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 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