Combining surface effects and non-local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates

Abstract

In this reported work, surface effects and non-local two variable refined plate theories are combined on the shear/biaxial buckling and vibration of rectangular nanoplates. A silver sheet is selected as the case study to investigate the numerical results. Surface effects are considered by Gurtin Murdoch's theory. The differential quadrature method is used to solve the governing equations. Differential quadrature solutions are verified by Navier's method. The influences of the non-local parameter on the surface effects of shear/biaxial buckling and vibration are investigated for various boundary conditions. Results show that by increasing the non-local parameter, the effects of surface on the buckling and vibration increase. This result is in contrast with the works of other researchers in the field. Moreover, the non-local effects on the shear buckling and vibration are more important than that of biaxial, whereas the surface effects on the biaxial buckling and vibration are more notable than that of shear.