Scientia Iranica

Scientia Iranica

A generalized differential quadrature-based computational model for describing free vibrations behavior of functionally graded circular plates around buckled configuration

Document Type : Research Note

Authors
A. Shahabodini 1
M. Saadatmand 2
B. Ahmadi 3
S. Nezamivand Chegini 4
1 Department of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
2 Laboratory Unit, Stam Sanat Company, Karaj, Iran
3 Department of Mechanical Engineering, University of Kurdistan, Sanandaj, Iran
4 Department of Mechanical Engineering, Ahrar Institute of Technology and Higher Education, Rasht, Iran
10.24200/sci.2021.56950.4994
Abstract
In the present article, the vibrational behavior of buckled functionally graded (FG) circular plates with clamped and simply-supported edge conditions is described. Considering von Kármán’s assumptions, the geometric nonlinearity is incorporated into the Kirchhoff plate theory and the nonlinear governing equations of motion are then derived using Hamilton’s principle. Critical buckling load and linear natural frequencies are first calculated using the generalized differential quadrature (GDQ) method. Afterward, the postbuckling characteristics of the circular plate are obtained via solving the nonlinear governing equations, directly. By several comparative studies, the reliability of the presented model is revealed. Finally, the fundamental natural frequency of the plate is evaluated for prebuckled and postbuckled configurations. The effects of material property and boundary conditions on the static bifurcation diagram and the natural frequency of the initial undeflected and bucked plate are studied. It is found that the trend of the fundamental natural frequency changes with the applied radial load around the prebuckled configuration is unlike the one around the buckled configuration.
Keywords
Free vibrations
Buckled circular plate
von Kármán’s nonlinearity
Functionally graded materials
GDQ method

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Scientia Iranica
Volume 29, Issue 3
Transactions on Mechanical Engineering (B)
May and June 2022
Pages 1250-1264

  • Receive Date 10 October 2020
  • Revise Date 15 May 2021
  • Accept Date 13 September 2021