静电驱动微悬臂梁静态吸合特性的尺寸效应研究  

SIZE EFFECT ON THE STATIC PULL-IN INSTABILITY OF THE ELECT ROSTATICALLY ACTUATED CANTILEVER MICRO-BEAMS

作　　者：芦非 孔胜利 袁艳琪 LU Fei;KONG ShengLi;YUAN YanQi(Department of Mechanical and Automotive Engineering,Qilu University of Technology,Jinan 250353,China)

机构地区：[1]齐鲁工业大学机械与汽车工程学院,济南250353

出　　处：《机械强度》2018年第6期1336-1340,共5页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(51405253)资助~~

摘　　要：基于修正偶应力理论研究了静电驱动微悬臂梁在考虑Casimir力时的静态吸合特性。利用最小势能原理得到了微悬臂梁弯曲的控制方程和边界条件,应用广义微分求积法(GDQM)求解后得到静电驱动微悬臂梁吸合电压与无量纲吸合位移的数值解。结果表明,基于修正偶应力理论的静电驱动微悬臂梁的吸合电压明显高于经典理论值,表现出明显的尺寸效应;同时Casimir力降低了微悬臂梁的吸合电压与无量纲吸合位移。当微悬臂梁的初始间隙g远远大于其厚度h时,Casimir力的影响可以忽略不计。The static pull-in instability of the electrostatically actuated cantilever micro-beams incorporating Casimir force was investigated based on the modified couple stress theory.The nonlinear governing equation and boundary conditions were derived using the principle of minimum total potential energy.The pull-in voltages and non-dimensional pull-in displacements of the electrostatically actuated cantilever micro-beams were calculated by applying the generalized differential quadrature method (GDQM).The resuhs show that the pull-in voltages of the electrostatically actuated cantilever micro-beams based on the modified couple stress theory are greater than the classical results and the size effects are obvious.The presence of the Casimir force can reduce the pull-in voltages and non-dimensional pull-in displacements of the cantilever micro-beams and the influence of the Casimir force can be neglected when the initial gap of the cantilever micro-beams g is far greater than the thickness of the beam h.

关 键 词：修正偶应力理论 尺寸效应 吸合特性 CASIMIR力 广义微分求积法 

分 类 号：O343.9[理学—固体力学]