In this study, the pull-in phenomenon of a Nano-actuator is investigated employing a nonlocal Bernoulli-Euler beam model with clamped-clamped conditions. The model accounts for viscous damping, residual stresses, the van der Waals (vdW) force and electrostatic forces with nonlocal effects. The hybrid differential transformation/finite difference method (HDTFDM) is used to analyze the nonlocal effects on a graphene sheet nanobeam, which is electrostatically actuated under the influence of the coupling effect, the von Kármán nonlinear strains and the fringing field effect. The pull-in voltage as calculated by the presented model deviates by no more than 0.29% from previous literature, verifying the validity of the HDTFDM. Furthermore, the nonlocal nonlinear behavior of the electrostatically actuated nanobeam is investigated, and the effects of viscous damping, residual stresses, and length-gap ratio are examined in detail. Overall, the results reveal that small scale effects significantly influence the characteristics of the graphene sheet nanobeam actuator.

The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Analyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.