A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects

2019 ◽  
Vol 220 ◽  
pp. 209-220 ◽  
Author(s):  
M.H. Jalaei ◽  
Ö. Civalek
Keyword(s):  
Graphene Sheet ◽  
Strain Gradient ◽  
Thermal Effects ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Refined Plate Theory ◽  
Nonlocal Strain Gradient

Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory

2016 ◽  
Vol 232 (1) ◽  
pp. 162-173 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Strain Gradient ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Gradient Elasticity ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Thermal Environments ◽  
Size Dependent ◽  
Dispersion Behavior ◽  
Nonlocal Strain Gradient

This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded nanoplate in thermal environments. The theory contains two scale parameters corresponding to nonlocal and strain gradient effects. A quasi-3D plate theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanoplate accounting for thickness stretching effect. These equations are solved analytically to find wave frequencies and phase velocities of functionally graded nanoplate. It is indicated that wave dispersion behavior of functionally graded nanoplates is significantly affected by temperature rise, nonlocality, length scale parameter, and material composition.

Nonlocal stress-strain gradient vibration analysis of heterogeneous double-layered plates under hygro-thermal and linearly varying in-plane loads

2017 ◽  
Vol 24 (19) ◽  
pp. 4630-4647 ◽  
Author(s):  
Mohammad Reza Barati
Keyword(s):  
Strain Gradient ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Load Factor ◽  
Governing Equations ◽  
Layered Plates ◽  
Accurate Analysis ◽  
Thermal Environments ◽  
Nonlocal Strain Gradient

This paper develops a nonlocal strain gradient plate model for vibration analysis of double-layered graded nanoplates under linearly variable in-plane mechanical loads in hygro-thermal environments. For more accurate analysis of nanoplates, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. The double-layered nanoplate is modeled via a four-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient nanoplate on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations. Effects of different factors such as in-plane loading, load factor, nonlocal parameter, length scale parameter, moisture percentage rise, temperature rise, elastic foundation, and boundary conditions on vibration characteristics of a double-layered nanoplate have been examined.

Vibration analysis of graphene sheets resting on the orthotropic elastic medium subjected to hygro-thermal and in-plane magnetic fields based on the nonlocal strain gradient theory

2017 ◽  
Vol 232 (13) ◽  
pp. 2469-2481 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Magnetic Field ◽  
Graphene Sheet ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Nonlocal Parameter ◽  
Strain Gradient Theory ◽  
Graphene Sheets ◽  
Gradient Theory ◽  
Governing Equations ◽  
Nonlocal Strain Gradient

This paper develops a nonlocal strain gradient plate model for vibration analysis of the graphene sheets under in-plane magnetic field and hygro-thermal environments. For more accurate analysis of the graphene sheets, the proposed theory contains two-scale parameters related to the nonlocal and strain gradient effects. The graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, elastic foundation, and magnetic field on vibration characteristics of the graphene sheets are examined.

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