In the present work, the free vibration behavior of rectangular graphene sheet under shear in-plane load is studied. Nonlocal elasticity theory has been implemented to study the vibration analysis of orthotropic single-layered graphenesheets (SLGSs) subjected to shear in-plane load. The SLGSs is embedded on a viscoelastic medium which is simulated as a Visco-Pasternak foundation. Using the principle of virtual work, the governing equations are derived for the rectangular nanoplates. Differential quadrature method (DQM) is employed and numerical solutions for the vibration frequency are obtained. The influence of surrounding elastic medium, material property, aspect ratio, nonlocal parameter, length of nanoplate and effect of boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) is studied. Six boundary conditions are investigated. Numerical results show that the vibration frequencies of SLGSs are strongly dependent on the small scale coefficient and shear in-plane load. The present analysis results can be used for the design of the next generation of nanodevices that make use of the vibration properties of the graphene. تفاصيل المقالة

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. It is seen from the figure that the influence of nonlocal effect increases with decreasing of the length of nanoplate and also all results at higher length converge to the local frequency. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration proper ties of the nanoplates. تفاصيل المقالة

In this study, the free vibration behavior of rotating nanobeam is studied. Surface effects on the vibration frequencies of nanobeam are considered. To incorporate surface effects, Gurtin–Murdoch model is proposed to satisfy the surface balance equations of the continuum surface elasticity. Differential quadrature method is employed and in order to establish the accuracy and applicability of the proposed model, the numerical results are presented to be compared with those available in the literature. The effects of angular velocity, boundary conditions and surface elastic constants on the vibration characteristics are presented. Numerical results show that the softer boundary conditions cause an increase in the influence of the angular velocity on the nanobeam vibration frequencies. تفاصيل المقالة

In this study, the vibration behavior of circular and annular graphene sheet embedded in a Visco-Pasternak foundation and coupled with temperature change and under in-plane pre-load is studied. The single-layered annular graphene sheet is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the nonlocal elasticity theory and classical plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets has been obtained and nonlocal parameter, in-plane pre-load, the parameters of elastic medium and temperature change appears into arguments of Bessel functions. To verify the accuracy of the present results, the new version differential quadrature method (DQM) is also developed. Closed-form results are successfully verified with those of the DQM results. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number, temperature change, elastic medium and boundary conditions on natural frequencies are investigated. The non-dimensional frequency decreases at high temperature case with increasing the temperature change for all boundary conditions. The effect of temperature change on the non-dimensional frequency vibration becomes the opposite at high temperature case in compression with the low temperature case. The present research work thus reveals that the nonlocal parameter, boundary conditions, temperature change and initial pre-load have significant effects on vibration response of the circular nanoplates. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the graphene. تفاصيل المقالة