Measurement the effects of temperature and fiber orientation on vibration of functionally graded beam



Temperature First-order shear deformation theory, Differential quadrature method, Fiber orientation functionally graded beam Natural frequencies


This paper concerned with analytical approach to study the thermal vibration of fiber orientation functionally graded (FOFG) beam, that fibers`oriented angles are variable and graded in the thickness direction of the beam. Uniform thermal distribution considered in the entire beam and properties of fiber orientation functionally graded (FOFG) beam considered as the temperature-dependent element. Symmetrical, asymmetrical, and classical distribution types for the mode of fiber angle presented in the thickness direction of the beam continuously. Equilibrium Equations derived from first- order shear deformation theory and Hamilton principle. Simply supported boundary condition is considered for both edges of the beam.Eneralized differential quadrature method usedto solve the system of coupled differential Equations. To study accuracy of the present analysis, a compression carried out with a known data. The results shows that different parameters such as thickness to radius ratio, effect of temperature variations, model of fibers angle variations and power-law index affected on the natural frequencies.


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Murín, J., Aminbaghai, M., Kuti. V., Exact solution of the bending vibration problem of FGM beams with variation of material properties. Engineering Structures.,2010, 32 (6),1631–1640.

Tanigawa, Y.,Some basic thermoelastic problems for nonhomogeneous structural materials. Appl. Mech. Rev.,1995, 48,377–389.

Chena, H., Wenbo Z., Danhui, Z., Xiangjie, K.,The thermal effects on high-frequency vibration of beams using energy flow analysis. Journal of Sound and Vibration.,2014, 9 (28),2588–2600.

Pradeepa, V., Ganesana, N., Bhaskar, K.,Vibration and thermal buckling of composite sandwich beams with viscoelastic core. Composite Structures. 2007, 81(1),60–69.

Hui-Shen, S., Zhen-Xin, W., Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments. International Journal of Mechanical Sciences.,201481,195–206.

Aboudi, J., Pindera, M., Arnold, S.M.,Coupled higher-order theory for functionally grade composites with partial homogenization. J. Compos Eng.,1995, 5(7),pp: 771-92.

Benatta, M.A., Tounsi, A., Mechab, I., Bouiadjra, M.B.,Mathematical solution for bending of short hybrid composite beams with variable fibers spacing. Appl Math Comput.,2009, 212, 337–48.

Sallai, B.O., Tounsi, A., Mechab, I., Bachir, M.B., Meradjah, M.B., Adda EA.,A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput Mater Sci.,2009, 44, 1344–50.

Kadoli, R., Akhtar, K., Ganesan, N., (),Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model.,2008, 32,2509–23.

Li, X-F., A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. J Sound Vib.,2008,318, 1210–29.

Huang, Y., Li, X-F.,Buckling of functionally graded circular columns including shear deformation. Mater Des.,2010, 31,3159–66.

Huang, Y., Li, X-F.,Bending and vibration of cylindrical beams with arbitrary radial nonhomogeneity. Int J Mech Sci.,2010,52, 595–601.

Simsek, M.,Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des.,2010, 240, 697–705.

Ke, L-L., Yang, J., Sritawat, K.,Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening. Compos Struct.,2009,90,52–160.

Ke, L-L., Yang, J., Sritawat, K.,Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mech Adv Mater Struct.,2009, 16, 488–502.

Yang, J., Chen, Y., Free vibration and buckling analyses of functionally graded beams with edge cracks. Compos Struct.,2008, 83,48–60.

Sankar, B.V.,An elasticity solution for functionally graded beams. Compos Sci Technol.,2001, 61,689–96.

Pradhan, S.C., Murmu, T.,Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. Journal of Sound and Vibration.,2009, 321,342–362.

Raki, M., Alipour, R., Kamanbedast, A., Thermal Buckling of Thin Rectangular FGM Plate.World Applied Sciences Journal.,2012, 16 (1), 52-62.

Farid, M., Zahedinejad, P., Malekzadeh, P.,Three dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two parameter elastic foundation using a hybrid semianalytic, differential quadrature method. J Mater Des.,2010, 31, 2–13.

Aydogdu, M., Taskin, V., Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design.,2007, 28, 1651–1656.




How to Cite

farzan barati, M. Esfandiari, S. . Babaei, A. Baraati, Z. Hoseini Tabar, and A. Atarod, “Measurement the effects of temperature and fiber orientation on vibration of functionally graded beam”, international journal of engineering and applied physics, vol. 1, no. 3, pp. 295–305, Sep. 2021.