Shear vibration and buckling of double-layer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects

Abstract

In this article, shear vibration and buckling of double-layer orthotropic nanoplates resting on elastic foundations are analyzed subjected to in-plane loadings including surface and nonlocal effects. These effects are considered by Gurtin---Murdoch's theory. Using the principle of virtual work, the governing equations for bulk and surface of double-layer orthotropic nanoplate are derived using refined plate theory. Differential quadrature method (DQM) is implemented. DQM solutions are validated by Navier's method and journal references. The influences of nonlocal parameter, van der Waals, Winkler, shear modulus, orthotropic material properties, boundary conditions, and in-plane biaxial, uniaxial, and shear loadings, are investigated on the surface effects of buckling and vibration modes of out-of-phase and in-phase. Results demonstrate that by augmenting nonlocal parameter, the surface effects on the vibration and buckling modes of both out-of-phase and in-phase increase. This result is in contrast with the works of other researchers in the field. Moreover, by enhancing in-plane loadings, the degree of surface effects on the vibration increase. On the other hand, the effects of nonlocal parameter on the vibration and buckling under in-plane shear load are more influential than those of biaxial and uniaxial, while the surface effects on the biaxial vibration and buckling are more remarkable than those of shear vibration and buckling.