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Free vibration analysis of pores functionally graded plates using new element based on Hellinger-Reissner functional

  • Majid Yaghoobi (Civil Engineering and Architecture Department, Engineering Faculty, University of Torbat Heydarieh) ;
  • Mohsen Sedaghatjo (Civil Engineering and Architecture Department, Engineering Faculty, University of Torbat Heydarieh) ;
  • Mohammad Karkon (Civil Engineering Department, Larestan Branch Islamic Azad University) ;
  • Lazreg Hadji (Civil Engineering Department, Faculty of Applied Sciences, University of Tiaret)
  • Received : 2022.10.02
  • Accepted : 2023.11.02
  • Published : 2023.12.25
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Abstract

This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

Keywords

Acknowledgement

This work has been financially supported by the University of Torbat Heydarieh. The grant number is UTH: 1401/04/18142.

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