Stability and bifurcation analysis of an electrostatically controlled highly deformable microcantilever-based resonator

A detailed numerical investigation on stability and bifurcation analysis of a highly nonlinear electrically driven MEMS resonator has been established. A nonlinear model has been developed by using Hamilton’s principle and Galerkin’s method considering both transverse and longitudinal displacement of the resonator. The special care has been paid by incorporating higher order correction of electrostatic pressure. The pull-in results and consequences of higher order correction on the pull-in stability have been investigated. Furthermore, investigation of nonlinear phenomenon for the consequences of air-gap, electrostatic forcing parameter and effective damping on overall responses has been thoroughly studied. The possible of undesirable catastrophic failure at the unstable critical points has been critically examined. Basins of attractions that postulate a unique response in multi-region state for a specific initial condition have been depicted. The obtained responses using first-order method of multiple scales have been cross compared with the findings obtained numerically. Findings from this work can significantly be adopted to identify the locus of instability in microcantilever-based resonator when subjected to AC voltage polarization. In addition, the present outcomes provide theoretical and practical ideas for controlling the systems and optimizing their operation.