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http://dx.doi.org/10.12989/scs.2020.36.3.293

Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models  

Ghandourh, Emad E. (Mining Engineering Dept., Faculty of Engineering, King Abdulaziz University)
Abdraboh, Azza M. (Physics Department, Faculty of Science, Banha University)
Publication Information
Steel and Composite Structures / v.36, no.3, 2020 , pp. 293-305 More about this Journal
Abstract
This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.
Keywords
free vibration; functionally graded nanobeam; porosity models; nonlocal elasticity theory; finite element method;
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1 Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011.   DOI
2 Thang, P.T., Nguyen-Thoi, T., Lee, D., Kang, J. and Lee, J. (2018), "Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions", Aerosp. Sci. Technol., 79, 278-287. https://doi.org/10.1016/j.ast.2018.06.010.   DOI
3 Thanh, C.L., Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2018), "Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory", Compos. Struct., 184, 633-649. https://doi.org/10.1016/j.compstruct.2017.10.025.   DOI
4 Thanh, C.L., Ferreira, A.J.M. and Wahab, M.A. (2019a), "A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis", Thin-Wall. Struct., 145, 106427. https://doi.org/10.1016/j.tws.2019.106427.   DOI
5 Thanh, C.L., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019b), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Method. Appl. M., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.   DOI
6 Thanh, C.L., Tran, L.V., Vu-Huu, T., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019c), "Size-dependent nonlinear analysis and damping responses of FG-CNTRC micro-plates", Comput. Method. Appl. M., 353, 253-276. https://doi.org/10.1016/j.cma.2019.05.002.   DOI
7 Thanh, C.L., Tran, L.V., Bui, T.Q., Nguyen, H.X. and Abdel-Wahab, M. (2019d), "Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates", Compos. Struct., 221, 110838. https://doi.org/10.1016/j.compstruct.2019.04.010.   DOI
8 Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupled Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.   DOI
9 Akbas, S.D. (2019c), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459   DOI
10 Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load", Eng. with Comput., https://doi.org/10.1007/s00366-020-01070-3.
11 Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.   DOI
12 Trabelssi, M., El-Borgi, S., Ke, L. L., & Reddy, J. N. (2017), "Nonlocal free vibration of graded nanobeams resting on a nonlinear elastic foundation using DQM and LaDQM", Compos. Struct., 176, 736-747. https://doi.org/10.1016/j.compstruct.2017.06.010.   DOI
13 Wang, Y.Q., Wan, Y.H. and Zhang, Y.F. (2017), "Vibrations of longitudinally traveling functionally graded material plates with porosities", Eur. J. Mech.-A/Solids, 66, 55-68. http://dx.doi.org/10.1016/j.euromechsol.2017.06.006.   DOI
14 Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.   DOI
15 Yousfi, M., Atmane, H.A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66(3), 353-368. https://doi.org/10.12989/sem.2018.66.3.353.   DOI
16 Yuksel, Y.Z. and Akbas, S.D. (2019), "Buckling analysis of a fiber reinforced laminated composite plate with porosity", J. Comput. Appl. Mech., 50(2), 375-380. 10.22059/JCAMECH.2019.291967.448.
17 Zhang, Y. and Wang, J. (2017), "Fabrication of functionally graded porous polymer structures using thermal bonding lamination techniques", Procedia Manufact., 10, 866-875. https://doi.org/10.1016/j.promfg.2017.07.073.   DOI
18 Zhao, X., Zheng, S. and Li, Z. (2020), "Effects of porosity and flexoelectricity on static bending and free vibration of AFG piezoelectric nanobeams", Thin-Wall. Struct., 151, 106754. https://doi.org/10.1016/j.tws.2020.106754.   DOI
19 Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013c), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016.   DOI
20 Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013b), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039.   DOI
21 Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014a), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.   DOI
22 Apuzzo, A., Barretta, R., Luciano, R., de Sciarra, F.M. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model", Compos. Part B: Eng., 123, 105-111. https://doi.org/10.1016/j.compositesb.2017.03.057.   DOI
23 Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35(4), 555-566. https://doi.org/10.12989/scs.2020.35.4.555.   DOI
24 Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi:10.1016/j.apm.2010.07.006.   DOI
25 Amar, L.H.H., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/sem.2017.64.5.527.   DOI
26 Aria, A.I. and Friswell, M.I. (2019), "A nonlocal finite element model for buckling and vibration of functionally graded nanobeams", Compos. Part B: Eng., 166, 233-246. https://doi.org/10.1016/j.compositesb.2018.11.071.   DOI
27 Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (Eds.). (2013), "Functionally graded materials: design, processing and applications" (Vol. 5), Springer Science & Business Media.
28 Mirzaei, M.M.H., Loghman, A. and Arefi, M. (2019), "Time-dependent creep analysis of a functionally graded beam with trapezoidal cross section using first-order shear deformation theory", Steel Compos. Struct., 30(6), 567-576. https://doi.org/10.12989/scs.2019.30.6.567.   DOI
29 Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model", Eng. with Comput., 1-14. https://doi.org/10.1007/s00366-020-00976-2.
30 Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014b), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.   DOI
31 Eltaher, M.A. and Agwa, M.A. (2016), "Analysis of size-dependent mechanical properties of CNTs mass sensor using energy equivalent model", Sensor. Actuat. A: Phys., 246, 9-17. https://doi.org/10.1016/j.sna.2016.05.009.   DOI
32 Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016a), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. ttps://doi.org/10.1016/j.apm.2015.11.026.   DOI
33 Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016b), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51. https://doi.org/10.12989/anr.2016.4.1.051.   DOI
34 Eltaher, M.A., El-Borgi, S. and Reddy, J.N. (2016c). "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013.   DOI
35 Heydari, A. (2018), "Exact vibration and buckling analyses of arbitrary gradation of nano-higher order rectangular beam", Steel Compos. Struct., 28(5), 589-606. https://doi.org/10.12989/scs.2018.28.5.589 .   DOI
36 Eltaher, M.A. and Mohamed, N. (2020b), "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
37 Eltaher, M.A. and Mohamed, S.A. (2020c), "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
38 Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.   DOI
39 Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020a), "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
40 Hamed M.A., Abu-bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020b), "Influence of Axial Load Function and Optimization on Static Stability of Sandwich Functionally Graded Beams with Porous Core", Eng. with Comput.. https://doi.org/10.1007/s00366-020-01023-w.
41 Jandaghian, A.A. and Rahmani, O. (2017), "Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions", Steel Compos. Struct., 25(1), 67-78. https://doi.org/10.12989/scs.2017.25.1.067.   DOI
42 Karami, B., Janghorban, M. and Rabczuk, T. (2020), "Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory", Compos. Part B: Eng., 182, 107622. https://doi.org/10.1016/j.compositesb.2019.107622.   DOI
43 Khater, M.E., Eltaher, M.A., Abdel-Rahman, E. and Yavuz, M. (2014), "Surface and thermal load effects on the buckling of curved nanowires", Eng. Sci. Technol. Int. J., 17(4), 279-283. https://doi.org/10.1016/j.jestch.2014.07.003.   DOI
44 Akbas, S.D. (2017a), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009.   DOI
45 Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.   DOI
46 Agwa, M.A. and Eltaher, M.A. (2016), "Vibration of a carbyne nanomechanical mass sensor with surface effect", Appl. Phys. A, 122(4), 335. https://doi.org/10.1007/s00339-016-9934-9.   DOI
47 Akbas, S.D. (2015), "Free vibration and bending of functionally graded beams resting on elastic foundation", Research on Engineering Structures and Materials, 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107   DOI
48 Akbas, S.D. (2017b), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764.   DOI
49 Akbas, S.D. (2017c), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.   DOI
50 Akbas, S.D. (2017d), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
51 Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39. https://doi.org/10.12989/anr.2018.6.1.039.   DOI
52 Akbas, S.D. (2018b), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059.   DOI
53 Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H. and Abdel-Wahab, M. (2017b), "Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads", Nonlinear Dynam., 87(2), 879-894. https://doi.org/10.1007/s11071-016-3085-6.   DOI
54 Nguyen, D.K. and Tran, T.T. (2018), "Free vibration of tapered BFGM beams using an efficient shear deformable finite element model", Steel Compos. Struct., 29(3), 363-377. https://doi.org/10.12989/scs.2018.29.3.363.   DOI
55 Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Method. Appl. M., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002.   DOI
56 Phung-Van, P., Ferreira, A.J.M., Nguyen-Xuan, H. and Wahab, M. A. (2017a), "An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates", Compos. Part B: Eng., 118, 125-134. https://doi.org/10.1016/j.compositesb.2017.03.012.   DOI
57 Phung-Van, P., Thanh, C.L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2018), "Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments", Compos. Struct., 201, 882-892. https://doi.org/10.1016/j.compstruct.2018.06.087.   DOI
58 Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2019), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B: Eng., 164, 215-225. https://doi.org/10.1016/j.compositesb.2018.11.036.   DOI
59 Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003.   DOI
60 Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Dynamic analysis of layered functionally graded viscoelastic deep beams with different boundary conditions due to a pulse load", Int. J. Appl. Mech., https://doi.org/10.1142/S1758825120500556.
61 Bambaeechee, M. (2019), "Free vibration of AFG beams with elastic end restraints", Steel Compos. Struct., 33(3), 403-432. https://doi.org/10.12989/scs.2019.33.3.403.   DOI
62 Barretta, R., Canadija, M., Feo, L., Luciano, R., de Sciarra, F.M., and Penna, R. (2018), "Exact solutions of inflected functionally graded nano-beams in integral elasticity", Compos. Part B: Eng., 142, 273-286. https://doi.org/10.1016/j.compositesb.2017.12.022.   DOI
63 Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.   DOI
64 Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999.   DOI
65 Eltaher, M.A., Attia, M.A., Soliman, A.E. and Alshorbagy, A.E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097.   DOI
66 Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.   DOI
67 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
68 Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Nonlocal nonlinear dynamic behavior of composite piezo-magnetic beams using a refined higher-order beam theory", Steel Compos. Struct., 35(4), 545-554. https://doi.org/10.12989/scs.2020.35.4.545.   DOI
69 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
70 Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115.   DOI
71 Gul, U. and Aydogdu, M. (2018), Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics", Compos. Part B: Eng., 137, 60-73. https://doi.org/10.1016/j.compositesb.2017.11.005.   DOI
72 Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038.   DOI
73 Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963.   DOI
74 Akbas, S.D. (2018c), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013   DOI
75 Akbas, S.D. (2019a), "Longitudinal forced vibration analysis of porous a nanorod", Muhendislik Bilimleri ve Tasarim Dergisi, 7(4), 736-743.   DOI
76 Rahmani, O., Hosseini, S.A.H., Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., 26(5), 607-20. https://doi.org/10.12989/scs.2018.26.5.607.   DOI
77 Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.   DOI
78 Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59(11), 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008.   DOI
79 Shaat, M., Eltaher, M.A., Gad, A.I. and Mahmoud, F.F. (2013), "Nonlinear size-dependent finite element analysis of functionally graded elastic tiny-bodies", Int. J. Mech. Sci., 77, 356-364. https://doi.org/10.1016/j.ijmecsci.2013.04.015.   DOI
80 Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013.   DOI
81 Simsek, M. (2019), "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.   DOI
82 Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.   DOI
83 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013a), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030. .   DOI
84 Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.   DOI
85 Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205.   DOI
86 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Mathematics Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090.   DOI
87 Eltaher, M.A., Omar, F.A., Abdalla, W.S. and Gad, E.H. (2019a), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Waves in Random and Complex Media, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693.   DOI
88 Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018c), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsystem Technologies, 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3.   DOI
89 Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018d), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsystem Technologies, 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.   DOI
90 Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.   DOI
91 Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019b), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039.   DOI
92 Eltaher, M.A. and Mohamed, N.A. (2020a), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart Struct. Syst., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501.   DOI
93 Matula, I., Dercz, G. and Barczyk, J. (2019), "Titanium/Zirconium functionally graded materials with porosity gradients for potential biomedical applications", Mater. Sci. Technol., 1-6. https://doi.org/10.1080/02670836.2019.1593603.
94 Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.   DOI
95 Khatir, S., Tiachacht, S., Thanh, C.L., Bui, T.Q. and Wahab, M.A. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.   DOI
96 Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. http://dx.doi.org/10.1016/j.matdes.2016.12.061.   DOI
97 Lee, J.C. and Ahn, S.H. (2018), "Bulk density measurement of porous functionally graded materials", Int. J. Precision Eng. Manufact., 19(1), 31-37. DOI: 10.1007/s12541-018-0004-4.   DOI
98 Liu, H., Lv, Z. and Wu, H. (2019), "Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory", Compos. Struct., 214, 47-61. https://doi.org/10.1016/j.compstruct.2019.01.090.   DOI
99 Mekerbi, M., Benyoucef, S., Mahmoudi, A., Bourada, F. and Tounsi, A. (2019), "Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution", Struct. Eng. Mech., 72(4), 513-524. https://doi.org/10.12989/sem.2019.72.4.513.   DOI
100 Melaibari, A., Khoshaim, A. B., Mohamed, S.A. and Eltaher, M. A. (2020), "Static stability and of symmetric and sigmoid functionally graded beam under variable axial load", Steel Compos. Struct., 35(5), 671-685. https://doi.org/10.12989/scs.2020.35.5.671.   DOI