1016/j.jsv.2005.04.014.
  28. Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
  29. Hill, R. (1964a), "Theory ofmechanical properties of fibre-strengthened materials Elastic behavior, J. Mech. Phys. Solids, 12, 199-212. https://doi.org/10.1016/0022-5096(64)90019-5.
  30. Hill, R. (1964b), "Theory of mechanical properties of fibre-strengthened materials: II. Inelastic behavior", J. Mech. Phys. Solids, 12, 213-218. https://doi.org/10.1016/0022-5096(64)90020-1.
  31. Hong, M. and Lee, U. (2015), "Dynamics of a functionally graded material axial bar, Spectral element modeling and analysis", Compos. Part B, 69, 427-434. https://doi.org/10.1016/j.compositesb.2014.10.022.
  32. Hosseini, S.M. and Zhang, C. (2018), "Elastodynamic and wave propagation analysis in a FG Graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel Compos. Struct., 27(3), 255-271. https://doi.org/10.12989/scs.2018.27.3.255.
  33. Jam, J.E., Noorabadi, M. and Namdaran, N. (2017), "Nonlinear free vibration analysis of micro-beams resting on viscoelastic foundation based on the modified couple stress theory", Arch. Mech. Eng., https://doi.org/10.1515/meceng-2017-0015.
  34. Kamarian, S., Yas, M.H. and Pourasghar, A. (2013), "Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations", Sandw. Strut. Mat., 15(3) 292-308. https://doi.org/10.1177/1099636213487363.
  35. Kashtalyan, M. and Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos. Struct., 87(1), 36-43. https://doi.org/10.1016/j.compstruct.2007.12.003.
  36. Lemaitre, J. and Chaboche, J.L. (1990), "Mechanics of SolidMaterials", Cambridge University Press: New York, NY, USA.
  37. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  38. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  39. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5.
  40. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Anal. Real World Appl., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001.
  41. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Contin. Mech. Thermodyn., 28, 1645-1657. https://doi.org/10.1007/s00161-016-0503-4.
  42. Marin, M., Craciun, E. and Pop, N. (2016), "Considerations on mixed initial-boundary value problems for micropolar porous bodies", Dyn. Syst. Appl., 25(1-2), 175-196.
  43. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpathian J. Math., 32(2), 219-232.
  44. Marin, M., Vlase, S., Ellahi, R and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry-Basel, 11(7), 1-16. https://doi.org/10.3390/sym11070863.
  45. Matsunaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2-D higher-order deformation theory", Compos. Struct., 84(2), 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006.
  46. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., 22(2), 277-299. https://doi.org/10.12989/scs.2016.22.2.277.
  47. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall., 21, 571-574. https://doi.org/10.1016/0001-6160(73)90064-3.
  48. Odegard, G.M., Gates, T.S., Wise, K.E., Park, C. and Siochi, E.J. (2003), "Constitutive modeling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63, 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0.
  49. Paliwal, D.N., Kanagasabapathy, H. and Gupta, K.M. (1995), "The large deflection of an orthotropic cylindrical shell on a Pasternak foundation", Compos. Struct., 31, 31-37. https://doi.org/10.1016/0263-8223(94)00068-9.
  50. Paliwal, D.N., Pandey, R.K. and Nath, T. (1996), "Free vibration of circular cylindrical shell on Winkler and Pasternak foundation", Int. J. Press. Vessel Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0.
  51. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  52. Patel, B.P., Gupta, S.S., Loknath, M.S.B. and Kadu, C.P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", Compos. Struct., 69(3), 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002.
  53. Pelletier Jacob, L. and Vel Senthil,S. (2006), "An exact solution for the steady state thermo elastic response of functionally graded orthotropic cylindrical shells", Int. J. Solid Struct., 43(5), 1131-1158. https://doi.org/10.1016/j.ijsolstr.2005.03.079.
  54. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000). "Vibration characteristic of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61(1), 119-129. https://doi.org/10.1016/S0003-682X(99)00063-8.
  55. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded panels using higher-order finite-element formulation", J. Sound Vib., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056.
  56. Shakeri, M., Akhlaghi, M. and Hosseini, S.M. (2006), Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", J Compos. Struct., 76(1), 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022.
  57. Shi, D.L., Huang, Y.Y., Hwang, K.C. and Gao, H., (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites", J. Eng. Mater. T. ASME, 126, 250-257. https://doi.org/10.1115/1.1751182.
  58. Shojaee, S., Valizadeh, N., Izadpanah, E., Bui, T.Q. and Vu, T.V. (2012), "Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method", Compos. Struct., 94(5), 1677-1693. https://doi.org/10.1016/j.compstruct.2012.01.012.
  59. Shu, C. (2000), Differential quadrature and its application in engineering. Springer, Berlin.
  60. Sobhani Aragh, B. and Yas, M.H. (2010), "Static and free vibration analyses of continuously graded fiber-reinforced cylindrical shells using generalized power-law distribution", Acta Mech., 215(1), 155-173. https://doi.org/10.1007/s00707-010-0335-4.
  61. Sobhani Aragh, B. and Yas, M.H. (2010), "Three dimensional free vibration of functionally graded fiber orientation and volume fraction of cylindrical panels", Mater. Des., 31(9), 4543-4552. https://doi.org/10.1016/j.matdes.2010.03.055.
  62. Tahouneh, V. (2014), "Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method", Struct. Eng. Mech., 52(4), 663-686. https://doi.org/10.12989/sem.2014.52.4.663.
  63. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623.
  64. Tahouneh, V. and Naei, M.H. (2014), "A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation", Meccanica, 49(1), 91-109. https://10.1007/s11012-013-9776-x.
  65. Tornabene, F., Bacciocchi, M., Fantuzzi, N. and Reddy, J.N. (2019), "Multiscale approach for three-phase cnt/polymer/fiber laminated nanocomposite structures", Polym. Compos., 40, 102-126. https://doi.org/10.1002/pc.24520.
  66. Tornabene, F. and Ceruti, A. (2013), "Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method", Math. Probl. Eng., 1-33. https://doi.org/10.1155/2013/867079.
  67. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. M., 198(37), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  68. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B, 67(1), 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012.
  69. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016a), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B, 89(1), 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016.
  70. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016b), "Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes", Compos. Part B, 115(1), 449-476. https://doi.org/10.1016/j.compositesb.2016.07.011.
  71. Tsai, S.W. (1964), Structural Behavior of Composite Materials; Philco Corporation: Newport Beach, CA, USA.
  72. Tsai, S.W. (1965), Strength Characteristics of Composite Materials; Philco Corporation: Newport Beach, CA, USA.
  73. Viola, E. and Tornabene, F. (2009), "Free vibrations of three-parameter functionally graded parabolic panels of revolution", Mech. Res. Commun., 36(5), 587-594. https://doi.org/10.1016/j.mechrescom.2009.02.001.
  74. Wagner, H.D., Lourie, O. and Feldman, Y. (1997), "Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix", Appl. Phys. Lett., 72(2), 188-190. https://doi.org/10.1063/1.120680.
  75. Wang, L. and Hu, H. (2014), "Thermal vibration single-walled carbon nanotubes with quantum effects", Proc. Math. Phys. Eng. Sci., 470(2168). https://doi.org/10.1098/rspa.2014.0087.
  76. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161.
  77. Yang, J. and Shen, S.H. (2003), "Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels", J. Sound Vib., 261(5), 871-893. https://doi.org/10.1016/S0022-460X(02)01015-5.
  78. Yang, R., Kameda, H. and Takada, S. (1998), "Shell model FEM analysis of buried pipelines under seismic loading", Bull Disaster Prev Res. Inst., 38, 115-146.
  79. Zenkour, A.M. (2005a), "A comprehensive analysis of functionally graded sandwich plates. Part 1-deflection and stresses", Int. J. Solid Struct., 42(1), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  80. Zenkour, A.M. (2005b), "A comprehensive analysis of functionally graded sandwich plates. Part 1-buckling and free vibration deflection and stresses", Int. J. Solid Struct., 42(18), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  81. Zhang, Y. and Wang, L. (2020), "Effects of Van der Waals force on the vibration of typical Multi-layered Two-dimensional nanostructures", Scientific Reports-natureresearch, 10(644). https://doi.org/10.1038/s41598-020-57522-9.