Free vibration analysis of sandwich beam with porous FGM core in thermal environment using mesh-free approach

Journal title

Archive of Mechanical Engineering




vol. 69


No 3


Hung, Tran Quang : Faculty of Civil Engineering, The University of Da Nang - University of Science and Technology, Da Nang, Vietnam ; Tu, Tran Minh : Hanoi University of Civil Engineering, Hanoi, Vietnam ; Duc, Do Minh : Faculty of Civil Engineering, The University of Da Nang - University of Science and Technology, Da Nang, Vietnam



thermal vibration ; mesh-free method ; sandwich beam ; porous materials

Divisions of PAS

Nauki Techniczne




Polish Academy of Sciences, Committee on Machine Building


[1] D.K. Jha, T. Kant, and R.K. Singh. A critical review of recent research on functionally graded plates. Composite Structures, 96:833–849, 2013. doi: 10.1016/j.compstruct.2012.09.001.
[2] A.S. Sayyad and Y.M. Ghugal. Modeling and analysis of functionally graded sandwich beams: a review. Mechanics of Advanced Materials and Structures, 26(21):1776–1795, 2019. doi: 10.1080/15376494.2018.1447178.
[3] A. Paul and D. Das. Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness. Engineering Science Technology, an International Journal, 19(3):1608–1625, 2016. doi: 10.1016/j.jestch.2016.05.014.
[4] A. Fallah and M.M. Aghdam. Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation. Composites Part B: Engineering, 43 (3):1523–1530, 2012. doi: 10.1016/j.compositesb.2011.08.041.
[5] A.I. Aria and M.I. Friswell. Computational hygro-thermal vibration and buckling analysis of functionally graded sandwich microbeams. Composites Part B: Engineering, 165:785–797, 2019. doi: 10.1016/j.compositesb.2019.02.028.
[6] S.E. Esfahani, Y. Kiani, and M.R. Eslami. Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations. International Journal of Mechanical Sciences, 69:10–20, 2013. doi: 10.1016/j.ijmecsci.2013.01.007.
[7] M. Lezgy-Nazargah. Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach. Aerospace Science and Technology, 45:154–164, 2015. doi: 10.1016/j.ast.2015.05.006.
[8] L.C. Trinh, T.P. Vo, H.-T. Thai, and T.-K. Nguyen. An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads. Composites Part B: Engineering, 100:152–163, 2016. doi: 10.1016/j.compositesb.2016.06.067.
[9] T.-K. Nguyen, B.-D. Nguyen, T.P. Vo, and H.-T. Thai. Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams. Composite Structures, 176:1050–1060, 2017. doi: 10.1016/j.compstruct.2017.06.036.
[10] P. Malekzadeh and S. Monajjemzadeh. Dynamic response of functionally graded beams in a thermal environment under a moving load. Mechanics of Advanced Materials and Structures, 23(3):248– 258, 2016. doi: 10.1080/15376494.2014.949930.
[11] N. Wattanasakulpong, B. Gangadhara Prusty, and D.W. Kelly. Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. International Journal of Mechanical Sciences, 53(9):734–743, 2011. doi: 10.1016/j.ijmecsci.2011.06.005.
[12] S.C. Pradhan and T. Murmu. Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. Journal of Sound and Vibration, 321(1- 2):342–362, 2009. doi: 10.1016/j.jsv.2008.09.018.
[13] G.-L. She, F.-G. Yuan, and Y.-R. Ren. Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Applied Mathematical Modelling, 47:340–357, 2017. doi: 10.1016/j.apm.2017.03.014.
[14] H.-S. Shen and Z.-X. Wang. Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments. International Journal of Mechanical Sciences, 81:195–206, 2014. doi: 10.1016/j.ijmecsci.2014.02.020.
[15] T.T. Tran, N.H. Nguyen, T.V. Do, P.V. Minh, and N.D. Duc. Bending and thermal buckling of unsymmetric functionally graded sandwich beams in high-temperature environment based on a new third-order shear deformation theory. Journal of Sandwich Structures & Materials, 23(3):906–930, 2021. doi: 10.1177/1099636219849268.
[16] A.R. Setoodeh, M. Ghorbanzadeh, and P. Malekzadeh. A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 226(12):2860–2873, 2012. doi: 10.1177/0954406212440669.
[17] L. Chu, G. Dui, and Y. Zheng. Thermally induced nonlinear dynamic analysis of temperature-dependent functionally graded flexoelectric nanobeams based on nonlocal simplified strain gradient elasticity theory. European Journal of Mechanics - A/Solids, 82:103999, 2020. doi: 10.1016/j.euromechsol.2020.103999.
[18] Y. Fu, J. Wang, and Y. Mao. Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Applied Mathematical Modelling, 36(9):4324–4340, 2012. doi: 10.1016/j.apm.2011.11.059.
[19] W.-R. Chen, C.-S. Chen, and H. Chang. Thermal buckling analysis of functionally graded Euler-Bernoulli beams with temperature-dependent properties. Journal of Applied and Computational Mechanics, 6(3):457–470, 2020. doi: 10.22055/JACM.2019.30449.1734.
[20] N. Wattanasakulpong and V. Ungbhakorn. Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1):111–120, 2014. doi: 10.1016/j.ast.2013.12.002.
[21] N. Wattanasakulpong and A. Chaikittiratana. Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica, 50(5):1331– 1342, 2015. doi: 10.1007/s11012-014-0094-8.
[22] D. Shahsavari, M. Shahsavari, L. Li, and B. Karami. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerospace Science and Technology, 72:134–149, 2018. doi: 0.1016/j.ast.2017.11.004.
[23] Z. Ibnorachid, L. Boutahar, K. EL Bikri, and R. Benamar. Buckling temperature and natural frequencies of thick porous functionally graded beams resting on elastic foundation in a thermal environment. Advances in Acoustics and Vibration, 2019:7986569, 2019. doi: 10.1155/2019/7986569.
[24] Ş.D. Akbaş. Thermal effects on the vibration of functionally graded deep beams with porosity. International Journal of Applied Mechanics, 9(5):1750076, 2017. doi: 10.1142/ S1758825117500764.
[25] H. Babaei, M.R. Eslami, and A.R. Khorshidvand. Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane. Journal of Thermal Stresses, 43(1):109–131, 2020. doi: 10.1080/01495739.2019.1660600.
[26] F. Ebrahimi and A. Jafari. A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities. Journal of Engineering, 2016:9561504, 2016. doi: 10.1155/2016/9561504.
[27] Y. Liu, S. Su, H. Huang, and Y. Liang. Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Composites Part B: Engineering, 168:236–242, 2019. doi: 10.1016/j.compositesb.2018.12.063.
[28] S.S. Mirjavadi, A. Matin, N. Shafiei, S. Rabby, and B. Mohasel Afshari. Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam. Journal of Thermal Stresses, 40(10):1201–1214, 2017. doi: 0.1080/01495739.2017.1332962.
[29] E. Salari, S.A. Sadough Vanini, A.R. Ashoori, and A.H. Akbarzadeh. Nonlinear thermal behavior of shear deformable FG porous nanobeams with geometrical imperfection: Snap-through and postbuckling analysis. International Journal of Mechanical Sciences, 178:105615, 2020. doi: 10.1016/j.ijmecsci.2020.105615.
[30] N. Ziane, S.A. Meftah, G. Ruta, and A. Tounsi. Thermal effects on the instabilities of porous FGM box beams. Engineering Structures, 134:150–158, 2017. doi: 10.1016/j.engstruct. 2016.12.039.
[31] A.I. Aria, T. Rabczuk, and M.I. Friswell. A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams. European Journal of Mechanics - A/Solids, 77:103767, 2019. doi: 10.1016/j.euromechsol.2019.04.002.
[32] G.R. Liu and Y.T. Gu. A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering, 50(4):937–951, 2001. doi: 10.1002/1097-0207(20010210)50:4937::AID-NME62>3.0.CO;2-X.
[33] Y.T. Gu and G.R. Liu. A local point interpolation method for static and dynamic analysis of thin beams. Computer Methods in Applied Mechanics and Engineering, 190(42):5515–5528, 2001. doi: 10.1016/S0045-7825(01)00180-3.
[34] T.H. Chinh, T.M. Tu, D.M. Duc, and T.Q. Hung. Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function. Archive of Applied Mechanics, 91:933–947, 2021. doi: 10.1007/s00419-020-01797-x.
[35] J.N. Reddy and C.D. Chin. Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, 21(6):593–626, 1998. doi: 10.1080/01495739808956165.
[36] H.-S. Shen. Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC Press, 2016. doi: 10.1201/9781420092578.
[37] T.-K. Nguyen, T.P. Vo, B.-D. Nguyen, and J. Lee. An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, 156:238–252, 2016. doi: 10.1016/j.compstruct.2015.11.074.
[38] M. Şimşek. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240(4):697–705, 2010. doi: 10.1016/j.nucengdes.2009.12.013.
[39] J.N. Reddy. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd ed. CRC Press, 2003.
[40] G.R. Liu. Meshfree Methods: Moving Beyond the Finite Element Method. 2nd ed. Taylor & Francis, 2009. doi: 10.1201/9781420082104.
[41] G.R. Liu, Y.T. Gu, and K.Y. Dai. Assessment and applications of point interpolation methods for computational mechanics. International Journal for Numerical Methods in Engineering, 59(10):1373– 1397, 2004. doi: 10.1002/nme.925.
[42] T.P. Vo, H.-T. Thai, T.-K. Nguyen, F. Inam, and J. Lee. A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119:1–12, 2015. doi: 10.1016/j.compstruct.2014.08.006.






DOI: 10.24425/ame.2022.140422 ; ISSN 0004-0738, e-ISSN 2300-1895