Insights into Relative Lower Frequencies and Buckling Loads of Monolayer Graphene Sheets via Nonlocal Elasticity Theory: Size-Dependent Young's Modulus Approach

2013 ◽  
Vol 5 (10) ◽  
pp. 1097-1102
Author(s):  
T. Murmu ◽  
S. Adhikari ◽  
M. A. McCarthy ◽  
C. Y. Wang
Keyword(s):  
Elasticity Theory ◽  
Young’S Modulus ◽  
Nonlocal Elasticity ◽  
Young's Modulus ◽  
Nonlocal Elasticity Theory ◽  
Monolayer Graphene ◽  
Graphene Sheets ◽  
Buckling Loads ◽  
Size Dependent ◽  
Lower Frequencies

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
K. M. Liew ◽  
Yang Zhang ◽  
L. W. Zhang
Keyword(s):  
Modeling And Simulation ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Single Layer ◽  
Nonlocal Elasticity Theory ◽  
Single Layer Graphene ◽  
Future Research ◽  
Graphene Sheets ◽  
Linear Modeling ◽  
Research Studies

Abstract:This paper presents a literature review of recent research studies on the applications of nonlocal elasticity theory in the modeling and simulation of graphene sheets (GSs). The history, development and excellent properties of GSs are introduced. The details of nonlocal elasticity theory are also presented. A systematic introduction to the application of nonlocal elasticity on linear modeling and nonlinear modeling for single-layer graphene sheets (SLGSs) and multilayered graphene sheets (MLGSs) is also provided. The necessity of determining mechanical parameters and nonlocal parameters is discussed. Recommendations for future work are particularly presented. This work is intended to review the development of GSs, give an introduction to the research studies on nonlocal elasticity theory in the modeling of GSs, and provide recommendations for future research.

CALIBRATION OF NONLOCAL SCALE EFFECT PARAMETER FOR BENDING SINGLE-LAYERED GRAPHENE SHEET UNDER MOLECULAR DYNAMICS

NANO ◽  
2012 ◽  
Vol 07 (05) ◽  
pp. 1250033 ◽  
Author(s):  
L. Y. HUANG ◽  
Q. HAN ◽  
Y. J. LIANG
Keyword(s):  
Molecular Dynamics ◽  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Md Simulations ◽  
Small Scale ◽  
Graphene Sheets ◽  
Small Scale Effect ◽  
Effect Parameter

In this article, the small scale effect parameter e0 of single-layered graphene sheets (SLGSs) is calibrated for the bending problem. Taking the SLGSs as a rectangular plate, the normal displacement of the simply supported plate under concentrated force was analyzed by both nonlocal elasticity theory and molecular dynamics (MD) simulations, then the small scale effect parameter e0 of SLGSs with different size was obtained by matching the displacement of the nonlocal elasticity theory and that obtained from MD simulations. The results show that the value of e0 is not a constant but has a relationship with the size of SLGSs, and the relationship of armchair-graphene sheets and zigzag-graphene sheets is different.

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