This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the mo...

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

The present paper deals with the dynamic behavior of nano-column subjected to follower force using the nonlocal elasticity theory. The nonlocal elasticity theory is used to analyze the mechanical behavior of nanoscale materials. The used method of solution is the Differential Quadrature Method (DQM). It is shown that the nonlocal effect plays an important role in the vibrational behavior of nan...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

In this article free vibration of a Timoshenko nanobeam with variable cross-section is investigated using nonlocal elasticity theory within the scope of continuum mechanics. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width through the beam length with constant thickness. Analytical solution is achiev...