Modeling of nonlinear vibration of graphene sheets using a meshfree method based on nonlocal elasticity theory

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)691-704
Journal / PublicationApplied Mathematical Modelling
Online published7 Mar 2017
Publication statusPublished - Sep 2017


Due to their valuable and unique properties, graphene sheets (GSs) have attracted increasing attention in recent years. This paper presents the mathematical modeling of the nonlinear vibration behavior of GSs using classic plate theory and nonlocal elasticity theory which accounts for the size effect. The numerical solutions are obtained through the element-free kp-Ritz method. The iteration process is dealt with using the linearized updated mode method. The transformation method is used to impose the boundary conditions. The published results are used to verify the correctness of the present nonlocal element-free kp-Ritz method. The effects of boundary conditions, side length, aspect ratio and nonlocal parameters on the frequency–amplitude response are examined.

Research Area(s)

  • Frequency amplitude response, Graphene sheets, Meshfree method, Nonlinear vibration, Nonlocal theory, Ritz method