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Free Vibration Analysis of Functionally Graded Beams

Authors: Gholam Reza Koochaki


This work presents the highly accurate numerical calculation of the natural frequencies for functionally graded beams with simply supported boundary conditions. The Timoshenko first order shear deformation beam theory and the higher order shear deformation beam theory of Reddy have been applied to the functionally graded beams analysis. The material property gradient is assumed to be in the thickness direction. The Hamilton-s principle is utilized to obtain the dynamic equations of functionally graded beams. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed. Comparison of the numerical results for the homogeneous beam with Euler-Bernoulli beam theory results show that the derived model is satisfactory.

Keywords: free vibration, functionally graded beam, Hamilton's principle

Digital Object Identifier (DOI):

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[1] M. Yamanouchi, M. Koizumi, and I. Shiota, Proc. the First Int. Symp. Funct. Grad. Mater., Sendai, Japan, 1990.
[2] M. Koizumi, "FGM Activites in Japan," Compos. Part B: Eng., Vol. 28, pp. 1-4 (1997).
[3] J. N. Reddy, and Z. Q. Cheng, "Three-dimensional trenchant deformations of functionally graded rectangular plates," Euro. J. Mech. A/solids, vol. 20, pp. 841-855, 2001.
[4] J. N. Reddy, C. M. Wang, and S. Kitipornchi, "Axisymmetric Bending of functionally graded circular and annular plates," Euro. J. Mech. A/solids, vol. 18, pp. 185-199, 1999.
[5] Y. Fukui, "Fundamental investigation of functionally gradient material manufacturing system using centrifugal force," Int. J. Japanese soci. mech. Eng., vol. 3, pp. 144-148, 1991.
[6] H. Abramovich, "Natural frequencies of timoshenko beams under compressive axial loads," J. Sound Vib., vol. 157, No. 1, pp. 183-189, 1992.
[7] J. R. Banerjee, "Frequency Equation and mode shape formulae for composite timoshenko beams," Compos. Struct., vol. 51, pp. 381-388, 2001.
[8] H. Abramovich, and M. Eisenberger, "Dynamic stiffness analysis of laminated beams using a first order shear deformation theory," Compos. Struct., vol. 31, pp. 265-271, 1995.
[9] A. A. Khdeir, and J. N. Reddy, "Buckling and vibration of laminated composite plates using various plate theories," AIAA J., vol. 27, pp. 1808-1817, 1989.
[10] J. N. Reddy, and G. N. Praveen, "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates," Int. J. Solids Struct., vol. 35, pp. 4467-4476, 1998.
[11] V. Birman, "Buckling of functionally graded hybrid composite plates," Proc. the 10th Conf. Eng. Mech. 2, pp. 1199-1202, 1995.
[12] J. N. Reddy, Theory and Anaslysis of Elastic Plates. Taylor & Francis Publication: Philadelphia, 1999.