Surface stress effects on the free vibration behavior of nanoplates

Surface stress is one of the most considerable reasons which cause extraordinary mechanical responses of nanomaterials and nanostructures due to the high surface to volume ratio of the systems at this submicron size. In the present study, the free vibration characteristics of nanoplates including surface stress effects are investigated based on the continuum modeling approach. To this end, Gurtin–Murdoch continuum elasticity approach is incorporated into the different types of plate theory namely as classical plate theory (CLPT) and first-order shear deformation theory (FSDT) to develop non-classical continuum plate models for free vibration analysis of the nanoplates including surface stress effects. Closed-form analytical solution accounting for the influence of surface stress on the vibrational behavior of nanoplates is derived. Selected numerical results are given to quantitatively assess the surface stress effects on the natural frequencies of the nanoplates. It is found that the difference between the results predicted by the classical and non-classical solutions relies on the sign and magnitude of the surface elastic constants.

► Incorporation of the Gurtin–Murdoch continuum elasticity into different plate theories.
► Development of non-classical plate models including surface stress effects.
► Investigation of surface stress effects on the free vibration characteristics of nanoplates.
► Exploring influences of the sign and magnitude of surface elastic constants on vibrations of nanoplates.