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Structural Engineering and Mechanics
  Volume 71, Number 5, September10 2019 , pages 525-544

Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM
Mehdi Mohammadimehr, Hasan Afshari, M. Salemi, K. Torabi and Mojtaba Mehrabi

    In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson\'s ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton\'s principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.
Key Words
    buckling and free vibration; annular thin sector FGM plate; visco- elastic Pasternak medium; generalized differential quadrature method
Mehdi Mohammadimehr, Hasan Afshari, M. Salemi, K. Torabi and Mojtaba Mehrabi: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Hasan Afshari: Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran
K. Torabi and Mojtaba Mehrabi: Department of Mechanics, Faculty of Engineering, University of Isfahan, Isfahan, Iran

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