Finite element method for axial and bending coupling effect on free vibration response of functionally graded beams under thermal environment

References

• J. N. Reddy, A simple higher-order theory of laminated composite plate, J Appl. Mech., vol. 51, no. 4, pp. 745–752, 1984. DOI: 10.1115/1.3167719.
   Web of Science ®Google Scholar
• M. Touratier, An efficient standard plate theory, Int. J. Eng. Sci., vol. 29, no. 8, pp. 901–916, 1991. DOI: 10.1016/0020-7225(91)90165-Y.
   Web of Science ®Google Scholar
• K. S. Afaq, M. Karama, and S. Mistou, Un nouveau modèle raffiné pour les structure smulticouches. In Comptes rendues des 13éme journées nationales sur les composites, Strasbourg, 2003, pp. 289–292.
   Google Scholar
• M. K. Rao, and Y. M. Desai, Analytical solution for vibrations of laminated and sandwich plates, Compos. Struct., vol. 63, no. 3–4, pp. 361–373, 2004. DOI: 10.1016/S0263-8223(03)00185-5.
   Web of Science ®Google Scholar
• M. K. RaO, K. Scherbatiuk, Y. M. Deesai, and A. H. Shah, Natural vibrations of laminated and sandwich plates, J. Eng. Mech., vol. 130, no. 11, pp. 1268–1278, 2004. DOI: 10.1061/(ASCE)0733-9399(2004)130:11(1268).
   Web of Science ®Google Scholar
• S. Kapuria, P. C. Dumir, and N. K. Jain, Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams, Compos. Struct., vol. 64, no. 3–4, pp. 317–327, 2004. DOI: 10.1016/j.compstruct.2003.08.013.
   Web of Science ®Google Scholar
• H. Youzera, S. A. Meftah, N. Challamel, and A. Tounsi, Nonlinear damping and forced vibration analysis of laminated composite beams, Compos. Part B. Eng., vol. 43, no. 3, pp. 1147–1154, 2012. DOI: 10.1016/j.compositesb.2012.01.008.
   Web of Science ®Google Scholar
• M. Koizumi, FGM activities in Japan, Compos. Part B. Eng., vol. 28, no. 1–2, pp. 1–4, 1997. DOI: 10.1016/S1359-8368(96)00016-9.
   Web of Science ®Google Scholar
• J. J. Sobczak, and L. Drenchev, Metallic functionally graded materials: a specific class of advanced composites, Mater. Sci. Technol., vol. 29, no. 4, pp. 297–316, 2013. DOI: 10.1016/j.jmst.2013.02.006.
   Google Scholar
• K. Koutoati, F. Mohri, and E. M. Daya, Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams, Mech. Adv. Mater. Struct., vol. 28, no. 15, pp. 1537–1553, 2021. DOI: 10.1080/15376494.2019.1685144.
   Web of Science ®Google Scholar
• A. I. Aria, T. Rabczuk, and M. I. Friswell, A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams, Eur. J. Mech. A., Solids, vol. 77, pp. 103767, 2019. DOI: 10.1016/j.euromechsol.2019.04.002.
   Web of Science ®Google Scholar
• H. M. Zhou, X. M. Zhang, and Z. Y. Wang, Thermal analysis of 2D FGM beam subjected to thermal loading using meshless weighted least-square method, Math. Prob. Eng., vol. 2019, pp. 1–10, 2019. DOI: 10.1155/2019/2541707.
   Web of Science ®Google Scholar
• Y. Chen, G. Jin, C. Zhang, T. Ye, and Y. Xue, Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory, Compos. Part B. Eng., vol. 153, pp. 376–386, 2018. DOI: 10.1016/j.compositesb.2018.08.111.
   Web of Science ®Google Scholar
• N. Wattanasakulpong, and V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained endsP FGM beams with porosities, Aerosp. Sci. Technol., vol. 32, no. 1, pp. 111–120, 2014. DOI: 10.1016/j.ast.2013.12.002.
   Web of Science ®Google Scholar
• M. Şimşek, Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions, Compos. Struct., vol. 149, pp. 304–314, 2016. DOI: 10.1016/j.compstruct.2016.04.034.
   Web of Science ®Google Scholar
• S. Pandey, and S. Pradyumna, Stress analysis of functional graded sandwich beams subjected to thermal shock, Proc. Eng., vol. 173, pp. 837–843, 2017. DOI: 10.1016/j.proeng.2016.12.121.
   Google Scholar
• D. K. Nguyen, and V. T. Bui, Dynamic analysis of functionally graded Timoshenko beams in thermal environment using a higher-order hierarchical beam element, Math. Prob. Eng., vol. 2017, pp. 1–12, 2017. DOI: 10.1155/2017/7025750.
   Web of Science ®Google Scholar
• S. Li, H. Su, and C. Cheng, Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment, Appl. Math. Mech. Engl. Ed., vol. 30, no. 8, pp. 969–982, 2009. DOI: 10.1007/s10483-009-0803-7.
   Web of Science ®Google Scholar
• Ş. D. Akbaş, Thermal effects on the vibration of functionally graded deep beams with porosity, Int. J. Appl. Mech., vol. 9, no. 5, pp. 1750076, 2017. DOI: 10.1142/S1758825117500764.
   Web of Science ®Google Scholar
• F. Ebrahimi, and A. Jafari, A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities, J. Eng., vol. 2016, pp. 1–20, 2016. DOI: 10.1155/2016/9561504.
   Web of Science ®Google Scholar
• I. Eshraghi, S. Dag, and N. Soltani, Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading, Compos. Struct., vol. 137, pp. 196–207, 2016. DOI: 10.1016/j.compstruct.2015.11.024.
   Web of Science ®Google Scholar
• R. Aghazadeh, S. Dag, and E. Cigeroglu, Thermal effect on bending, buckling and free vibration of functionally graded rectangular micro-plates possessing a variable length scale parameter, Microsyst. Technol., vol. 24, no. 8, pp. 3549–3572, 2018. DOI: 10.1007/s00542-018-3773-x.
   Web of Science ®Google Scholar
• H.-S. Shen, and Z.-X. Wang, Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments, Int. J. Mech. Sci., vol. 81, pp. 195–206, 2014. DOI: 10.1016/j.ijmecsci.2014.02.020.
   Web of Science ®Google Scholar
• R. Javaheri, and M. R. Eslami, Thermal buckling of functionally graded plates based on higher order theory, J. Therm. Stresses, vol. 25, no. 7, pp. 603–625, 2002. DOI: 10.1080/01495730290074333.
   Web of Science ®Google Scholar
• P. Malekzadeh, and S. M. Monajjemzadeh, Dynamic response of functionally graded beams in a thermal environment under a moving load, Mech. Adv. Mater. Struct., vol. 23, no. 3, pp. 248–258, 2016. DOI: 10.1080/15376494.2014.949930.
   Web of Science ®Google Scholar
• H. Youzera, S. A. Meftah, and E. M. Daya, Superharmonic resonance of cross-ply laminates by the method of multiple scales, J. Comput. Nonlinear Dynam., vol. 12, no. 5, pp. 5, 2017. DOI: 10.1115/1.4036914.
   Web of Science ®Google Scholar
• P. Shi, C. Dong, F. Sun, W. Liu, and Q. Hu, A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis, Compos. Struct., vol. 204, pp. 342–358, 2018. DOI: 10.1016/j.compstruct.2018.07.080.
   Web of Science ®Google Scholar
• M. Şimşek, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nucl. Eng. Des., vol. 240, no. 4, pp. 697–705, 2010. DOI: 10.1016/j.nucengdes.2009.12.013.
   Web of Science ®Google Scholar
• C. T. Luan, 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, Compos. Part B. Eng., vol. 100, pp. 152–163, 2016. DOI: 10.1016/j.compositesb.2016.06.067.
   Web of Science ®Google Scholar