Nonlocality refers to correlations between spatially separated parties that are stronger than those explained by the existence of local hidden variables. Quantum mechanics is known to allow some nonlocal correlations between particles in a phenomena known as entanglement. We explore several aspects of nonlocality in general and how they relate to quantum mechanics. First, we construct a hierarc...

In this article, small scale effects on free vibration analysis of non-uniform nanobeams is discussed. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width among the beams length with constant thickness. Analytical solution is achieved for free vibration with different boundary conditions. It is shown th...

in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

The equations of motion and bending of Euler-Bernoulli beam are formulated using the nonlocal elasticity theory for cantilever microtubules (MTs). The method of differential quadrature (DQ) has been used for numerical modeling. The size effect is taken into consideration using the Eringen’s non-local elasticity theory. Frequencies and deflections of MTs are obtained. Numerical results are prese...

In the present study the free vibration analysis of the functionally graded rectangular nanoplates is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of tr...

This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal elasticity theory. The nano-beam is sandwiched with two piezoelectric layers through it’s upper and lower sides. The electromechanical coupled equations governing the problem are derived based nonlocal theory considering to Euler-Bernoulli beam assumptions and based on the nonlocal piezoelectricity acco...

In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal e...