On Sensitivity of Capacitive Microresonators Near Three Half Natural Frequency

This paper deals with sensitivity of electrostatically actuated micro resonator sensors near three half natural frequency. Mass deposition changes resonance frequencies of structures. Resonator sensitivity, defined as a fraction of change in frequency per unit deposited mass, can be found for microcantilever sensors electrostatically actuated to include fringe and Casimir effects. These actuation forces produce nonlinear parametric oscillations. Constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular cross-section was assumed. The Euler-Bernoulli theory was used under the assumption that the beams are slender. Mass deposition on the free end surface of the cantilever was neglected. The deposition thickness was considered uniform and very small compared to any beam dimension. The deposited mass had no contribution to the stiffness, only to the mass. Analytical expression of the sensitivity of electrostatically actuated uniform microcantilever resonators sensor near natural frequency can be determined.