静电驱动微浅拱梁跳跃和吸合特性的尺寸效应研究

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

基于修正偶应力理论研究了静电驱动微浅拱梁在考虑Casimir力时的跳跃和吸合特性。利用最小势能原理得到了微浅拱梁弯曲的控制方程和边界条件,应用广义微分求积法(GDQM)和广义积分求积法(GIQM)求解得到静电驱动微浅拱梁跳跃电压和吸合电压以及无量纲跳跃位移和吸合位移的数值解。结果表明,静电驱动微浅拱梁的跳跃特性和吸合特性具有明显的尺寸效应;基于修正偶应力理论的静电驱动微浅拱梁的跳跃和吸合电压低于经典理论值;Casimir力降低了微浅拱梁的跳跃和吸合电压以及无量纲跳跃和吸合位移;微浅拱梁初始拱高对其跳跃和吸合特性有着重要的影响。

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.