Static deflection and natural frequency analysis of a two-layered electrostatically actuated microcantilever for finding the optimum configuration

In this study, the static deflection and natural frequency of an electrostatically excited patch-coated microcantilever beam are analyzed. The proposed model is considered as the main element of many microsensors and microswitches. Firstly, the nonlinear motion equation is extracted by means of Hamilton principle, assuming shortening effect. Secondly, differential equations, governing the static deflection and free vibration equation around the stability point, are solved using Galerkin method and the three mode shapes of a uniform microbeam are employed as the comparison function. By assuming that the volume of deposited layer is constant, the variation of natural frequency and static deflection are examined in three different cases. In any cases, it is presumed that the second layer is initially deposited on the entire length of microbeam. In the first case, one end of coated layer is considered fix at the clamped side of microcantilever, and then its length is decreased from other side, where its thickness is increased. In the second case, one end of coated layer is perceived fix at the free side of microcantilever, and then its length is decreased from other side, where its thickness is escalated. In the third case, the length of second layer is decreased from both of left and right ends, where its thickness is expanded. In addition, the effect due to the change of the second layer position is considered on mechanical behavior of the system.