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Free vibration analysis of functionally graded coupled circular plate with piezoelectric layers

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Abstract

Based on classical plate theory (CLPT), free vibration analysis of a circular plate composed of functionally graded material (FGM) with its upper and lower surfaces bounded by two piezoelectric layers was performed. Assuming that the material properties vary in a power law manner within the thickness of the plate the governing differential equations are derived. The distribution of electric potential along the thickness direction in piezoelectric layers is considered to vary quadratically such that the Maxwell static electricity equation is satisfied. Then these equations are solved analytically for two different boundary conditions, namely clamped and simply supported edges. The validity of our analytical solution was checked by comparing the obtained resonant frequencies with those of an isotropic host plate. Furthermore, for both FGM plate and FGM plate with piezoelectric layers, natural frequencies were obtained by finite element method. Very good agreement was observed between the results of finite element method and the method presented in this paper. Then for the two aforementioned types of boundary conditions, the values of power index were changed and its effect on the resonant frequencies was studied. Also, the effect of piezoelectric thickness layers on the natural frequencies of FGM piezoelectric plate was investigated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Islamic Azad University, Science and Research Branch of Tehran, Tehran, Iran

    Saeed Jafari Mehrabadi

  2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    M. H. Kargarnovin

  3. Department of Mechanical Engineering, Azad University, Arak Branch, Azad, Iran

    M. M. Najafizadeh

Authors
  1. Saeed Jafari Mehrabadi
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  2. M. H. Kargarnovin
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  3. M. M. Najafizadeh
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Correspondence to Saeed Jafari Mehrabadi.

Additional information

This paper was recommended for publication in revised form by Associate Editor Seockhyun Kim

Saeed Jafari Mehrabadi received his B.S. in mechanical Engineering from Azad University, Arak, Iran, in 1992. He then received his M.S. from Azad University, Tehran, Iran in 1995. Now he is a faculty member of the department of mechanical engineering in Azad university of Arak, Iran and PhD student of Azad University, Science and Research Campus, Pounak, Tehran, Iran. His interests include computational methods and solid mechanics such as vibration, buckling.

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Jafari Mehrabadi, S., Kargarnovin, M.H. & Najafizadeh, M.M. Free vibration analysis of functionally graded coupled circular plate with piezoelectric layers. J Mech Sci Technol 23, 2008–2021 (2009). https://doi.org/10.1007/s12206-009-0519-9

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  • DOI: https://doi.org/10.1007/s12206-009-0519-9

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