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 - Karimi, Morteza; Mirdamadi, Hamid Reza; Shahidi, Ali Reza (Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017)
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.