Using grapheme material with functionally graded beam structures - A comprehensive review
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Published:
Dec 28, 2021
Keywords:
Graphene Composite beam structures Functionally Graded Materials (FGMs)
Main Article Content
Abstract
Graphene materials (GPLs) have attracted a lot of attention. Owing to their superior mechanical properties such as Young’s modulus, high strength, large specific surface area and and good thermal conductivity etc. The structures considered in this paper are in form functionally graded materials (FGMs) with varying properties over a changing dimension. The present paper (1) briefly reviews the mechanical properties of graphene and graphene composites; (2) summarizes the characteristics of functionally graded materials (FGM) and fabrication (3) the prediction of effective mechanical properties of composite materials (4) presents a comprehensive review on the mechanical analyses and conclusion respectively.
Article Details
Section
Research Articles
Copyright @2021 Engineering Transactions
Faculty of Engineering and Technology
Mahanakorn University of Technology
References
[1] M. Simsek, “Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories”,
Nuclear Engineering and Design, Vol. 240, pp. 697-705, 2010.
[2] S. Iijima, “Helical microtubules of graphitic carbon”, Nature, Vol. 354, pp. 56-58, 1991.
[3] K. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva and A.A. Firsov, “Electric field effect in
atomically thin carbon films”, Science, Vol. 306(5696), pp. 666-669, 2004.
[4] S. Zhaoa, Z. Zhaob, Z. Yangc, L. Ked, S. Kitipornchaia and J. Yangb, “Functionally graded graphene reinforced composite
structures: A review”, Engineerng Structures, Vol. 210, 2020.
[5] แมนมนัส ศรีแก้ว และสายันต์ แสงสุวรรณ,”วัสดุมหัศจรรย์แกรฟีน : กลยุทธ์การสังเคราะห์สมบัติการพัฒนา
การพิสูจน์เอกลักษณ์และการประยุกต์ใช้ (Graphene (The miracle material) : Strategies for Synthesis, Properties,
Development, Characterizations and Applications)”, วารสารวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัยอุบลราชธานี, ปีที่ 22 ฉบับที่ 2 เดือน
พฤษภาคม-สิงหาคม, หน้า 39-49, 2563.
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[7] C. Lee, X. Wei, JW. Kysar and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer grapheme”,
Science, Vol. 321, pp. 385-388, 2008.
[8] SP. Koenig, NG. Boddeti, ML. Dunn and JS. Bunch, “Ultrastrong adhesion of grapheme membranes”, Nat Nanotechnol, Vol. 6,
pp. 543-546, 2011.
[9] A. Politano, AR. Marino, D. Campi, D. Farias, R. Miranda and G. Chiarello, “Elastic properties of a macroscopic grapheme sample
from phonon dispersion measurements”, Carbon, Vol. 50, pp. 4903-4910, 2012.
[10] GV. Lier, CV. Alsenoy, VV. Doren and P. Geerlings, “Ab initio study of the elastic properties of single-walled carbon nanotubes
and grapheme”, Chem Phys Lett, Vol. 326, pp. 181-185, 2000.
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2487-2499, 2003.
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Vol. 76, 2007.
[13] MM. Shokrieh and R. Rafiee, “Prediction of Young’s modulus of grapheme sheets and carbon nanotubes using nanoscale
continuum mechanics approach”, Mater Des, Vol. 31, pp. 790-795, 2010.
[14] DG. Kvashnin and PB. Sorokin, “Effect of ultrahigh stiffness of defective grapheme from atomistic point of view”, J Phys Chem
Lett, Vol. 6, pp. 2384-2387, 2015.
[15] J.N. Reddy, “Mechanics of Laminated composite plates and shells Theory and Analysis”, 2nd ed., U.S.A: CRC Press, 2004.
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Materials, Vol. 13, pp.257-264, 1987.
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materials,” Journal of Composite Materials, Vol. 17(3), pp. 210-223. 1983.
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materials and structures”. Progress in Aerospace Sciences, Vol.79, pp. 1-14, 2015.
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materials and structures”. Progress in Aerospace Sciences, Vol.79, pp. 1-14, 2015.
[20] M. Naebe, and K. Shirvanimoghaddam, “Functionally graded materials: A review
of fabrication and properties,” Applied Materials Today, Vol. 5, pp.223-245. 2016.
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York: Springer Science Business Media, 1999.
[22] C. Feng, S. Kitipornchai and J. Yang, “Nonlinear bending of polymer nano composite beams reinforce with
non-uniformly distributed grapheme platelets (GPLs)”, Compos B Eng., Vol. 110, pp. 132-140, 2017.
[23] M. Song, S. Kitipornchai and J. Yang, “Free and forced vibrations of functionally graded polymer composite plates reinforced
With grapheme nanoplatelets”, Compos Struct, Vol. 159, pp. 579-588, 2017.
[24] J. Yang, H. Wu and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer grapheme platelet-reinforced
composite beams”, Compos Struct, Vol. 161, pp. 111-118, 2017.
[25] M. Piggott, “Load bearing fiber composites”, Moscow: Kluwer Academic Publisher; 2002.
[26] RM. Jones, “Mechanics of composite materials”, Taylor & Francis, 1999.
[27] V. Ungbhakorn and N. Wattanasakulpong, “Thermo-elasic vibration analysis of third-order shear deformable functionally
Graded plates with distributed patch mass under thermal environment”, Applied Acoustics, Vol. 74, pp. 1045-1059, 2013.
[28] Z.X. Lei, L.W. Zhang and K.M. Liew, “Analysis of laminated CNT reinforced functionally graded plates using the element-free
kp-Riz method”, Composites Part B, Vol. 84, pp. 211-221, 2016.
[29] L. Li, L. Xiaobai and H. Yujin, “Free vibration analysis of nonlocal strain gradient beams made of functionally graded material”,
International Journal of Engineering Science, Vol. 102, pp. 77-92, 2016.
[30] M. Royal, B. Shubhankar and N.S. Kashi, “Stress and deformation of functionally graded rotating
Disk based on modified rule of mixture”, Materialstoday:PROCEEDINGS, Vol. 9, pp. 17778-17785, 2018.
[31] M.B. Yihumie, E.W. Dereje, T.C. Ewnetu, A.A. Solomon, K.S. Senthil and P. Velmurugan, “Effect of volumetric fraction index on
temperature distribution in thick-walled functionally graded material made cylinder”, Materialstoday:PROCEEDINGS, Vol. 46, pp. 7442-7447, 2021.
[32] HL. Cox, “The elasticity and strength of paper and other fibrous materials”, Br. J. Appl. Phys., Vol. 3, pp. 72, 1952.
[33] T. Abhishek and K.S. Sunil, “Modified shear lag theory based fatigue crack growth life prediction model for short-fiber
reinforced metal matrix composites”, International Journal of Fatigue, Vol. 70, pp. 123-129, 2015.
[34] JC. Halpin, “Stiffness and expansion estimates for oriented short fiber composites”, J. Compos. Mater., Vol. 3, pp. 732-734,
1969.
[35] JC. Halpin and JL. Kardos, “The Halpin-Tsai equations: a review”, Polym Eng. Sci., Vol. 16, pp. 344-352, 1976.
[36] E.Farzad and D. Ali, “Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization
model”, Composites Part B: Engineering, Vol. 173, 2019.
[37] Z. Yasser, Y.R. Kyong and P. Soo-Jin, “A developed equation for electrical conductivity of polymer carbon nanotubes (CNT)
nanocomposites based on Halpin-Tsai model”, Results in Physis, Vol. 14, 2019.
[38] F. Mustapha, J. Mohammad, Z. Abdelkabir and B. Naoual, “Bending analysis of functionally graded graphene oxide
powder-reinforced composite beams using a meshfree method”, Aerospace Science and Technology, Vol. 110, 2021.
[39] JD. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion and related problems”, Proc. Roy. Soc. London.,
Vol. 241, pp. 379-396, 1957.
[40] L. Sergey, V.B. Dmitrii, L. Anatolii and A. Elias, “Eshelby’s inclusion problem in the gradient theory of elasticity: Applications to
composite materials”, International Journal of Engineering Science, Vol. 49, pp. 1517-1525, 2011.
[41] T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions”, Acta.
Metall., Vol. 21, pp. 571-574, 1973.
[42] V.P. Tran, S. Brisard, Guilleminot, K. Sab, “Mori–Tanaka estimates of the effective elastic properties of
stress-gradient composites”, International Journal of Solids and Structures, Vol. 146, pp. 55-68, 2018.
[43] R. Sun, L. Li, S. Zhao, C. Feng, S. Kitipornchai and J. Yang, “Temperature-dependent mechanical properties of defective
grapheme Reinforced polymer nanocomposite”, Mech. Adv. Mater. Struct., pp. 1-10, 2019.
[44] F. Lin, Y. Xiang and H-S. Shen, “Temperature dependent mechanical properties of grapheme reinforced polymer
nanocomposite-A molecular dynamics simulation”, Compos Part B Eng, Vol. 111, pp. 261-269, 2017.
[45] M.A. Rafiee, J. Rafiee, Z. Wang, H. Song, Z-Z. Yu and N. Koratkar, “Enhanced mechanical properties of nanocomposites at low
grapheme conten”, ACS Nano, Vol. 3, pp. 3884-3890, 2009.
[46] H-S. Shen, F. Lin and Y. Xiang, “Nonlinear bending and thermal postbuckling of functionally graded
graphene-reinforced composite laminated beams resting on elastic foundations”, Engineering Structures, Vol. 140, pp. 89-97,
2017.
[47] M. Rafuee, F. Nitzsche and M.R. Labrosse, “Modeling and mechanical analysis of multiscale fiber-reinforced graphene
composites: Nonlinear bending, thermal post-buckling and large amplitude vibration”, International Journal of Non-Linear
Mechanics, Vol. 103, pp. 104-112, 2018.
[48] B. Anirudh, T.B. Zineb, O. Polit, M. Ganapathi and G. Prateek, “Nonlinear bending of porous curved beams reinforced by
functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach”,
Mechanics, Vol. 119, 2020.
[49] M. Fouaidi, M. Jamal, A. Zaite and N. Beloaggadia, “Bending analysis of functionally graded graphene oxide
powder-reinforced composite beams using a meshfree method”, Aerospace Science and Technology, Vol. 110, 2021.
[50] J. Yang, H. Wu and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced
composite beams”, Composite Structures, Vol. 161, pp. 111-118, 2017.
[51] S. Kitipornchai, D. Chen and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by
graphene platelets”, Materials & Design, Vol. 116, pp. 656-665, 2017
[52] M. Song, L. Chen, J. Yang, W. Zhu and S. Kitipornchai, “Thermal buckling and postbuckling of edge-cracked functionally graded
multilayer graphene nanocomposite beams on an elastic foundation”, International Journal of Mechanical Sciences, Vol. 161-
162, 2019.
[53] M. Song, L. Chen, J. Yang, W. Zhu and S. Kitipornchai, “Free vibration and buckling analyses of edge-cracked functionally
graded multilayer graphene nanoplatelet-reinforced composite beams resting on an elastic foundation”, Journal of Sound and
Vibration, Vol. 458, pp. 89-108, 2019.
[54] M. Tam, Z. Yang, S. Zhao, H. Zhang, Y. Zhang and J. Yang, “Nonlinear bending of elastically restrained functionally graded
graphene nanoplatelet reinforced beams with an open edge crack”, Thin-Walled Structures, Vol. 156, 2020.
[55] H. Wu, J. Yang and S. Kitipornchai, “Dynamic instability of functionally graded multilayer graphene nanocomposite beams in
thermal environment”, Composite Structures, Vol. 162, pp. 244-254, 2017.
[56] Y. Wang, K. Xie, T. Fu and C. Shi, “Vibration response of a functionally graded graphene nanoplatelet reinforced composite
beam under two successive moving masses”, Composite Structures, Vol. 209, pp. 928-939, 2019.
Nuclear Engineering and Design, Vol. 240, pp. 697-705, 2010.
[2] S. Iijima, “Helical microtubules of graphitic carbon”, Nature, Vol. 354, pp. 56-58, 1991.
[3] K. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva and A.A. Firsov, “Electric field effect in
atomically thin carbon films”, Science, Vol. 306(5696), pp. 666-669, 2004.
[4] S. Zhaoa, Z. Zhaob, Z. Yangc, L. Ked, S. Kitipornchaia and J. Yangb, “Functionally graded graphene reinforced composite
structures: A review”, Engineerng Structures, Vol. 210, 2020.
[5] แมนมนัส ศรีแก้ว และสายันต์ แสงสุวรรณ,”วัสดุมหัศจรรย์แกรฟีน : กลยุทธ์การสังเคราะห์สมบัติการพัฒนา
การพิสูจน์เอกลักษณ์และการประยุกต์ใช้ (Graphene (The miracle material) : Strategies for Synthesis, Properties,
Development, Characterizations and Applications)”, วารสารวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัยอุบลราชธานี, ปีที่ 22 ฉบับที่ 2 เดือน
พฤษภาคม-สิงหาคม, หน้า 39-49, 2563.
[6] AK. Geim and KS. Novoselov, “The rise of graphen”, Nat Mater, Vol. 6, pp. 183-191, 2007.
[7] C. Lee, X. Wei, JW. Kysar and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer grapheme”,
Science, Vol. 321, pp. 385-388, 2008.
[8] SP. Koenig, NG. Boddeti, ML. Dunn and JS. Bunch, “Ultrastrong adhesion of grapheme membranes”, Nat Nanotechnol, Vol. 6,
pp. 543-546, 2011.
[9] A. Politano, AR. Marino, D. Campi, D. Farias, R. Miranda and G. Chiarello, “Elastic properties of a macroscopic grapheme sample
from phonon dispersion measurements”, Carbon, Vol. 50, pp. 4903-4910, 2012.
[10] GV. Lier, CV. Alsenoy, VV. Doren and P. Geerlings, “Ab initio study of the elastic properties of single-walled carbon nanotubes
and grapheme”, Chem Phys Lett, Vol. 326, pp. 181-185, 2000.
[11] C. Li and T-W. Chou, “A structural mechanics approach for the analysis of carbon nanotubes”, Int J Solids Struct, Vol. 40, pp.
2487-2499, 2003.
[12] F. Liu, P. Ming and J. Li, “Ab initiocalculation of ideal strength and phonon instability of grapheme under tension”, Phys Rev B,
Vol. 76, 2007.
[13] MM. Shokrieh and R. Rafiee, “Prediction of Young’s modulus of grapheme sheets and carbon nanotubes using nanoscale
continuum mechanics approach”, Mater Des, Vol. 31, pp. 790-795, 2010.
[14] DG. Kvashnin and PB. Sorokin, “Effect of ultrahigh stiffness of defective grapheme from atomistic point of view”, J Phys Chem
Lett, Vol. 6, pp. 2384-2387, 2015.
[15] J.N. Reddy, “Mechanics of Laminated composite plates and shells Theory and Analysis”, 2nd ed., U.S.A: CRC Press, 2004.
[16] M. Niino, T. Hirai and R. Watanabe, “The functionally gradient materials”, Journal of the Japan Society for Composite
Materials, Vol. 13, pp.257-264, 1987.
[17] S.S. Wang, “Fracture mechanics for delamination problems in composite
materials,” Journal of Composite Materials, Vol. 17(3), pp. 210-223. 1983.
[18] A. Gupta, and M. Talha, “Recent development in modeling and analysis of
materials and structures”. Progress in Aerospace Sciences, Vol.79, pp. 1-14, 2015.
[19] A. Gupta, and M. Talha, “Recent development in modeling and analysis of
materials and structures”. Progress in Aerospace Sciences, Vol.79, pp. 1-14, 2015.
[20] M. Naebe, and K. Shirvanimoghaddam, “Functionally graded materials: A review
of fabrication and properties,” Applied Materials Today, Vol. 5, pp.223-245. 2016.
[21] Y. Miyamoto, WA. Kaysser, BH. Rabin and A. Kawasaki, “Functionally graded material:design processing and applications”. New
York: Springer Science Business Media, 1999.
[22] C. Feng, S. Kitipornchai and J. Yang, “Nonlinear bending of polymer nano composite beams reinforce with
non-uniformly distributed grapheme platelets (GPLs)”, Compos B Eng., Vol. 110, pp. 132-140, 2017.
[23] M. Song, S. Kitipornchai and J. Yang, “Free and forced vibrations of functionally graded polymer composite plates reinforced
With grapheme nanoplatelets”, Compos Struct, Vol. 159, pp. 579-588, 2017.
[24] J. Yang, H. Wu and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer grapheme platelet-reinforced
composite beams”, Compos Struct, Vol. 161, pp. 111-118, 2017.
[25] M. Piggott, “Load bearing fiber composites”, Moscow: Kluwer Academic Publisher; 2002.
[26] RM. Jones, “Mechanics of composite materials”, Taylor & Francis, 1999.
[27] V. Ungbhakorn and N. Wattanasakulpong, “Thermo-elasic vibration analysis of third-order shear deformable functionally
Graded plates with distributed patch mass under thermal environment”, Applied Acoustics, Vol. 74, pp. 1045-1059, 2013.
[28] Z.X. Lei, L.W. Zhang and K.M. Liew, “Analysis of laminated CNT reinforced functionally graded plates using the element-free
kp-Riz method”, Composites Part B, Vol. 84, pp. 211-221, 2016.
[29] L. Li, L. Xiaobai and H. Yujin, “Free vibration analysis of nonlocal strain gradient beams made of functionally graded material”,
International Journal of Engineering Science, Vol. 102, pp. 77-92, 2016.
[30] M. Royal, B. Shubhankar and N.S. Kashi, “Stress and deformation of functionally graded rotating
Disk based on modified rule of mixture”, Materialstoday:PROCEEDINGS, Vol. 9, pp. 17778-17785, 2018.
[31] M.B. Yihumie, E.W. Dereje, T.C. Ewnetu, A.A. Solomon, K.S. Senthil and P. Velmurugan, “Effect of volumetric fraction index on
temperature distribution in thick-walled functionally graded material made cylinder”, Materialstoday:PROCEEDINGS, Vol. 46, pp. 7442-7447, 2021.
[32] HL. Cox, “The elasticity and strength of paper and other fibrous materials”, Br. J. Appl. Phys., Vol. 3, pp. 72, 1952.
[33] T. Abhishek and K.S. Sunil, “Modified shear lag theory based fatigue crack growth life prediction model for short-fiber
reinforced metal matrix composites”, International Journal of Fatigue, Vol. 70, pp. 123-129, 2015.
[34] JC. Halpin, “Stiffness and expansion estimates for oriented short fiber composites”, J. Compos. Mater., Vol. 3, pp. 732-734,
1969.
[35] JC. Halpin and JL. Kardos, “The Halpin-Tsai equations: a review”, Polym Eng. Sci., Vol. 16, pp. 344-352, 1976.
[36] E.Farzad and D. Ali, “Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization
model”, Composites Part B: Engineering, Vol. 173, 2019.
[37] Z. Yasser, Y.R. Kyong and P. Soo-Jin, “A developed equation for electrical conductivity of polymer carbon nanotubes (CNT)
nanocomposites based on Halpin-Tsai model”, Results in Physis, Vol. 14, 2019.
[38] F. Mustapha, J. Mohammad, Z. Abdelkabir and B. Naoual, “Bending analysis of functionally graded graphene oxide
powder-reinforced composite beams using a meshfree method”, Aerospace Science and Technology, Vol. 110, 2021.
[39] JD. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion and related problems”, Proc. Roy. Soc. London.,
Vol. 241, pp. 379-396, 1957.
[40] L. Sergey, V.B. Dmitrii, L. Anatolii and A. Elias, “Eshelby’s inclusion problem in the gradient theory of elasticity: Applications to
composite materials”, International Journal of Engineering Science, Vol. 49, pp. 1517-1525, 2011.
[41] T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions”, Acta.
Metall., Vol. 21, pp. 571-574, 1973.
[42] V.P. Tran, S. Brisard, Guilleminot, K. Sab, “Mori–Tanaka estimates of the effective elastic properties of
stress-gradient composites”, International Journal of Solids and Structures, Vol. 146, pp. 55-68, 2018.
[43] R. Sun, L. Li, S. Zhao, C. Feng, S. Kitipornchai and J. Yang, “Temperature-dependent mechanical properties of defective
grapheme Reinforced polymer nanocomposite”, Mech. Adv. Mater. Struct., pp. 1-10, 2019.
[44] F. Lin, Y. Xiang and H-S. Shen, “Temperature dependent mechanical properties of grapheme reinforced polymer
nanocomposite-A molecular dynamics simulation”, Compos Part B Eng, Vol. 111, pp. 261-269, 2017.
[45] M.A. Rafiee, J. Rafiee, Z. Wang, H. Song, Z-Z. Yu and N. Koratkar, “Enhanced mechanical properties of nanocomposites at low
grapheme conten”, ACS Nano, Vol. 3, pp. 3884-3890, 2009.
[46] H-S. Shen, F. Lin and Y. Xiang, “Nonlinear bending and thermal postbuckling of functionally graded
graphene-reinforced composite laminated beams resting on elastic foundations”, Engineering Structures, Vol. 140, pp. 89-97,
2017.
[47] M. Rafuee, F. Nitzsche and M.R. Labrosse, “Modeling and mechanical analysis of multiscale fiber-reinforced graphene
composites: Nonlinear bending, thermal post-buckling and large amplitude vibration”, International Journal of Non-Linear
Mechanics, Vol. 103, pp. 104-112, 2018.
[48] B. Anirudh, T.B. Zineb, O. Polit, M. Ganapathi and G. Prateek, “Nonlinear bending of porous curved beams reinforced by
functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach”,
Mechanics, Vol. 119, 2020.
[49] M. Fouaidi, M. Jamal, A. Zaite and N. Beloaggadia, “Bending analysis of functionally graded graphene oxide
powder-reinforced composite beams using a meshfree method”, Aerospace Science and Technology, Vol. 110, 2021.
[50] J. Yang, H. Wu and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced
composite beams”, Composite Structures, Vol. 161, pp. 111-118, 2017.
[51] S. Kitipornchai, D. Chen and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by
graphene platelets”, Materials & Design, Vol. 116, pp. 656-665, 2017
[52] M. Song, L. Chen, J. Yang, W. Zhu and S. Kitipornchai, “Thermal buckling and postbuckling of edge-cracked functionally graded
multilayer graphene nanocomposite beams on an elastic foundation”, International Journal of Mechanical Sciences, Vol. 161-
162, 2019.
[53] M. Song, L. Chen, J. Yang, W. Zhu and S. Kitipornchai, “Free vibration and buckling analyses of edge-cracked functionally
graded multilayer graphene nanoplatelet-reinforced composite beams resting on an elastic foundation”, Journal of Sound and
Vibration, Vol. 458, pp. 89-108, 2019.
[54] M. Tam, Z. Yang, S. Zhao, H. Zhang, Y. Zhang and J. Yang, “Nonlinear bending of elastically restrained functionally graded
graphene nanoplatelet reinforced beams with an open edge crack”, Thin-Walled Structures, Vol. 156, 2020.
[55] H. Wu, J. Yang and S. Kitipornchai, “Dynamic instability of functionally graded multilayer graphene nanocomposite beams in
thermal environment”, Composite Structures, Vol. 162, pp. 244-254, 2017.
[56] Y. Wang, K. Xie, T. Fu and C. Shi, “Vibration response of a functionally graded graphene nanoplatelet reinforced composite
beam under two successive moving masses”, Composite Structures, Vol. 209, pp. 928-939, 2019.