[1] Udupa G, Rao SS, Gangadharan K (2014) Functionally graded composite materials :an overview. Proc Mat Sci 5: 1291-1299.
[2] Rafiee M, Yang J, Kitipornchai S (2013) Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers. Compos Struct 96: 716-725.
[3] Smith B, Szyniszewski S, Hajjar J, Schafer B, Arwade S (2012) Steel foam for structures: are view of applications, manufacturing and material properties. J Constr Steel Res 71: 1-10.
[4] Ashby MF, Evans T, Fleck NA, Hutchinson J, Wadley H, Gibson L (2000) Metal foams :A design guide. Elsevier.
[5] Badiche X, Forest S, Guibert T, Bienvenu Y, Bartout J-D, Ienny P, Croset M, Bernet H (2000) Mechanical properties and non-homogeneous deformation of open-cell nickel foams :Application of the mechanics of cellular solids and of porous materials. Mat Sci Eng A-Struct 289(1): 276-288.
[6] Banhart J (2001) Manufacture, characterization and application of cellular metals and metal foams. Prog Mater Sci 46(6): 559-632.
[7] Lopatnikov SL, Gama BA, Haque MJ, Krauthauser C, Gillespie JW ,Guden M, Hall IW (2003) Dynamics of metal foam deformation during Taylor cylinder–Hopkinson bar impact experiment. Compos Struct 61(1): 61-71.
[8] Pinnoji PK, Mahajan P, Bourdet N, Deck C, Willinger R (2010) Impact dynamics of metal foam shells for motorcycle helmets: experiments and numerical modeling. Int J Impact Eng 37(3): 274-284.
[9] Lefebvre L-P, Banhart J, Dunand D(2008) Porous metals and metallic foams: current status and recent developments. Adv Eng Mater 10(9): 775-787.
[10] Ahmad Z, Thambiratnam DP (2009) Dynamic computer simulation and energy absorption of foam-filled conical tubes under axial impact loading. Compos Struct 87(3): 186-197.
[11] Toupin RA (1962) Elastic materials with couple stresses. Arch Ration Mech An 11: 385-414.
[12] Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech An 11: 415-448.
[13] Mindlin RD (1963) Influence of couple-stresses on stress concentrations. Exp Mech 3: 1-7.
[14] Koiter WT (1964) Couple-stresses in the theory of elasticity: I and II. Proc K Ned Akad B-Ph 67: 17-44.
[15] Aifantis EC (1999) Strain gradient interpretation of size effects. Int J Fracture 95: 1-4.
[16] Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1-16.
[17] Gurtin ME, Weissmuller J, Larche F (1998) The general theory of curved deformable interfaces in solids at equilibrium. Philos Mag A 1093-1109.
[18] Yang F, Chong ACM, Lam DCC, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39: 2731-2743.
[19] Salehipour H, Shahidi AR, Nahvi H (2015) Modified nonlocal elasticity theory for functionally graded materials. Int J Eng Sci 90: 44-57.
[20] Shafiei N, Mirjavad S, MohaselAfshari B, Rabby S, Kazemi m (2017) Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams. Comput Method Appl M 322: 615-632.
[21] Ebrahimi F, Barati MR (2017) Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams. Mech Syst Signal Pr 93: 445-459.
[22] Shahverdi H, Barati MR (2017) Vibration analysis of porous functionally graded nanoplates. Int J Eng Sci 120: 82-99.
[23] Faleh NM, Ahmed RA, Fenjan RM (2018) On vibrations of porous FG nanoshells. Int J Eng Sci 133: 1-14.
[24] Aria AI, Rabczuk T, Friswell MI (2019) A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams. Eur J Mech A-Solid 77: 103767.
[25] Mohammadi M, Hosseini M, Shishesaz M, Hadi A, Rastgoo A (2019) Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads. Eur J Mech A-Solid 77: 103793.
[26] Phung-Van P, Thai CH, Nguyen-Xuan H, Abdel-Wahab M (2019) An isogeometric approach of static and free vibration analyses for porous FG nanoplates. Eur J Mech A-Solid 78: 103851.
[27] Phung-Van P, Thai CH, Nguyen-Xuan H, Abdel-Wahab M (2019) Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis. Compos Part B-Eng 164: 215-225.
[28] Rahmani A, Faroughi S, Friswell MI (2020) The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory. Mech Syst Signal Pr 144: 106854.
[29] Behdad Sh, Fakher M, Hosseini-Hashemi Sh (2021) Dynamic stability and vibration of two-phase local/nonlocal VFGP nanobeams incorporating surface effects and different boundary conditions. Mech Mater 153: 103633.
]30[ صیدی ج، محمدی ی (1394) بررسی تحلیلی و عددی تیرهای ساندویچی هدفمند تحت بار موضعی و خواص وابسته به دما. نشریه علمی مکانیک سازهها و شارهها 137-127 :(4)5.
]31[ مختاری ع، میردامادی ح، غیور م (1395) آنالیز دینامیکی تیر تیموشنکوی پیش تنیده به کمک روش المان محدود طیفی بر پایه تبدیل موجک. نشریه علمی مکانیک سازهها و شارهها 22-11 :(4)6.
]32[ فروزنده س، آریایی ع (1395) تحلیل ارتعاشات مجموعه‌ای از چند تیر تیموشنکوی موازی با اتصالات انعطاف پذیر میانی تحت عبور جرم متحرک. نشریه علمی مکانیک سازهها و شارهها 86-69 :(2)6.
[33] Talebizadehsardari P, Salehipour H, Shahgholian-Ghahfarokhi D, Shahsavar A, Karimi M (2020) Free vibration analysis of the macro-micro-nano plates and shells made of a material with functionally graded porosity: A closed-form solution. Mech Based Des Struc. (Under Publication)
[34] Shu C (2000) Differential quadrature and its application in engineering. Springer, Berlin
[35] Chen D, Yang J, Kitipornchai S (2016) Free and forced vibrations of shear deformable functionally graded Porous beams. Int J Mech Sci 108-109: 14-29.
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