SIZE EFFECT ON THE SNAP-THROUGH AND PULL-IN INSTABILITY OF THE ELECTROSTATICALLY ACTUATED MICRO SHALLOW ARCH

Abstract

The snap-through and pull-in instability of the electrostatically actuated micro shallow arches incorporating Casimir force was investigated based on the modified couple stress theory. The nonlinear governing equation and boundary conditions were derived by using the principle of minimum total potential energy. The snap-through voltages, the pull-in voltages, the non-dimensional snap-through displacements and the non-dimensional pull-in displacements of the electrostatically actuated micro shallow arches were calculated by applying the generalized differential quadrature method（GDQM） and the generalized integral quadrature method（GIQM）. The results show that the snap-through and the pull-in instability of the electrostatically actuated micro shallow arches are size-dependent. The snap-through and pull-in voltages of the electrostatically actuated micro shallow arches based on the modified couple stress theory are smaller than the classical results. The Casimir force can reduce the snap-through voltages, the pull-in voltages, the non-dimensional snap-through and the pull-in displacements of the micro shallow arches. The initial rise of the micro shallow arches affects the snap-through and pull-in instability.

Keywords

• The modified couple stress theory;Snap-through;Pull-in;Size effect;Casimir force