scholarly journals Vibration Analysis of Bilayered Graphene Sheets for Building Materials in Thermal Environments Based on the Element-Free Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Zhengtian Wu ◽  
Yang Zhang ◽  
Fuyuan Hu ◽  
Qing Gao ◽  
Xinyin Xu ◽  
...  
Keyword(s):  
Energy Conservation ◽  
Building Materials ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Graphene Sheets ◽  
Classical Plate Theory ◽  
Thermal Environments ◽  
Element Free Method ◽  
Element Free ◽  
Foundation Parameter

Graphene sheets are widely applied due to their unique and highly valuable properties, such as energy conservation materials in buildings. In this paper, we investigate the vibration behavior of double layer graphene sheets (DLGSs) in thermal environments which helps probe into the mechanism of energy conservation of graphene sheets in building materials. The nonlocal elastic theory and classical plate theory (CLPT) are used to derive the governing equations. The element-free method is employed to analyze the vibration behaviors of DLGSs embedded in an elastic medium. The accuracy of the solutions in this study is demonstrated by comparison with published results in the literature. Furthermore, a number of numerical results are presented to investigate the effects of various parameters (boundary conditions, nonlocal parameter, aspect ratio, side length, elastic foundation parameter, and temperature) on the frequency of DLGSs.

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.

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.

scholarly journals Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 515
Author(s):  
Olga Mazur ◽  
Jan Awrejcewicz
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Magnetic Parameter ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Graphene Sheets ◽  
Classical Plate Theory ◽  
Foundation Parameters

Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage.

scholarly journals NEMS Resonators for Detection of Chemical Warfare Agents Based on Graphene Sheet

2019 ◽  
Vol 2019 ◽  
pp. 1-23
Author(s):  
Nikola Anđelić ◽  
Zlatan Car ◽  
Marko Čanađija
Keyword(s):  
Graphene Sheet ◽  
Plate Theory ◽  
Chemical Warfare Agents ◽  
Chemical Warfare ◽  
Single Layer Graphene ◽  
Mode Shapes ◽  
Graphene Sheets ◽  
Classical Plate Theory ◽  
Layer Graphene ◽  
Warfare Agents

Graphene sheets are the basis of nanoelectromechanical (NEMS) mass resonators that are in recent years experimentally used for detection of specific gas molecules in air. The aim of this paper is to theoretically investigate the possibility of application of graphene sheets in detection of Chemical Warfare Agents (CWA’s). By application of the nonlocal theory of elasticity and classical plate theory, equations that describe natural vibrations of the simply supported single-layer graphene sheet (SLGS) and double-layer graphene sheet (DLGS) were derived. In order to detect attached CWA molecule, the frequency shift method was applied. The results indicate that the proposed methodology could be successfully implemented in order to detect an attached CWA molecule. However, only specific mode shapes could be employed for such detection.

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

2014 ◽  
Vol 30 (5) ◽  
pp. 443-453 ◽  
Author(s):  
M. Sobhy
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Graphene Sheets ◽  
Elastic Foundations ◽  
Various Boundary Conditions ◽  
Mechanics Of Composite Materials

AbstractIn this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

The effect of bi-axial in-plane loads on the natural frequency of nano-plates

2017 ◽  
Vol 24 (19) ◽  
pp. 4513-4528 ◽  
Author(s):  
Seyed Ghasem Enayati ◽  
Morteza Dardel ◽  
Mohammad Hadi Pashaei
Keyword(s):  
Natural Frequency ◽  
Nonlocal Elasticity ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Classical Plate Theory ◽  
First Order ◽  
Compressive Loads ◽  
Comprehensive Study

In this paper, natural frequencies of nano-plates subjected to two-sided in-plane tension or compressive loads, based on Eringen nonlocal elasticity theory and displacement field of first-order shear deformation plate theory (FSDT), are investigated. By considering total rotational variables as the two rotations due to bending and shear, another formulation form of FSDT nano-plate is achieved, that can simultaneously consider classical plate theory (CLPT) and FSDT. In a comprehensive study, the effects of different parameters such as a nonlocal parameter, aspect ratio, thickness to length ratio, mode number, boundary conditions and also length of nano-plate are examined on the dimensionless natural frequency. The results show that simultaneously applying two-sided tension and compressive in-plane loads changes frequency in a manner which is different to one-directional loading.

scholarly journals Forced Response of Polar Orthotropic Tapered Circular Plates Resting on Elastic Foundation

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. H. Ansari
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Ritz Method ◽  
Forced Response ◽  
Bending Moments ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Different Types ◽  
Foundation Parameter ◽  
Polar Orthotropic

Forced axisymmetric response of polar orthotropic circular plates of linearly varying thickness resting on Winkler type of elastic foundation has been studied on the basis of classical plate theory. An approximate solution of problem has been obtained by Rayleigh Ritz method, which employs functions based upon the static deflection of polar orthotropic circular plates. The effect of transverse loadings has been studied for orthotropic circular plate resting on elastic foundation. The transverse deflections and bending moments are presented for various values of taper parameter, rigidity ratio, foundation parameter, and flexibility parameter under different types of loadings. A comparison of results with those available in literature shows an excellent agreement.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Vibration of Single- and Double-Layered Graphene Sheets

2011 ◽  
Vol 2 (1) ◽  
Author(s):  
Behrouz Arash ◽  
Quan Wang
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Molecular Dynamics Simulations ◽  
Nonlocal Parameter ◽  
Small Scale ◽  
Graphene Sheets ◽  
Elastic Model ◽  
Resonant Frequencies ◽  
Nonlocal Continuum Theory ◽  
Dynamics Simulations

Free vibration of single- and double-layered graphene sheets is investigated by employing nonlocal continuum theory and molecular dynamics simulations. Results show that the classical elastic model overestimated the resonant frequencies of the sheets by a percentage as high as 62%. The dependence of small-scale effects, sizes of sheets, boundary conditions, and number of layers on vibrational characteristic of single- and double-layered graphene sheets is studied. The resonant frequencies predicted by the nonlocal elastic plate theory are verified by the molecular dynamics simulations, and the nonlocal parameter is calibrated through the verification process. The simulation results reveal that the calibrated nonlocal parameter depends on boundary conditions and vibrational modes. The nonlocal plate model is found to be indispensable in vibration analysis of grapheme sheets with a length less than 8 nm on their sides.

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