scholarly journals Thermal Buckling Analysis of Graphene Nanoplates Based on the Modified Couple Stress Theory using Finite Strip Method and Two-Variable Refined Plate Theory

2020 ◽  
Vol 38 (02) ◽  
Keyword(s):  
Couple Stress ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Refined Plate Theory ◽  
Stress Theory ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Modified Couple Stress ◽  
Graphene Nanoplates

Determination of vibration of single-layered graphene sheets using nonlocal modified couple stress theory

2021 ◽  
pp. 2250011
Author(s):  
F. Attar ◽  
R. Khordad ◽  
A. Zarifi
Keyword(s):  
Couple Stress ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Nonlocal Parameter ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Vibration Modes ◽  
Classical Plate Theory ◽  
Stress Theory ◽  
Modified Couple Stress

The free vibration of single-layered graphene sheet (SLGS) has been studied by nonlocal modified couple stress theory (NMCS), analytically. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle for two cases: (1) using nonlocal parameter only for stress tensor, (2) using nonlocal parameter for both stress and couple stress tensors. Navier’s approach has been used to solve the governing equations for simply supported boundary conditions. It is found that the frequency ratios decrease with increasing nonlocal parameter and also with enhancing vibration modes, but increase with raising length scale parameter. The nonlocal and length scale parameters are more prominent in higher vibration modes. The obtained results have been compared with the previous studies obtained by using classical plate theory, the modified couple stress theory and nonlocal elasticity theory, separately.

scholarly journals Bending, buckling and Vibrations Analysis of the graphene nanoplate using the modified couple stress theory

Mechanika ◽  
2021 ◽  
Vol 27 (5) ◽  
pp. 376-384
Author(s):  
Majid Eskandari Shahraki ◽  
Mahmoud Shariati ◽  
Mohsen Heydari Beni ◽  
Jafar Eskandari Jam
Keyword(s):  
Stress Tensor ◽  
Couple Stress ◽  
Strain Energy ◽  
Couple Stress Theory ◽  
Strain Tensor ◽  
Modified Couple Stress Theory ◽  
External Work ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Graphene Nanoplates

In this paper using the modified couple stress theory, to study the bending, buckling and vibration characteristics of the rectangular Mindlin's nanoplates with graphene material was investigated. With the aim of considering the effects of small scales, the modified couple stress theory, which has only one parameter of length scale and also was presented by Yang in 2002, was used. In the modified couple stress theory; the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equation and placing them in the Hamilton's equation, the basic and auxiliary equations of the nanoplates were obtained. Then, by applying boundary and force conditions in the governing equations, the bending, buckling and vibration of the rectangular graphene nanoplates with thickness h and simply-supported conditions were explored. Also, the solution method was the Navier's solution.

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