Bifurcation Behavior of a Capacitive Micro-Beam Suspended between Two Conductive Plates

A. Azizi, Hamed Mobki, G. Rezazadeh
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引用次数: 7

Abstract

In this paper, bifurcation and pull-in phenomena of a capacitive micro switch suspended between two stationary plates have been studied. The governing dynamic equation of the switch has been attained using Euler Bernoulli beam theorem. Due to the nonlinearity of the electrostatic force, the analytical solution for the derived equation is not available. So the governing differential equation has been solved using combined Galerkin weighted residual and Step-By-Step Linearization Methods (SSLM). To obtain the fixed points and study the local and global bifurcational behavior of the switch, a mass-spring model has been utilized and adjusted so that to have similar static/dynamic characteristics with those of Euler-Bernoulli beam model (in the first mode). Using 1-DOF model, mathematical and physical equilibrium points of the switch have been obtained for three different cases. It is shown that the pull-in phenomenon in the present micro-switch can be occurred due to a pitchfork or transcritical bifurcations as well as saddle node bifurcation which are transpired in the classical micro-switches. And for some cases primary and secondary pull-in phenomena are observed where the first one is due to a transcritical bifurcation and the second one is due to a saddle node bifurcation. In addition the dynamic response of the switch to a step DC voltage has also been studied and the results show that in contrast to the classical microswitches, the ratio of the dynamic pull-in to the static one depends on the gaps and voltages ratio where for the classical one is approximately a constant value.
悬浮在两个导电板之间的电容性微梁的分岔行为
本文研究了悬浮在两块固定板之间的电容微动开关的分岔和拉入现象。利用欧拉-伯努利梁定理,得到了开关的控制动力学方程。由于静电力的非线性,推导方程的解析解是不可用的。为此,采用伽辽金加权残差法和逐步线性化法(SSLM)相结合的方法求解控制微分方程。为了获得不动点,研究开关的局部和全局分岔行为,采用了质量弹簧模型,并对其进行了调整,使其具有与欧拉-伯努利梁模型(第一模态)相似的静态/动态特性。利用1自由度模型,得到了三种不同情况下开关的数学和物理平衡点。结果表明,由于传统微开关存在干草叉分岔、跨临界分岔和鞍节点分岔,导致了当前微开关的拉入现象。在某些情况下,我们观察到初级和次级拉入现象第一个是由跨临界分岔引起的第二个是由鞍节点分岔引起的。此外,还研究了开关对阶跃直流电压的动态响应,结果表明,与经典微动开关相比,动态拉入与静态拉入的比值取决于间隙和电压比,其中经典拉入近似为恒定值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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