Nonlinear behavior of a nano-scale beam considering length scale-parameter

Size dependent behavior of materials arises for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of size dependence on static and dynamic behavior of electro-statically actuated nano-beams have been studied. The fixed points of the Aluminum nano-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the calculated fixed points using classic beam theory and modified couple stress theory. In addition, it has been also shown that ignoring couple stress theory results in an order of magnitude error in calculated static and dynamic pull-in voltages. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to justify the discrepancies between experimental and theoretical results.