Theoretical study of an electrostatically actuated torsional microsensor for biological applications

We develop an analytical formulation to calculate the induced resonance frequency shifts of an electrostatically actuated torsional microsensor due to an added bio-mass (E. coli). Based on a lumped-parameter model, we investigate the static and the linear eigenvalue problem of the torsional microsensor. The added mass is modeled as a point mass load placed on different locations along the x-axis of the microsensor. A closed-form expression is determined to calculate the frequency shift under a DC voltage as a function of the added mass. Finite Element Analysis (FEA) results show good agreement with the analytical approach.