Surface stress effect on the postbuckling and free vibrations of axisymmetric circular Mindlin nanoplates subject to various edge supports

Abstract

Postbuckling behavior of circular nanoplates and their free vibration characteristics in the vicinity of postbuckling domain are investigated with the consideration of surface stress effect. To this end, Mindlin’s plate theory in conjunction with the Gurtin–Murdoch elasticity theory is utilized to derive nonlinear equations of motion incorporating geometric nonlinearity and surface stress effect. On the basis of generalized differential quadrature (GDQ) method, the non-classical governing differential equations are discretized along simply-supported and clamped boundary conditions and are then parameterized and solved using the pseudo arc-length continuation method. The postbuckling configurations of axisymmetric circular nanoplates are obtained as a function of applied axial compressive load based on the static analysis. Afterward, on the basis of dynamic analysis, the natural frequencies and associated mode-shapes of circular nanoplates corresponding to both prebuckling and postbuckling domains are predicted including surface stress effect. It is revealed that by decreasing the magnitude of thickness, the surface stress effect on the postbuckling configurations of nanoplates becomes more prominent. Moreover, the effect of surface stress may shift the postbuckling domain to higher or lower applied axial loads, depending on the magnitude and sign of surface elastic constants. These anticipations are the same corresponding to various edge supports.