Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field (original) (raw)
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Meccanica
The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. The interaction between layers is taken into account due to van der Waals forces. The investigation is based on the nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. The effect of the magnetic field is due to the Lorentz force based on Maxwell’s equations. The governing equations are used in mixed form by introducing the stress Airy function. The analytical presentation of the nonlinear frequency ratio for in-phase vibration and anti-phase vibration modes is presented. It is shown that the nonlocal parameter in the compatibility equation can significantly change the vibration characteristics.
Applied and Computational Mechanics, 2020
In this article, the vibration and buckling of a double-layer Graphene sheet (DLGS) coupled with a piezoelectric nanoplate through an elastic medium (Pasternak and Winkler models) are under consideration. DLGS are subjected to biaxial in-plane forces and van der Waals force existing between each layer. Polyvinylidene fluoride (PVDF) piezoelectric nanoplate is subjected to an external electric potential. For the sake of this study, sinusoidal shear deformation theory of orthotropic plate expanded with Eringen’s nonlocal theory is selected The results indicate that nondimensional frequency and nondimensional critical buckling load rise, when the ratio of width to thickness increases. Furthermore, incrementing the effect of elastic medium parameter results in increasing the stiffness of the system and, consequently, rising nondimensional frequency and critical buckling load.
Journal of Intelligent Material Systems and Structures, 2017
This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.
A Structural Mechanics Approach for the Vibrational Analysis of Single-Layered Graphene Sheets
Indonesian Journal of Physics, 2016
A structural mechanics approach has been employed to analyze the vibrational behavior of single-layered graphene sheets. By adopting this approach, natural frequencies and mode shapes are obtained for different chirality and imposed boundary conditions. Numerical results from the implemented modeling are examined to provide predictive equations for fundamental frequencies of cantilevered and bridged graphene sheets. With the proposed equations, the natural frequencies can be predicted and are comparable to those obtained from theoretical consideration and experimental results.
Lateral Vibrations of Single-Layered Graphene Sheets Using Doublet Mechanics
Journal of Solid Mechanics, 2016
This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. Using doublet mechanics, the relation between natural frequency and length scale parameter is obtained in the lateral mode of vibration for single-layered graphene. It is shown that length scale parameter plays a significant role in the lateral vibration behavior of single-layered graphene sheets. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However with increasing the length of the plate, the effect of scale parameter on the natural frequency decreases. For validating the results of this method, the results obtained herein are compared with the existing nonlocal and molecular...
Applied Mathematical Modelling, 2016
Vibration of orthotropic double-layered graphene sheets under hygrothermal conditions is investigated in this paper using the trigonometric shear deformation plate theory. This theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional shear deformation theory, the present trigonometric theory contains only two unknowns. The two layers are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundations. The equations of motion are derived based on the nonlocal theory. The motion equations contain the small scale effect as will as hygrothermal effect. The present solution is examined by comparing the present results with those being in the open literature. The effects played by small scale parameter, temperature rise, the degree of moisture concentration, plate aspect ratio and side-to-thickness ratio are studied.
Physica E: Low-dimensional Systems and Nanostructures, 2014
The sinusoidal shear deformation plate theory is used to analyze the bending and vibration of the nanoplates. The nanoplates are assumed to be embedded in two-parameter elastic foundations and subjected to mechanical and thermal loads. The governing equations are solved analytically for various boundary conditions. A detailed parametric study is carried out to highlight the influences of the different parameters on the bending and the frequency of the nanoplates.
Transverse vibration of single-layer graphene sheets
2011
Abstract We investigate the vibrational properties of zigzag and armchair single-layer graphene sheets (SLGSs) using the molecular mechanics (MM) approach. The natural frequencies of vibration and their associated intrinsic vibration modes are obtained. Vibrational analysis is performed with different chirality and boundary conditions. The simulations are carried out for three types of zigzag and armchair SLGS. The universal force field potential is used for the MM approach.