Vibration Of Rectangular Nanoplates Research Articles

Positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in-plane loadings based on nonlocal elasticity theory

In this paper, positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in-plane loadings are investigated based on the nonlocal elasticity theory. Aluminum and silicon materials, respectively, with positive and negative surface properties are considered. The surface effect is considered using Gurtin–Murdoch’s theory. Using Hamilton’s principle, the governing equations considering small scale for both bulk and surface properties of nanoplate are derived. Generalized differential quadrature method (GDQM) is used. GDQM results are validated by comparing with the Navier’s method. The influence of nonlocal parameter, boundary conditions, in-plane biaxial and shear loads, and width-to-length aspect ratio, on the positive and negative surface effects influencing buckling and vibration are investigated. Numerical results show that by increasing the nonlocal parameter, the effect of positive surface property increases on the buckling and vibration behavior of nanoplate, while this conclusion is reversed for negative surface property.

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

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.