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On Free Vibration of Functionally Graded Mindlin Plate and Effect of In-Plane Displacements

Published online by Cambridge University Press:  29 January 2013

A. Hasani Baferani ,
A.R. Saidi  and
H. Ehteshami
A. Hasani Baferani
Affiliation:
Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave., 424, Tehran, Iran
A.R. Saidi*
Affiliation:
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
H. Ehteshami
Affiliation:
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
*
*Corresponding author ([email protected])
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Abstract

In this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.

Keywords

Free vibrationFunctionally gradedIn-Plane displacementsAnalytical solution
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 373 - 384
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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References

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