Nonlocal mass-nanosensor model based on the damped vibration of single-layer graphene sheet influenced by in-plane magnetic field (original) (raw)
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Theoretical Analysis of Vibration Frequency of Graphene Sheets Used as Nanomechanical Mass Sensor
Electronics, 2015
Nanoelectromechanical resonator sensors based on graphene sheets (GS) show ultrahigh sensitivity to vibration. However, many factors such as the layer number and dimension of the GSs will affect the sensor characteristics. In this study, an analytical model is proposed to investigate the vibration behavior of double-layered graphene sheets (DLGSs) with attached nanoparticles. Based on nonlocal continuum mechanics, the influences of the layer number, dimensions of the GSs, and of the mass and position of nanoparticles attached to the GSs on the vibration response of GS resonators are discussed in detail. The results indicate that nanomasses can easily be detected by GS resonators, which can be used as a highly sensitive nanomechanical element in sensor systems. A logarithmically linear relationship exists between the frequency shift and the attached mass when the total mass attached to GS is less than about 1.0 zg. Accordingly, it is convenient to use a linear calibration for the calculation and determination of attached nanomasses. The simulation approach and the parametric investigation are useful tools for the design of graphene-based nanomass sensors and devices.
Vibrating nonlocal multi-nanoplate system under inplane magnetic field
European Journal of Mechanics - A/Solids
The recent development in nanotechnology resulted in growing of various nanoplate like structures. High attention was devoted to graphene sheet nanostructure, which enforced the scientist to start developing various theoretical models to investigate its physical properties. Magnetic field effects on nanoplates, especially graphene sheets, have also attracted a considerable attention of the scientific community. Here, by using the nonlocal theory, we examine the influence of in-plane magnetic field on the viscoelastic orthotropic multi-nanoplate system (VOMNPS) embedded in a viscoelastic medium. We derive the system of m partial differential equations describing the free transverse vibration of VOMNPS under the uniaxial in-plane magnetic field using the Eringen's nonlocal elasticity and Kirchhoff's plate theory considering the viscoelastic and orthotropic material properties of nanoplates. Closed form solutions for complex natural frequencies are derived by applying the Navier's and trigonometric method for the case of simply supported nanoplates. The results obtained with analytical method are validated with the results obtained by using the numerical method. In addition, numerical examples are given to show the effects of nonlocal parameter, internal damping, damping and stiffness of viscoelastic medium, rotary inertia and uniaxial in-plane magnetic force on the real and the imaginary parts of complex natural frequencies of VOMNPS. This study can be useful as a starting point for the research and design of nanoelectromechanical devices based on graphene sheets.
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.
International Journal of Engineering, 2015
The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nanoplates based on Kirchhoff's plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relations of MEE materials, the governing equations are derived by applying Maxwell's equation and Hamilton's principle. By employing Galerkin method, the eigen matrix form of the governing equation is obtained. The effect of magneto-electric potential on instability of the system is investigated and consequently critical values of applied potentials are calculated. A detailed numerical study is conducted to study the influences of the small scale effect, thickness and radius of the nano-plate and piezoelectric volume fraction of the MEE material on the natural frequencies of nano-plate. Furthermore, the effects of the applied magnetic and electric potentials on the size-dependent natural frequencies are investigated numerically.
Advances in Engineering and Intelligence Systems, 2023
Based on the potential applications of graphene nanosheets as super-sensitive sensors, this paper examines the vibrations of graphene nanoplates under the influence of axial motion. For this purpose, Kirchhoff's nonlinear plate model will be used in conjunction with the modified couple stress theory (MCST). Using Hamilton's principle, nonlinear equations governing motion are extracted and then discretized using the Galerkin method. Based on the numerical method, the dynamic response and vibration characteristics of these systems are determined. According to our results, the small size parameter increases the critical speed of the system. The first non-dimensional critical speed of the system at 0, 1.2, and 1.8 is approximately 3.14, 3.18, and 3.42, respectively. A small size parameter also increases the system's oscillation frequency. It is unnecessary to apply the modified stress coupling theory to nanosheets with thicker thicknesses (h > 1.25l) since the effect of the size scale parameter increases with decreasing thickness. In contrast, the frequency increases significantly for thinner nanosheets. Due to the nonlinear behavior of these systems, the instability of the motion of the system can be attributed to chaotic behavior based on the study of the dynamic response. Graphene nanosheets and other plate-like nanostructures may be identified based on the results presented here.
Nonlinear Dynamics
Parametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant altera...
Curved and Layered Structures
The present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.
Journal of Vibroengineering, 2016
The vibration analysis of a single-layered graphene sheet (SLGS) embedded in viscoelastic medium is presented by using the nonlocal elasticity theory. The medium is considered by adding the damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus. The governing dynamical equation is obtained and solved for simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak's foundation, damping coefficient, and mode numbers on the vibration frequencies of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.