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Nonlinear free vibration analysis of in-plane Bi-directional functionally graded plate with porosities resting on elastic foundations

Hashemi, S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1142/S1758825121501313
  3. Publisher: World Scientific , 2022
  4. Abstract:
  5. This paper deals with the nonlinear free vibration analysis of in-plane bi-directional functionally graded (IBFG) rectangular plate with porosities which are resting on Winkler-Pasternak elastic foundations. The material properties of the IBFG plate are assumed to be graded along the length and width of the plate according to the power-law distribution, as well as, even and uneven types are taken into account for porosity distributions. Equations of motion are developed by means of Hamilton's principle and von Karman nonlinearity strain-displacement relations based on classical plate theory (CPT). Afterward, the time-dependent nonlinear equations are derived by applying the Galerkin procedure. The nonlinear frequency is determined by using modified Poincare-Lindstedt method (MPLM). Numerical results are obtained in tabular and graphical form to examine the effects of some system key parameters such as porosity coefficients, distribution patterns, gradient indices, elastic foundation coefficients, aspect ratio and vibration amplitude on the nonlinear frequency of the porous IBFG plate. To validate the analysis, the results of this paper have been compared to the published data and good agreements have been found. © 2022 World Scientific Publishing Europe Ltd
  6. Keywords:
  7. Aspect ratio ; Control nonlinearities ; Equations of motion ; Foundations ; Nonlinear analysis ; Nonlinear equations ; Vibration analysis ; Bi-directional ; Elastic foundation ; Free-vibration analysis ; Functionally graded ; Functionally graded plates ; In-plane bi-directional functionally graded ; Modified poincare-lindstedt method ; Nonlinear free vibrations ; Nonlinear frequency ; Poincare ; Porosity
  8. Source: International Journal of Applied Mechanics ; Volume 14, Issue 1 , 2022 ; 17588251 (ISSN)
  9. URL: https://www.worldscientific.com/doi/10.1142/S1758825121501313