The study of the effects of thermal environment on Free Vibration analysis of two-dimensional Functionally Graded Rectangular plates on Pasternak elastic foundation

Authors

Abstract

This paper is the study of the effects of thermal environment on vibration analysis of a two-dimensional functionally graded rectangular plate on Pasternak elastic foundation. The natural frequencies of the plate are calculated by using the Rayleigh–Ritz method based on minimizing the total energy of the plate.analysis procedure is. The transverse displacement of the plate based on the third-order shear deformation plate theory(TSDT) is approximated by a set of admissible trial functions which is required to satisfy the clamped (CL) and simply supported geometric boundary conditions. For verifying the accuracy of this method, results are compared with those reported in the literature. As we seeit is shown a good conformance is derived from the obtained results and the exact solution. In the numerical results, the effects of volume fraction coefficients, thickness ratios ,aspect ratios of the FG plates, foundation stiffness parameters, temperature and boundary conditions on the natural frequencies are examined and discussed in detail.

Keywords

Main Subjects

References

[1] Hosseini-Hashemi S, Taher HRD, Akhavan H, Omidi M (2010) Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Model 34(5): 1276-1291.
[2] Zhao X, Lee Y, Liew KM (2009) Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. J Sound Vib 319(3): 918-939.
[3] Talha M, Singh B (2010) Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model 34(12): 3991-4011.
[4] Hosseini-Hashemi S, Fadaee M, Atashipour SR (2011) Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure. Compos Struct 93(2): 722-735.
[5] Zhou D, Cheung Y, Lo S, Au F (2004) Three‐dimensional vibration analysis of rectangular thick plates on Pasternak foundation. Int J Numer Meth Eng 59(10): 1313-1334.
[6] Kim YW (2005) Temperature dependent vibration analysis of functionally graded rectangular plates. J Sound Vib 284(3): 531-549.
[7] Li Q, Iu V, Kou K (2009) Three-dimensional vibration analysis of functionally graded material plates in thermal environment. J Sound Vib 324(3): 733-750.
[8] Qian L, Batra R, Chen L (2004) Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method. Compos Part B-Eng 35(6): 685-697.
[9] Zhang DG (2013) Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory. Int J Mech Sci 68: 92-104.
[10] Shen HS, Wang ZX (2012) Assessment of Voigt and Mori–Tanaka models for vibration analysis of functionally graded plates. Compos Struct 94(7): 2197-2208.
[11] HS Shen (2016) Functionally graded materials: nonlinear analysis of plates and shells. CRC press.
[12] Hosseini-Hashemi S, Fadaee M, Atashipour SR (2011) A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates. Int J Mech Sci 53(1): 11-22.
[13] Asemi K, Salehi M, Akhlaghi M (2013) Three dimensional static analysis of two dimensional functionally graded plates. IJMECH 2(2): 21-32.
[14] Amabili M, Karazis K, Khorshidi K (2011) Nonlinear vibrations of rectangular laminated composite plates with different boundary conditions. Int J Struct Stab Dy 11(4): 673-695.
[15] Xiang Y, Wang C, Kitipornchai S (1994) Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. Int J Mech Sci 36(4): 311-316.
Journal of Solid and Fluid Mechanics
Volume 6, Issue 3
September and October 2016
Pages 137-147

Files

Share

How to cite

Statistics