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Free vibration analysis of multi-directional functionally graded circular and annular plates

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Abstract

This paper addresses the free vibration of multi-directional functionally graded circular and annular plates using a semianalytical/ numerical method, called state space-based differential quadrature method. Three-dimensional elasticity equations are derived for multi-directional functionally graded plates and a solution is given by the semi-analytical/numerical method. This method gives an analytical solution along the thickness direction, using a state space method and a numerical solution using differential quadrature method. Some numerical examples are presented to show the accuracy and convergence of the method. The most of simulations of the present study have been validated by the existing literature. The non-dimensional frequencies and corresponding displacements mode shapes are obtained. Then the influences of thickness ratio and graded indexes are demonstrated on the non-dimensional natural frequencies.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Iman Davoodi Kermani, Mostafa Ghayour & Hamid Reza Mirdamadi

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  1. Iman Davoodi Kermani
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  2. Mostafa Ghayour
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  3. Hamid Reza Mirdamadi
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Corresponding author

Correspondence to Hamid Reza Mirdamadi.

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Recommended by Associate Editor Cheolung Cheong

Iman Davoodi Kermani received his B.Sc. degree in mechanical engineering in Shahid Bahonar University of Kerman, Kerman, Iran, in 2008. He received his M.Sc. degree in department of mechanical engineering of Isfahan University of Technology, Isfahan, Iran, in 2011. His research interests are vibration and stress analysis of plates and functionally graded materials (FGMs).

Mostafa Ghayour received his B.Sc. and M.Sc. degrees in Mechanical Engineering from University of Tehran, Tehran, Iran, in 1978. He received his Ph.D degree in Robotics from Isfahan University of Technology, Isfahan, Iran, in 1998. Now, he is Associate Professor of Mechanical Engineering on Robotics in Isfahan University of technology. His research interests include robotics, vibrations and control.

Hamid Reza Mirdamadi received his BSc in Civil Engineering, in 1986, MSc with honour, in Structural Engineering, in 1990, and Ph.D with honour, in Structural- Earthquake Engineering in 1999, all from Sharif University of Technology (SUT), Iran. Currently, he is an Assistant Professor at the Department of Mechanical Engineering, Isfahan University of Technology, Iran. His main research interests include smart structures (dynamics, vibrations, and controls), smart piezoelectric materials, micro/nano electromechanical systems (MEMS/NEMS), fluid-structure interaction, structural health monitoring (SHM), and structural system identification.

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Kermani, I.D., Ghayour, M. & Mirdamadi, H.R. Free vibration analysis of multi-directional functionally graded circular and annular plates. J Mech Sci Technol 26, 3399–3410 (2012). https://doi.org/10.1007/s12206-012-0860-2

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  • DOI: https://doi.org/10.1007/s12206-012-0860-2

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