POST BUCKLING OF MICROMACHINED BEAMS

The static deformation of micromachined beams under prescribed in-plan e compressive stress is studied through analytical and experimental me ans over the prebuckling, transition and postbuckling load ranges. The finite amplitude of the beam in its postbuckled state is predicted by modeling the non-linear dependence of the out-of-plane deformation on the compressive stress. In addition, the model explicitly considers t he net effect of slight imperfections, which can include fabrication d efects, geometric irregularities, or non-ideal loading, on the beam's behavior in the near-buckling regime. As an application, clamped-clamp ed silicon dioxide beams are fabricated through conventional bulk micr omachining, and their deflected profiles are measured through three-di mensional optical profilometry. The measurements are compared to the p ostbuckled amplitudes and shapes that are predicted by the model, and by existing simpler models that do not include the effects of either n on-linearity or imperfection. As borne out by the data, when imperfect ions are considered, the beams exhibit continuous growth of the out-of -plane amplitude during transition from the prebuckled state to a post buckled one, in contrast to sudden bifurcation at a critical load. By accounting for this behavior, the estimate of residual stress in the t hin film from which the beams are fabricated can be improved, and the amplitude of common postbuckled micromachined structures can be predic ted during the design phase.