**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31819

##### Effect of Shear Theories on Free Vibration of Functionally Graded Plates

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

**Abstract:**

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

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

**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. DÃ¶kmeci, "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.