[1] C.T. Loy, K.Y. Lam, and J.N. Reddy. Vibration of functionally graded cylindrical shells.
International Journal of Mechanical Sciences, 41(3):309–324, 1999. doi:
10.1016/S0020-7403(98)00054-X .
[2] B.V. Sankar. An elasticity solution for functionally graded beams.
Composites Science and Technology, 61(5):689–696, 2001. doi:
10.1016/S0266-3538(01)00007-0.
[3] M. Aydogdu and V. Taskin. Free vibration analysis of functionally graded beams with simply supported edges.
Materials & Design, 28(5):1651–1656, 2007. doi:
10.1016/j.matdes.2006.02.007.
[4] A. Chakraborty, S. Gopalakrishnan, and J.N. Reddy, A new beam finite element for the analysis of functionally graded materials.
International Journal of Mechanical Sciences, 45(3):519–539, 2003. doi:
10.1016/S0020-7403(03)00058-4.
[5] A.J. Goupee and S.S. Vel. Optimization of natural frequencies of bidirectional functionally graded beams.
Structural and Multidisciplinary Optimization, 32:473–484, 2006. doi:
10.1007/s00158-006-0022-1.
[6] H.J. Xiang and J. Yang. Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction.
Composites Part B:Engineering, 39(2):292–303, 2008. doi:
10.1016/j.compositesb.2007.01.005.
[7] M.T. Piovan and R. Sampaio. A study on the dynamics of rotating beams with functionally graded properties.
Journal of Sound and Vibration, 327(1-2):134–143, 2009. doi:
10.1016/j.jsv.2009.06.015.
[8] M Şimşek and T. Kocatürk. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load.
Composite Structures, 90(4):465–473, 2009. doi:
10.1016/j.compstruct.2009.04.024.
[9] P. Malekzadeh, M.R. Golbahar Haghighi, and M.M. Atashi. Out-of-plane free vibration of functionally graded circular curved beams in thermal environment.
Composite Structures, 92: 541–552, 2010. doi:
10.1016/j.compstruct.2009.08.040.
[10] Y. Huang and X.F. Li. A new approach for free vibration of axially functionally graded beams with non-uniform cross-section.
Journal of Sound and Vibration, 329(11):2291–2303, 2010. doi:
10.1016/j.jsv.2009.12.029.
[11] A. Shahba, R. Attarnejad, M.T. Marvi, and S. Hajilar. Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions.
Composites Part B: Engineering, 42(4):801–808, 2011. doi:
10.1016/j.compositesb.2011.01.017.
[12] I. Elishakoff and Y. Miglis. Some intriguing results pertaining to functionally graded columns.
Journal of Applied Mechanics, 80(4):1021–1029, 2013. doi:
10.1115/1.4007983.
[13] M. Soltani and B. Asgarian. New hybrid approach for free vibration and stability analyses of axially functionally graded Euler-Bernoulli beams with variable cross-section resting on uniform Winkler-Pasternak foundation.
Latin American Journal of Solids and Structures, 16(3):e173, 2019. doi:
10.1590/1679-78254665.
[14] J.H. Kim and G.H. Paulino. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials.
Journal of Applied Mechanics, 69(4):502–514, 2002. doi:
10.1115/1.1467094.
[15] P. Zahedinejad, C. Zhang, H. Zhang, and S. Ju. A comprehensive review on vibration analysis of functionally graded beams.
International Journal of Structural Stability and Dynamics, 20(4):2030002, 2020. doi:
10.1142/S0219455420300025.
[16] N. Zhang, T. Khan, H. Guo, S. Shi, W. Zhong, and W. Zhang. Functionally graded materials: An overview of stability, buckling, and free vibration analysis.
Advances in Material Science and Engineering, 1354150, 2019. doi:
10.1155/2019/1354150.
[17] Ö. Özdemir. Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams.
Journal of Theoretical and Applied Mechanics, 54(4):1205–1217, 2016.
[18] B. Kılıç.
Vibration analysis of axially functionally graded rotor blades. M.Sc.Thesis, Istanbul Technical University, İstanbul, Turkey, 2019.
[19] S. Rajasekaran. Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams.
International Journal of Mechanical Sciences, 74. 15-31, 2013.
[20] A.D. Wright, C.E. Smith, R.W. Thresher, and J.L.C. Wang. Vibration modes of centrifugally stiffened beams.
Journal of Applied Mechanics, 49(1):197–202, 1982. doi:
10.1115/1.3161966.
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