Stability and vibration of a nanoplate under body force using nonlocal elasticity theory

In the present study, the problem of stability and vibration of a square single-layer graphene sheet under body force is studied using Eringen's theory. The body force is constant and parallel with the plate. The boundary conditions correspond to the dynamical model of a nanoplate clamped at all its sides. Classical plate theory, upgraded with nonlocal elasticity theory, is used to formulate the differential equation of stability and vibration of the nanoplate. Natural frequencies of transverse vibrations, depending on the effects of body load and nonlocality, are obtained using Galerkin's method. Critical values of the body load parameter, i.e., the values of the body load parameter when the plate loses its stability, are determined for different values of nonlocality parameter. The mode shapes for a square nanoplate under influences of body load and nonlocality are presented as well.