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  4. TSDT theory for free vibration of functionally graded plates with various material properties

TSDT theory for free vibration of functionally graded plates with various material properties

MMC.
2021;
Volume 8, Number 4
: pp. 691–704
https://doi.org/10.23939/mmc2021.04.691
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 691–704 (2021)

Authors:
  1. M. Janane Allah
  2. Y. Belaasilia
  3. A. Timesli
  4. A. El Haouzi
1
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
2
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
3
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
4
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates.  The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model.  In this contribution, the formulation is written without any homogenization technique as the rule of mixture.  The Hamilton principle is used to establish the resulting equations of motion.  For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node.  An implicit algorithm is used for solving the obtained problem.  To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies.  Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM".  In addition, we study the influence of the thickness on "E-FGM" plates.

third order shear deformation theory (TSDT)
nonlinear dynamic analysis
laminate composite
functionally graded material (FGM)
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