References
- Abrate, S. (1998), "Impact on composite structures", Cambridge UK: Cambridge University Press.
- 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
- 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
- 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
- Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent 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
- 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
- Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct.,, 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
- 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
- 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. https://doi.org/10.12989/scs.2015.19.3.679
- Brischetto, S., Tornabene, F., Fantuzzi, N. and 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
- 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
- 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
- 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
- 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
- Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R., (2016), "Free vibration analysis of arbitrarily shaped functionally carbon nanotube-reinforced plates", Composites: Part B, 115(1), 384-408.
- Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Composites: Part A, 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
- 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
- Ghavamian, A., Rahmandoust, M. and O chsner, 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
- Gojny, F.H., Wichmann, M.H.G., Fiedler, B. and Schulte K. (2005), "Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites-A comparative study", Compos. Sci. Technol., 65(15-16), 2300-2313. https://doi.org/10.1016/j.compscitech.2005.04.021
- Gunawan, H. 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
- Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
- Heshmati, M. and Yas, M.H. (2013), "Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load", Mater. Des., 46, 206-218. https://doi.org/10.1016/j.matdes.2012.10.002
- Hong, M. and Lee, U. (2015), "Dynamics of a functionally graded material axial bar, Spectral element modeling and analysis", Composites: Part B, 69, 427-434. https://doi.org/10.1016/j.compositesb.2014.10.022
- 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. Mater., 15(3) 292-308.
- 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
- 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
- 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
- Marin, M. (2010), "A domain of influence theorem for microstretch elastic materials, Nonlinear Anal. Real World Appl., 11(5), 3446-3452. https://doi.org/10.1016/j.nonrwa.2009.12.005
- Marin, M. and Lupu, M. (1998), "On harmonic vibrations in thermoelasticity of micropolar bodies", J. Vib. Control, 4(5), 507-518. https://doi.org/10.1177/107754639800400501
- Marin, M. and Marinescu, C. (1998), "Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36(1), 73-86. https://doi.org/10.1016/S0020-7225(97)00019-0
- Martone, A., Faiella, G., Antonucci, V., Giordano, M. and Zarrelli, M. (2011), "The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix", Compos. Sci. Technol., 71(8), 1117-1123. https://doi.org/10.1016/j.compscitech.2011.04.002
- 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
- Montazeri, A., Javadpour, J., Khavandi, A., Tcharkhtchi, A. and Mohajeri, A. (2010), "Mechanical properties of multi-walled carbon nanotube/epoxy composites", Mater. Des., 31, 4202-4208. https://doi.org/10.1016/j.matdes.2010.04.018
- 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
- 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
- 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
- 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
- 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
- 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
- Pradhan, S.C., Loy, C.T., Lam, K.Y., Reddy, J.N. (2000). "Vibration characteristic of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61(1), 119-129.
- Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded panels using higher-order finiteelement formulation", J. Sound Vib., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
- 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
- Shu, C. (2000), Differential quadrature and its application in engineering. Springer, Berlin.
- 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
- 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
- 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
- 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
- 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://doi.org/10.1007/s11012-013-9776-x
- Tornabene, F. (2009), "Free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a fourparameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
- 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.
- 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", Composites: Part B, 67(1), 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012
- Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016b), "Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes", Composites: Part B, 115(1), 449-476.
- 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", Composites: Part B, 89(1), 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016
- Viola, E., and Tornabene, F. (2009), "Free vibrations of threeparameter functionally graded parabolic panels of revolution", Mech. Res. Commun., 36(5), 587-594. https://doi.org/10.1016/j.mechrescom.2009.02.001
- 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
- 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
- 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
- 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.
- Yeh, M.K., Tai, N.H. and Liu, J.H. (2006), "Mechanical behavior of phenolic-based composites reinforced with multi-walled carbon nanotubes", Carbon, 44(1), 1-9. https://doi.org/10.1016/j.carbon.2005.07.005
- 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
- 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
Cited by
- Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive vol.2020, pp.None, 2017, https://doi.org/10.1155/2020/7358930