Pull-in instability of two opposing microcantilever arrays with different bending rigidities

Comb-drive structures consisting of two opposing parallel arrays of microcantilevers are commonly adopted in many designs of MEMS. This work studies pull-in instability of comb-drive structures in which two opposing arrays have different bending rigidities. Based on a simplified spring model, it is verified that equilibrium deflections of all intermediate microcantilevers in the arrays are negligibly small prior to the onset of instability, and non-negligible deflections of the end microcantilevers cause a significant end-effect on pull-in instability of the comb-drive array. With this concept, the critical value for instability of the comb-drive arrays is estimated, with or without the end-effect, for varying bending rigidity ratios. Compared to the results without the end-effect, the end-effect is found to lower the critical interaction coefficient for instability, and the reduction in the critical value for instability increases with decreasing bending rigidities of the end microcantilevers. These results for varying bending rigidity ratios indicate the significance of the end design on the instability of comb-drive structures. In particular, the results obtained by the present method are in good agreement with some known experimental data available in the literature and the exact results obtained by iteration numerical method for the spring model.