Abstract
In this research, nonlinear dynamics of a parametrically excited clamped–clamped micro-beam is investigated for mass sensing applications. The ability to detect mass change opens up implementation of various precise chemical and biological sensors due to their small size and high sensitivity; one of the factors which limit the sensitivity of the MEMS mass sensor is the quality factor (Q). In the proposed model, the micro beam is sandwiched with two piezoelectric layers undergoing a combination of DC and AC voltages which leads to a parametric excitation. The governing differential equation of the motion is derived by the minimization of the Hamiltonian and discretized to a single-degree of freedom system in terms of nonlinear damped Mathieu equation. Based on shooting method, the periodic solutions are captured, the stability of the periodic solutions is determined by means of Floquet theory and the stability margins are determined. We showed that in the plane of excitation frequency and the amplitude of harmonic voltage, there are two distinctive regions, including damped and parametrically resonated regions; these regions are separated via limit cycles (periodic motions). The micro beam is set to operate in the damped region in the vicinity of the limit cycles, before the response is damped once the added mass is deposited on the micro beam the response is pushed inside the resonance region and the amplitude magnification is used as a measure of mass detection. The effect of geometric nonlinearity on the system response is investigated.
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Azizi, S., Rezaei Kivi, A. & Marzbanrad, J. Mass detection based on pure parametric excitation of a micro beam actuated by piezoelectric layers. Microsyst Technol 23, 991–998 (2017). https://doi.org/10.1007/s00542-016-2813-7
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DOI: https://doi.org/10.1007/s00542-016-2813-7