Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Effect of Shear Theories on Free Vibration of Functionally Graded Plates

Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061589

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1219

References:


[1] M. Yamanouchi, M. Koizumi, and I. Shiota, in Proc. First Int. Symp. Functionally Gradient Materials, Sendai, Japan (1990).
[2] 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.
[3] M. Koizumi, "FGM Activites in Japan," Composite: Part B, Vol. 28, no. 1, pp. 1-4, 1997.
[4] J. N. Reddy, "Analysis of functionally graded plates," Int. J. Num. Methods Eng., Vol. 47, pp. 663-684, 2000.
[5] G. N. Praveen and J. N. Reddy, "Nonlinear transient thermoelastic analysis of functionlly graded ceramic-metal plates," Int. J. Solids Struct., Vol. 35, pp. 4457-4471, 1998.
[6] C. T. Loy, K. Y. Lam, and J. N. Reddy, "Vibration of functionally graded cylindrical shells," Int. J. Mech. Sic., Vol. 41, pp. 309-324, 1999.
[7] R. Javaheri and M. R. Eslami, "Buckling of functionally graded plates under in-plane compressive loading," ZAMM J., Vol. 82, pp. 277-283, 2002.
[8] R. Javaheri and M. R. Eslami, "Thermal buckling of functionally graded plates," AIAA J., Vol. 40, no. 1, pp. 162-169, 2002.
[9] R. Javaheri and M. R. Eslami, "Thermal buckling of functionally graded plates based on higher order theory," J. Thermal Stresses, Vol. 25, pp. 603-625, 2003.
[10] V. Birman, "Buckling of functionally graded hybrid composite plates," in Proc. 10th Conf. Eng. Mech., pp. 1199-1202, 1995.
[11] M. M. Najafizadeh and M. R. Eslami, "Buckling analysis of circular plates of functionally graded materials under uniform redial compression," Int. J. Mech. Sci., Vol. 4, pp. 2479-2493, 2002.
[12] M. M. Najafizadeh and M. R. Eslami, "First-Order-Theory based thermoelastic stability of functionally graded material circular plates," AIAA J., Vol. 40, pp. 1444-1450, 2002.
[13] M. M. Najafizadeh and M. R. Eslami, "Thermoelastic stability of orthotropic circular plates," J. Thermal Stresses, Vol. 25, no. 10, pp. 985-1005, 2002.
[14] M. M. Najafizadeh and B. Hedayati, "Refined theory for thermoelastic stability of functionally graded circular plates," J. Thermal Stresses, Vol. 27, pp. 857-880, 2004.
[15] M. M. Najafizadeh and H. R. Heydari, "Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory," Euro. J. Mech. A/Solids, Vol. 23, pp. 1085- 1100, 2004.
[16] R. C. Batra and S. Aimmanee, "Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories," Compu. Struct., Vol. 83, pp. 934-955, 2005.
[17] S. S. Vel and R. C. Batra, "Three-dimensional exact solution for the vibration of functionally graded rectangular plates," J. Sound Vib., Vol. 272, pp. 703-730, 2004.
[18] L. F. Qian, R. C. Batra, and L. M. Chen, "Elastostatic deformationsof a thick plate by using a higher-order shear and normal deformable plate theory and two Meshless Local Petrov-Galerkin (MLPG) methods," Compu. Modeling Eng. Sci., Vol. 4, pp. 161-176, 2003.
[19] L. F. Qian, R. C. Batra, and L. M. Chen, "Free and forced vibrations of thick rectangular plates by using a higher-order shear and normal deformable plate theory and Meshless Local Petrov-Galerkin (MLPG) method," Compu. Modeling Eng. Sci., Vol. 4, pp. 519-534, 2003.
[20] L. F. Qian, R. C. Batra, and L. M. Chen, "Static and dynamic deformations of thick functionally graded elastic plates by using higherorder shear and normal deformable plate theory and Meshless Local Petrov-Galerkin method," Composite: Part B, Vol. 35, no. (6-8), pp. 685-697, 2004.
[21] A. J. M. Ferreira, R. C. Batra, C. M. C. Roque, L. F. Qian, and P. A. L. S. Martins, "Static analysis of functionally graded plates using thirdorder shear deformatoion theory and a Meshless Method," Compo. Struct., Vol. 69, pp. 449-457, 2005.
[22] J. Woo, S. A. Meguid, and L. S. Ong, "Nonlinear free vibration behavior of functionally graded plates," J. Sound Vib., Vol. 289, pp. 595-611, 2006.
[23] J. -S. Park and J. -H. Kim, "Thermal postbuckling and vibration analyses of functionally graded plates," J. Sound Vib., Vol. 289, no. (1-2), pp. 77- 93, 2006.
[24] Y. -W. Kim, "Temperature dependent vibration analysis of functionally graded rectangular plates," J. Sound Vib., Vol. 284, no. (3-5), pp. 531- 549, 2005.
[25] G. Altay and M. C. Dökmeci, "Variational principles and vibrations of a functionally graded plate," Compu. Struct., Vol. 83, pp. 1340-1354, 2005.
[26] C. -Sh. Chen, "Nonlinear vibration of a shear deformable functionally graded plate," Compo. Struct., Vol. 68, pp. 295-302, 2005.
[27] J. N. Reddy and A. A. Khdeir, "Buckling and vibration of laminated composite plates using various plate theories," AIAA J., Vol. 27, pp. 1808-2346, 1989.
[28] S. Sirinivas and A. K. Rao, "Bending, vibration, and buckling of simply supported thick orthotropic rectangular plates and laminates," Int. J. Solids Struct., Vol. 6, pp. 1463-1481, 1970.
[29] H. Reisman and Y. -C. Lee, "Forced motions of rectangular plates," Develop. Theoretical Applied Mech., Pergamon, New York, Vol. 4, p. 3, 1969.
[30] J. N. Reddy, Theory and Analysis of Elastic Plates. Philadelphia: Taylor and Francies, p. 462, 1999.