Free Vibration Analysis of Functionally Graded Beams
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51107", author = "Gholam Reza Koochaki", title = "Free Vibration Analysis of Functionally Graded Beams", abstract = "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 = "Functionally graded beam, Free vibration, Hamilton's principle.", volume = "5", number = "2", pages = "315-4", }