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http://dx.doi.org/10.12989/anr.2019.7.4.277

Assessment of new 2D and quasi-3D nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates  

Bendaho, Boudjema (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Belabed, Zakaria (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Benatta, Mohamed Atif (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie)
Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Publication Information
Advances in nano research / v.7, no.4, 2019 , pp. 277-292 More about this Journal
Abstract
In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.
Keywords
free vibration; functionally graded nanoplate; nonlocal elasticity; stretching effect;
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82 Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1
83 Kiani, K., Gharebaghi, S.A. and Mehri, B. (2017), "In-plane and out-of-plane waves in nanoplates immersed in bidirectional magnetic fields", Struct. Eng. Mech., Int. J., 61(1), 65-76. http://dx.doi.org/10.12989/sem.2017.61.1.065   DOI
84 Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., Int. J., 63(4), 439-446. http://dx.doi.org/10.12989/sem.2017.63.4.439
85 Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016   DOI
86 Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, Int. J., 17(5), 567-578. http://dx.doi.org/10.12989/cac.2016.17.5.567   DOI
87 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. http://dx.doi.org/10.12989/anr.2018.6.2.147
88 Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. http://dx.doi.org/10.12989/sss.2017.19.2.115   DOI
89 Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070   DOI
90 Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140   DOI
91 Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. http://dx.doi.org/10.12989/scs.2015.18.1.187   DOI
92 Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 464-453. http://dx.doi.org/10.12989/sem.2018.65.4.453
93 Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., Int. J., 55(4), 871-884. http://dx.doi.org/10.12989/sem.2015.55.4.871   DOI
94 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. http://dx.doi.org/10.12989/scs.2019.30.6.603
95 Boukhari, A., Ait Atmane, H., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. http://dx.doi.org/10.12989/sem.2016.57.5.837   DOI
96 Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dyn., 90, 479-492. https://doi.org/10.1007/s11071-017-3676-x   DOI
97 Kolahchi, R. and Moniri Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8   DOI
98 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. http://dx.doi.org/10.12989/scs.2013.14.1.085   DOI
99 Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. http://dx.doi.org/10.12989/sem.2016.58.3.397   DOI
100 Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., Int. J., 66(1), 61-73. http://dx.doi.org/10.12989/sem.2018.66.1.061
101 Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. http://dx.doi.org/10.12989/scs.2019.31.5.503
102 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016   DOI
103 Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., Int. J., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145
104 Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., Int. J., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125
105 Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032   DOI
106 Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023   DOI
107 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039   DOI
108 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017c), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039   DOI
109 Chakraverty, S. and Behera, L. (2015), "Small scale effect on the vibration of non-uniform nanoplates", Struct. Eng. Mech., Int. J., 55, 495-510. http://dx.doi.org/10.12989/sem.2015.55.3.495   DOI
110 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2). [Accepted]
111 Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. http://dx.doi.org/10.12989/gae.2016.11.5.671   DOI
112 Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017d), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., p. 1099636217731071. https://doi.org/10.1177/1099636217731071
113 Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1   DOI
114 Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. http://dx.doi.org/10.12989/sss.2017.19.3.289   DOI
115 Chong, A.C.M., Yang, F., Lam, D.C.C. and Tong, P. (2001), "Torsion and bending of micron-scaled structures", J. Mater. Res., 16(4), 1052-1058. https://doi.org/10.1557/JMR.2001.0146   DOI
116 Daneshmehr, A., Rajabpoor, A. and Hadi, A. (2015), "Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories", Int. J. Eng. Sci., 95, 23-35. https://doi.org/10.1016/j.ijengsci.2015.05.011   DOI
117 Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117   DOI
118 Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel. Compos. Struct., Int. J., 18(2), 425-442. http://dx.doi.org/10.12989/scs.2015.18.2.425   DOI
119 Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. http://dx.doi.org/10.12989/scs.2016.22.4.889   DOI
120 Lam, D.C.C., Yang, F., Chong, A.C.M. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech . Phys. Solids, 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X   DOI
121 Lee, Z., Ophus, C., Fischer, L., Nelson-Fitzpatrick, N., Westra, K.L., Evoy, S., Radmilovic, V., Lu, C., Wu, D. and Chen, W. (2011), "Non-linear responses of nano-scale FGM films including the effects of surface energies", IEEE T. Nanotechnol., 10(6), 1321-1327. https://doi.org/10.1109/TNANO.2011.2139223   DOI
122 Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct., 44(16), 5289-5300. https://doi.org/10.1016/j.ijsolstr.2006.12.034   DOI
123 Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045   DOI
124 Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., Int. J., 4(1), 51-64. http://dx.doi.org/10.12989/anr.2016.4.1.051
125 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. http://dx.doi.org/10.12989/scs.2016.20.2.227   DOI
126 Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. http://dx.doi.org/10.12989/scs.2015.18.2.409   DOI
127 Ebrahimi, F. and Heidari, E. (2018), "Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method", Struct. Eng. Mech., Int. J., 68(1), 131-157. http://dx.doi.org/10.12989/sem.2018.68.1.131
128 Ebrahimi, F. and Shaghaghi, G.R. (2016), "Thermal effects on nonlocal vibrational characteristics of nanobeams with nonideal boundary conditions", Smart Struct. Syst., Int. J., 18(6), 1087-1109. http://dx.doi.org/10.12989/sss.2016.18.6.1087   DOI
129 El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595. http://dx.doi.org/10.12989/sem.2017.63.5.585
130 Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC face sheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109-123. http://dx.doi.org/10.12989/anr.2019.7.2.109   DOI
131 Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5   DOI
132 Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. http://dx.doi.org/10.1142/S0219876213500825   DOI
133 Malekzadeh, P. and Shojaee, M. (2013), "Free vibration of nanoplates based on a nonlocal two-variable refined plate theory", Compos. Struct., 95, 443-452. https://doi.org/10.1016/j.compstruct.2012.07.006   DOI
134 Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., Int. J., 68(6), 661-675. http://dx.doi.org/10.12989/sem.2018.68.6.661
135 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. http://dx.doi.org/10.12989/was.2019.28.1.019
136 Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. http://dx.doi.org/10.12989/anr.2019.7.3.189
137 Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082. http://dx.doi.org/10.1142/S0219876213500825   DOI
138 Mehala, T., Belabed, Z., Tounsi, A. and Beg, O.A. (2018), "Investigation of influence of homogenization models on stability and dynamic of FGM plates on elastic foundations", Geomech. Eng., Int. J., 16(3), 257-271. http://dx.doi.org/10.12989/gae.2018.16.3.257
139 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803   DOI
140 Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., Int. J., 13(3), 385-410. http://dx.doi.org/10.12989/gae.2017.13.3.385
141 Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw . Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443   DOI
142 Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175. http://dx.doi.org/10.12989/scs.2017.25.2.157
143 Meziane, M.A.A, Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852   DOI
144 Mindlin, R. and Tiersten, H. (1962), "Effects of couple-stresses in linear elasticity", Arch. Ration. Mech. An., 11, 415-448. https://doi.org/10.1007/BF00253946   DOI
145 Mohammadi-Alasti, B., Rezazadeh, G., Borgheei, A.M., Minaei, S. and Habibifar, R. (2011), "On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure", Compos. Struct., 93(6), 1516-1525. https://doi.org/10.1016/j.compstruct.2010.11.013   DOI
146 Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., Int. J., 27(1), 109-122. http://dx.doi.org/10.12989/scs.2018.27.1.109
147 Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036   DOI
148 Farajpour, A., Farokhi, H. and Ghayesh, M.H. (2019), "Chaotic motion analysis of fluid-conveying viscoelastic nanotubes", Eur. J. Mech.-A/Solids, 74, 281-296. https://doi.org/10.1016/j.euromechsol.2018.11.012   DOI
149 Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994), "Strain gradient plasticity: theory and experiment", Acta Metall. Mater., 42(2), 475-487. https://doi.org/10.1016/0956-7151(94)90502-9   DOI
150 Fu, Y., Du, H. and Zhang, S. (2003), "Functionally graded TiN/TiNi shape memory alloy films", Mater Lett., 57(20), 2995-2999. https://doi.org/10.1016/S0167-577X(02)01419-2   DOI
151 Nix, W.D. and Gao, H. (1998), "Indentation size effects in crystalline materials: a law for strain gradient plasticity", J. Mech. Phys. Solids, 46, 411-425. https://doi.org/10.1016/S0022-5096(97)00086-0   DOI
152 Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. http://dx.doi.org/10.12989/sss.2018.21.4.397
153 Fu, J., Bernard, S.K., Bernard, F. and Cornen, M. (2018), "Comparison of mechanical properties of C-S-H and portlandite between nano-indentation experiments and a modeling approach using various simulation techniques", Compos. Part B: Eng., 151, 127-138. https://doi.org/10.1016/j.compositesb.2018.05.043   DOI
154 Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, Int. J., 21(4), 431-440. http://dx.doi.org/10.12989/cac.2018.21.4.431
155 Gupta, T.D., Dutta, D. and Shahadat, M.R.B. (2018), "Temperature and Strain Rate Dependent Mechanical Properties of a Square Nickel Plate with Different Shaped Central Cracks: A Molecular Dynamics Study", J. Nano Res., 55, 32-41. https://doi.org/10.4028/www.scientific.net/JNanoR.55.32   DOI
156 Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383. http://dx.doi.org/10.12989/sss.2017.20.3.369
157 Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001   DOI
158 Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9   DOI
159 Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the 3rd International Conference on Micro- and Nanosystems, San Diego, CA, USA, September.
160 Rong, D.L., Fan, J.H., Lim, C.W., Xu, X.S. and Zhou, Z.H. (2018), "A new analytical approach for free vibration, buckling and forced vibration of rectangular nanoplates based on nonlocal elasticity theory", Int. J. Struct. Stab. Dyn., 18(4), 1850055. https://doi.org/10.1142/S0219455418500554   DOI
161 She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H. (2018), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., Int J., 66(6), 729-736. https://doi.org/10.12989/sem.2018.66.6.729