In this article, surface and nonlocal effects are explored in the analysis of buckling and vibration in rectangular single-layered graphene sheets embedded in elastic media and subjected to coupled in-plane loadings and thermal conditions. The small-scale and surface effects are taken into account using the Eringen's nonlocal elasticity and Gurtin-Murdoch's theory, respectively. Using the principle of virtual work, the governing equations considering small-scale are derived for the nanoplate bulk and surface. The differential quadrature method (DQM) is utilized for the solution of the relevant problems and the results are validated against Navier's solutions. The impacts of the nonlocal parameter, Winkler and shear elastic moduli, temperature rise, boundary conditions, and the in-plane biaxial, uniaxial, and shear loadings on the surface effects of buckling and vibration are investigated. Numerical results show that increasing nonlocal parameter leads to enhanced surface effects on both buckling and vibration. This is in contrast to those reported elsewhere. Moreover, increasing in-plane loads are observed to enhance surface effects on vibration. On the other hand, the nonlocal parameter is observed to have more pronounced effects on shear buckling and vibration of plates subjected to coupled in-plane shear loads than those subjected to biaxial and uniaxial loads. This is while surface effects have greater impacts on biaxial buckling and vibration of nanoplates than on shear buckling and vibration.

This paper reports an investigation on thermo-electro-mechanical vibration of graphene/piezoelectric graphene/piezoelectric/graphene sandwich nanobeams. Based on the nonlocal elasticity theory, Timoshenko beam theory and Hamilton's principles, the governing equations are developed and solved using generalized differential quadrature (GDQ) method. The effects of the nonlocal parameter, external electrical voltage, temperature change and axial force on vibration of graphene/piezoelectric/graphene sandwich nanobeams are examined. The performance and the accuracy of the presented model are highlighted through numerical examples with different boundary conditions. This study reports that the nonlocal parameter and thermo-electro-mechanical loadings have important effect on the natural frequencies and the deflection mode shapes of the graphene/piezoelectric/graphene sandwich nanobeam. The present work can serve as guideline for the design of a nanoscale graphene/piezoelectric/graphene beams based electromechanical resonator sensors.

An elastic Bernoulli–Euler beam model is developed for thermal-mechanical vibration and buckling instability of a single-walled carbon nanotube (SWCNT) conveying fluid and resting on an elastic medium by using the theories of thermal elasticity mechanics and nonlocal elasticity. The differential quadrature method is adopted to obtain the numerical solutions to the model. The effects of temperature change, nonlocal parameter and elastic medium constant on the vibration frequency and buckling instability of SWCNT conveying fluid are investigated. It can be concluded that at low or room temperature, the first natural frequency and critical flow velocity for the SWCNT increase as the temperature change increases, on the contrary, while at high temperature the first natural frequency and critical flow velocity decrease with the increase of the temperature change. The first natural frequency for the SWCNT decreases as the nonlocal parameter increases, both the first natural frequency and critical flow velocity increase with the increase of the elastic medium constant.