In this paper, the Ritz method has been employed to analyze the free in-plane vibration of heterogeneous (non-uniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal pol...

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...

in this article, an analytical solution is developed to study the free vibration analysis offunctionally graded rectangular nanoplates. the governing equations of motion are derived basedon second order shear deformation theory using nonlocal elasticity theory. it is assumed that thematerial properties of nanoplate vary through the thickness according to the power lawdistribution. our numerical...

Abstract Free vibrations of the orthotropic micro/nanoplate with nonclassical shape are investigated. The considered model is based on nonlocal elasticity theory. developed method uses Ritz as well R-function theory for construction system coordinate functions. linear frequencies obtained a rectangular plate two cutouts opposite sides, while boundary conditions several types, including simply s...

in this article, finite difference method (fdm) is used to study the size-dependent free vibration characteristics of rectangular nanoplates considering the surface stress effects. to include the surface effects in the equations, gurtin-murdoch continuum elasticity approach has been employed. the effects of surface properties including the surface elasticity, surface residual stress and surface...

For this work, a β-phase Cu2−xSe nanowire and nanoplate, and a Na-doped Cu2−xSe nanoplate were successfully synthesized using solution syntheses. The morphologies of the Cu2−xSe nanowire and nanoplate could be easily controlled by changing the synthetic condition. The Na-doped Cu2−xSe nanoplate was prepared by a simple treatment of the Cu2−xSe nanoplate with a sodium hydroxide-ethylene glycol s...

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assum...

In this paper a third order shear deformation rectangular nanoplate with simply supported boundary conditions is developed for bending, buckling and vibration analysis. to consider the small-scale effects, modified couple stress theory, one length scale parameter, used. The bending rates dimensionless values under uniform surface traction sinusoidal load, critical force uniaxial in x direction ...

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...