Lee C., Kim W.

The effect of fabrication error on dynamic performance of MEMS structures is becoming more significant than macro-scaled structures, because the present fabrication methods for MEMS structures are likely to be exposed to relatively large dimensional inaccuracy. These fabrication errors are often large enough to result in malfunction or performance degradation of the produced device especially in mechanical responses such as resonant frequency and mode shape of vibratory MEMS resonator. MEMS resonator is operated as a filter that selects a desired frequency. MEMS resonator considered in this paper forms a periodic structure to reduce motional resistance. The periodic structures are vulnerable to fabrication error and this trend becomes severe as the number of substructure increases. Therefore, a robust optimal design is needed to make the system response less sensitive to the fabrication error, guarantee reliable performances and thus improve yield rate in mass production. In this paper a simple and cost-efficient robust optimal design method for MEMS resonator is presented. The robust configuration of MEMS resonator to fabrication error is implemented by changing the regularity of periodic structure, according to the following steps. First, the MEMS resonator is mathematically modeled by multi-pendulum system. Second, the index representing the measure of mode variation is introduced using the perturbation method and the Modal Assurance Criterion. Finally, for the normal distributed fabrication error, the optimal intentional mistuning minimizing the expectation value of the irregularity measure for each substructure is determined. It is also demonstrated that this optimal intentional mistuning in the design of MEMS resonator shows the robustness of MEMS resonator to the fabrication error.