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http://dx.doi.org/10.12989/anr.2021.11.3.239

Natural frequencies of FGM nanoplates embedded in an elastic medium  

Bouafia, Halima (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Chikh, Abdelbaki (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Heireche, Houari (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Al-Zahrani, Mesfer Mohammad (Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals)
Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
Publication Information
Advances in nano research / v.11, no.3, 2021 , pp. 239-249 More about this Journal
Abstract
The small scale impact on the vibrational properties of "functionally graded" (FG) nanoplate embedded in an elastic medium is examined. The formulation is based on the four-unknown refined integral plate theory on aggregate with the nonlocal elasticity theory. Contrary to other theories, this one involves only four unknown variables. The solution procedure is obtained by employing the motion differential equations of physical phase that are converted into set of "linear algebraic equations". After, these are solved by a computer code. The influences of aspect ratio, material index, nonlocal parameter and elastic medium stiffness on the different modal vibrations of FG nanoplate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of FG nanoplate.
Keywords
elastic medium; FG nanoplate; four-unknown refined integral plate theory; nonlocal theory; vibration;
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Times Cited By KSCI : 5  (Citation Analysis)
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1 Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/s0217984916504212.   DOI
2 Karami, B. and Janghorban, M. (2019a), "A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams", Thin Wall. Struct., 143, 106-227.https://doi.org/10.1016/j.tws.2019.106227.   DOI
3 Kar, V.R. and Panda, S.K. (2020), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. http://doi.org/10.12989/scs.2015.18.3.693.   DOI
4 Avcar, M., and Mohammed, W.K.M., (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.   DOI
5 Eltaher, M.A. and Mohamed, S.A. (2020b), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.   DOI
6 Karami, B. and Janghorban, M. (2020), "On the mechanics of functionally graded nanoshells", Int. J. Eng. Sci., 153, 103309. https://doi.org/10.1016/j.ijengsci.2020.103309.   DOI
7 Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun Yaylaci, E., Oner, E. and Birinci, A. (2021a), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/j.mechmat.2020.103730.   DOI
8 Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(asce)em.1943-7889.0001519.   DOI
9 Sedighi, H.M., Keivani, M. and Abadyan, M. (2015a), "Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect", Compos. Part B Eng., 83, 117-133. https://doi.org/10.1016/j.compositesb.2015.08.029.   DOI
10 Timesli, A. (2020c), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. http://doi.org/10.12989/cac.2020.26.1.053   DOI
11 Hamed, M.A., Salwa A Mohamed, S.A., Mohamed, A. and Eltaher, M.A., (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.   DOI
12 Kolahchi, R, Bidgoli, A., Mohammad M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55(5), 1001-1014. https://doi.org/10.12989/SEM.2015.55.5.1001.   DOI
13 Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018b), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 095440621875645.
14 Karami, B., Shahsavari, D., Ordookhani, A., Gheisari, P., Li, L. and Eyvazian, A. (2020), "Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions", Steel Compos. Struct., 36(6), 689-702. https://doi.org/10.12989/SCS.2020.36.6.689.   DOI
15 Khazaei, P. and Mohammadimehr, M. (2020), "Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FG-SWCNTs based on a nonlocal strain gradient theory", Comput. Concrete, 26(1), 31-52. http://doi.org/10.12989/cac.2020.26.1.031.   DOI
16 Fenjan, R.M., Ahmed, R.A., Faleh, N.M. (2019), "Investigating dynamic stability of metal foam nanoplates under periodic in-plane loads via a three-unknown plate theory", Adv. Aircr. Spacecr. Sci., 6(4), 297-314. https://doi.org/10.12989/aas.2019.6.4.297.   DOI
17 Eltaher, M.A., Agwa, M. and Kabeel, A. (2018a), "Vibration analysis of material size-dependent CNTs using energy equivalent model", J. Appl. Comput. Mech., 4(2), 75-86. https://doi.org/10.22055/JACM.2017.22579.1136.   DOI
18 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "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
19 Mehar, K., Panda, S.K. (2020), "Nonlinear deformation and stress responses of a graded carbon nanotube sandwich plate structure under thermoelastic loading", Acta Mech., 231, 1105-1123. https://doi.org/10.1007/s00707-019-02579-5.   DOI
20 Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018a), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/SCS.2018.29.3.349.   DOI
21 Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037   DOI
22 Ghannadpour, S.A.M. and Moradi, F. (2019), "Nonlocal nonlinear analysis of nano-graphene sheets under compression using semi-Galerkin technique", Adv. Nano Res., 7(5), 311-324. http://doi.org/10.12989/anr.2019.7.5.311.   DOI
23 Hadji, L. (2020), "Vibration analysis of FGM beam: Effect of the micromechanical models", Coupled Syst. Mech., 9(3), 265-280. https://doi.org/10.12989/csm.2020.9.3.265.   DOI
24 Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.   DOI
25 Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. http://doi.org/10.12989/scs.2015.18.3.693.   DOI
26 Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperature-dependent and temperature-independent properties", J. Press. Vess. T., 138(6), 061202. https://doi.org/10.1115/1.4033701.   DOI
27 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
28 Sedighi, H.M. and Yaghootian, A. (2016), "Dynamic instability of vibrating carbon nanotubes near small layers of graphite sheets based on nonlocal continuum elasticity", J. Appl. Mech. Tech. Phys., 57(1), 90-100. https://doi.org/10.1134/s0021894416010107.   DOI
29 Rahmani, O. and Asemani, S.S. (2020), "Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories", Struct. Eng. Mech., 74(2), 175-187. https://doi.org/10.12989/SEM.2020.74.2.175.   DOI
30 Safa, A., Hadji, L., Bourada, M., and Zouatnia, N., (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329.   DOI
31 Timesli, A. (2020a), "Buckling analysis of double walled carbon nanotubes embedded in Kerr elastic medium under axial compression using the nonlocal Donnell shell theory", Adv. Nano Res., 9(2), 69-82. http://doi.org/10.12989/anr.2020.9.2.069   DOI
32 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.   DOI
33 Sedighi, H.M., Daneshmand, F. and Abadyan, M. (2015b), "Modified model for instability analysis of symmetric FGM double-sided nano-bridge: Corrections due to surface layer, finite conductivity and size effect", Compos. Struct., 132, 545-557. https://doi.org/10.1016/j.compstruct.2015.05.076.   DOI
34 Selmi, A. (2020b), "Dynamic behavior of axially functionally graded simply supported beams", Smart Struct. Syst., 25(6), 669-678. https://doi.org/10.12989/sss.2020.25.6.669.   DOI
35 Shanab, R.A., Attia, M.A., Mohamed, S.A. and Mohamed, N.A. (2020), "Effect of microstructure and surface energy on the static and dynamic characteristics of FG Timoshenko nanobeam embedded in an elastic medium", J. Nano Res., 61, 97-117. https://doi.org/10.4028/www.scientific.net/jnanor.61.97.   DOI
36 Adiyaman, G., Yaylaci, M. and Birinci, A. (2015), "Analytical and finite element solution of a receding contact problem", Struct. Eng. Mech., 54(1), 69-85. http://doi.org/10.12989/sem.2015.54.1.069   DOI
37 Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.   DOI
38 Akbas, S.D. (2020a), "Modal analysis of viscoelastic nanorods under an axially harmonic load", Adv. Nano Res., 8(4), 277-282. http://doi.org/10.12989/anr.2020.8.4.277   DOI
39 Taherifar, R., Zareei, S.A., Bidgoli, M.R. and Kolahchi, R. (2020), "Seismic analysis in pad concrete foundation reinforced by nanoparticles covered by smart layer utilizing plate higher order theory", Steel Compos. Struct., 37(1), 99-115. https://doi.org/10.12989/SCS.2020.37.1.099.   DOI
40 Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.   DOI
41 Timesli, A. (2020b), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. http://doi.org/10.12989/cac.2020.26.1.053.   DOI
42 Tounsi, A., Ait Atmane, H., Khiloun, M., Sekkal, M., Ouahiba Taleb, O. and Abdelmoumen Anis Bousahla, A.A. (2019), "On buckling behavior of thick advanced composite sandwich plates", Compos. Mater. Eng., 1(1), 1-19. https://doi.org/10.12989/cme.2019.1.1.001.   DOI
43 Akbas, S. D. (2020b), "Dynamic responses of laminated beams under a moving load in thermal environment", Steel Compos. Struct., 35(6), 729-737. https://doi.org/10.12989/SCS.2020.35.6.729.   DOI
44 Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102.   DOI
45 Abdulrazzaq, M.A. Kadhim, Z.D., Faleh, N.M. and Moustafa, N.M. (2020a), "A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads", Struct. Monit. Maint., 7(1), 27-42. https://doi.org/10.12989/smm.2020.7.1.027.   DOI
46 Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.   DOI
47 Ebrahimi, F. and Barati, M.R. (2017a), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science., 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518.   DOI
48 Yaylac, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. http://doi.org/10.12989/sem.2013.48.2.241   DOI
49 Yaylaci, E.U., Yaylaci, M., O lmez, H., Birinci, A. (2020b), "Artificial neural network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. http://dx.doi.org/10.12989/cac.2020.25.6.551.   DOI
50 Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous-cellular core reinforced with graphene nanoplatelets", Compos. Struct., 112700. https://doi.org/10.1016/j.compstruct.2020.112700.   DOI
51 Eltaher, M.A. Mohamed, S.A. and Melaibari, A. (2020b), "Static stability of a unified composite beams under varying axial loads", Thin Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.   DOI
52 Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020a), "Static stability of a unified composite beams under varying axial loads", Thin Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.   DOI
53 Eltaher, M.A. and Mohamed, N.A. (2020a), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart Struct. Syst., 25(4), 501-514. http://doi.org/10.12989/sss.2020.25.4.501.   DOI
54 Civalek, O., Dastjerdi, S., Akbas, S.D. amd Akgoz, B. (2020), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method. Appl. Sci. https://doi.org/10.1002/mma.7069.   DOI
55 Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/jnanor.62.108.   DOI
56 Bouhadra, A., Menasria, A. and Ali Rachedi, M. (2021), "Boundary conditions effect for buckling analysis of porous functionally graded nanobeam", Adv. Nano Res., 10(4), 313-325. http://doi.org/10.12989/anr.2021.10.4.313   DOI
57 Chami, K, Messafer, T., and Hadji, L., (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., 19(2), 91-101. https://doi.org/10.12989/eas.2020.19.2.091.   DOI
58 Ebrahimi, F. and Barati, M.R. (2017b), "Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams", Wave. Random Complex., 28(2), 326 342. https://doi.org/10.1080/17455030.2017.1346331.   DOI
59 Pandey, H.K., Agrawal, H., Panda, S.K., Hirwani, C.K., Katariya, P.V., Dewangan, H.C. (2020), "Experimental and numerical bending deflection of cenosphere filled hybrid (Glass/Cenosphere/Epoxy) composite", Struct. Eng. Mech., 73(6), 715-724. http://doi.org/10.12989/sem.2020.73.6.715.   DOI
60 Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.   DOI
61 Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. http://doi.org/10.12989/scs.2020.36.3.293.   DOI
62 Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano Res., 10(3), 281-293. http://doi.org/10.12989/anr.2021.10.3.281.   DOI
63 Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/jnanor.51.24.   DOI
64 Yaylaci, M., Adiyaman, G., Oner, E., Birinci, A. (2021b), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. http://doi.org/10.12989/cac.2021.27.3.199.   DOI
65 Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. http://doi.org/10.12989/sem.2016.57.6.1143.   DOI
66 Attia, M.A. and Mohamed, S.A. (2020), "Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory", Eng. Comput., 1-30. https://doi.org/10.1007/s00366-020-01080-1.   DOI
67 Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/SEM.2016.60.4.707.   DOI
68 Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114. https://doi.org/10.12989/CAC.2020.26.2.107.   DOI
69 Yaylaci, M., Adiyaman, G., Oner, E., Birinci, A. (2020a), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. http://doi.org/10.12989/sem.2020.76.3.325.   DOI
70 Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775-783. http://doi.org/10.12989/sem.2019.72.6.775.   DOI
71 Zghal, S., Frikha, A. and Dammak, F. (2018), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B Eng., 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037.   DOI
72 Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177.   DOI
73 Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007.   DOI
74 Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle" Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.   DOI
75 Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities" Struct. Monit. Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.   DOI
76 Malekzadeh, P. and Shojaee, M. (2013), "Free vibration of nanoplates based on a nonlocal two-variable refined plate theory", Composite Structures, 95, 443-452. https://doi.org/10.1016/j.compstruct.2012.07.006.   DOI
77 Kiani, Y. and Eslami, M.R. (2010), "Thermal buckling analysis of functionally graded material beams", Int. J. Mech. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4.   DOI
78 Kiani, Y. and Eslami, M.R. (2013), "An exact solution for thermal buckling of annular FGM plates on an elastic medium", Compos. Part B Eng., 45(1), 101-110. https://doi.org/10.1016/j.compositesb.2012.09.034.   DOI
79 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
80 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017a), "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
81 Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019b), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/jnanor.57.136.   DOI
82 Eltaher, M.A., Omar, F.A., Abdalla, W.S. and Gad, E.H. (2018b), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Wave. Random Complex., 29(2). 264-280. https://doi.org/10.1080/17455030.2018.1429693.   DOI
83 Barati, M.R. (2017), "Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading", Appl. Phys. A., 123(5), 332. https://doi.org/10.1007/s00339-017-0908-3.   DOI
84 Selmi, A. (2020a), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. http://doi.org/10.12989/sss.2020.26.3.361.   DOI
85 Nejadi, M.M. and Mohammadimehr, M. (2020), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, 25(3), 215-224. https://doi.org/10.12989/cac.2020.25.3.215.   DOI
86 Oner, E., Yaylaci, M., Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. http://doi.org/10.12989/sem.2015.54.4.607   DOI
87 Patnaik, S.S., Swain, A. and Roy, T. (2020), "Creep compliance and micromechanics of multi-walled carbon nanotubes based hybrid composites", Compos. Mater. Eng., 2(2), 141-152. http://doi.org/10.12989/cme.2020.2.2.141.   DOI
88 Attia, M.A. and Abdel Rahman, A.A. (2018), "On vibrations of functionally graded viscoelastic nanobeams with surface effects", Int. J. Eng. Sci., 127, 1-32. https://doi.org/10.1016/j.ijengsci.2018.02.005.   DOI
89 Attia, M.A., Shanab, R.A., Mohamed, S.A. and Mohamed, N.A. (2019), "Surface energy effects on the nonlinear free vibration of functionally graded Timoshenko nanobeams based on modified couple stress theory", Int. J. Struct. Stabil. Dyn., 19(11), 1950127. https://doi.org/10.1142/s021945541950127x.   DOI
90 Avcar, M. (2016), "Free vibration of non-homogeneous beam subjected to axial force resting on pasternak foundation", J. Polytechnic Politeknik Dergisi., 19(4), 507-512. https://doi.org/10.2339/2016.19.4.507-512.   DOI
91 Eltaher, M.A., Almalki, T.A., Almitani, K. and Ahmed, K.I. (2019a), "Participation factor and vibration of carbon nanotube with vacancies", J. Nano Res., 57, 158-174. https://doi.org/10.4028/www.scientific.net/jnanor.57.158.   DOI
92 Timesli, A., Braikat, B., Jamal, M. and Damil, N. (2017), "Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression", Comptes Rendus Mcanique, 345, 158-168. https://doi.org/10.1016/j.crme.2016.12.002.   DOI
93 Abed, Z.A.K. and Majeed, W.I. (2020), "Effect of boundary conditions on harmonic response of laminated plates", Compos. Mater. Eng., 2(2), 125-140. https://doi.org/10.12989/cme.2020.2.2.125.   DOI
94 Karami, B., Janghorban, M. (2019b), "On the dynamics of porous nanotubes with variable material properties and variable thickness", Int. J. Eng. Sci., 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.   DOI
95 Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. https://doi.org/10.1177/1077546320947302.   DOI
96 Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Damped dynamic responses of a layered functionally graded thick beam under a pulse load" Struct. Eng. Mech., 75(6), 713-722. https://doi.org/10.12989/SEM.2020.75.6.713.   DOI