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<p>This paper theoretically investigates the nonlinear dynamics and sensitivity enhancement method of an electrostatically coupled resonant mass sensor at 2:1 internal resonance. A reduced-order model of the sensor considering geometric and electrostatic nonlinearities is developed, and the equations of motion are solved with the method of multiple scales (MMS), and validated using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). For the case of response symmetry destruction under the dominance of geometric nonlinearities, a bifurcated topology tuning scheme is introduced to cancel the effects of the quadratic non-resonant terms and the cubic terms on the dynamic behavior, restoring the symmetry of the M-shaped frequency response, similar to the system with only two quadratic resonant terms. The results show that compared to the frequency shift output, the sensitivity defined as the sum of relative amplitude shifts is three orders of magnitude higher and can be further enhanced up to 85% when using the proposed bifurcation topology tuning approach. This symmetry recovery strategy opens new avenues towards the functionalization of nonlinearities to enhance the performances of coupled MEMS sensors in the presence of modal interactions.</p>

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A new sensitivity enhancement scheme for resonant mass sensors based on 2:1 internal resonance bifurcation topology tuning

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Rongjian Sun,
  • Jian Zhao,
  • Najib Kacem,
  • Zeyuan Dong,
  • Jiahao Song,
  • Pengbo Liu

摘要

This paper theoretically investigates the nonlinear dynamics and sensitivity enhancement method of an electrostatically coupled resonant mass sensor at 2:1 internal resonance. A reduced-order model of the sensor considering geometric and electrostatic nonlinearities is developed, and the equations of motion are solved with the method of multiple scales (MMS), and validated using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). For the case of response symmetry destruction under the dominance of geometric nonlinearities, a bifurcated topology tuning scheme is introduced to cancel the effects of the quadratic non-resonant terms and the cubic terms on the dynamic behavior, restoring the symmetry of the M-shaped frequency response, similar to the system with only two quadratic resonant terms. The results show that compared to the frequency shift output, the sensitivity defined as the sum of relative amplitude shifts is three orders of magnitude higher and can be further enhanced up to 85% when using the proposed bifurcation topology tuning approach. This symmetry recovery strategy opens new avenues towards the functionalization of nonlinearities to enhance the performances of coupled MEMS sensors in the presence of modal interactions.