Super Sensitive Mass Detection in Nonlinear Regime

Abstract

Nonlinear dynamics of a clamped–clamped micro-beam exposed to a two sided electrostatic actuation is investigated to determine super sensitive regions for mass detection. The objective is to investigate the sensitivity of the frequency spectrum of various regions in the phase space to the added mass and force the system to operate in its super sensitive regions by applying an appropriate pulse to its control electrodes. The electrostatic actuation in the top electrode is a combination of a DC, AC and a pulse voltage, the excitation on the lower electrode is only a DC and a pulse voltage. The governing equation of the motion, derived using the Hamiltonian principle, is discretized to an equivalent single-degree of freedom system using the Galerkin method. Depending on the applied electrostatic voltage to the micro-beam, it is demonstrated that the number and types of equilibrium points of the system can be modified. In this study, the level of the DC electrostatic voltage is chosen such a way that the system has three equilibrium points including two centers and a saddle node where the homoclinic orbit originates. According to the reported results, the mass sensing sensitivity depends on the operating orbit; some orbits exhibit considerably higher mass detection sensitivity to the added mass compared to that of a typical quartz crystal micro balance instrument.