Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory

2016 ◽  
Vol 30 (36) ◽  
pp. 1650421 ◽  
Author(s):  
Behrouz Karami ◽  
Maziar Janghorban
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Strain Gradient ◽  
Plate Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Governing Equations ◽  
Refined Plate Theory ◽  
Bulk Waves ◽  
First Time

In this paper, the effect of magnetic field on the wave propagation in rectangular nanoplates based on two-variable refined plate theory is studied. In order to capture the size effects, the strain gradient theory with one length scale parameter is used. From our knowledge, it is the first time that two-variable refined plate theory is adopted for studying bulk waves in nanoplates. This type of refined plate theory has only two unknowns which reduces the complexity of the governing equations. To show the accuracy of this work, several comparisons are made with available results in open literature.

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.

Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory

2018 ◽  
Vol 25 (3) ◽  
pp. 439-451
Author(s):  
Meisam Mohammadi ◽  
Afshin Iranmanesh ◽  
Seyed Sadegh Naseralavi ◽  
Hamed Farahmand
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Governing Equations ◽  
Micro Plates ◽  
Micro Structures

Abstract In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

2020 ◽  
pp. 095440622096561
Author(s):  
Amir-Reza Asghari Ardalani ◽  
Ahad Amiri ◽  
Roohollah Talebitooti ◽  
Mir Saeed Safizadeh
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Surface Elasticity ◽  
Shear Deformation Theory ◽  
Wave Dispersion ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Specific Domain ◽  
Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

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