Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements

Authors

  • Nikita F. Morozov St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, V.O., Bolshoi pr., St. Petersburg, 199178, Russian Federation
  • Dmitriy A. Indeitsev Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, V.O., Bolshoi pr., St. Petersburg, 199178, Russian Federation; Peter the Great St. Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St. Petersburg, 195251, Russian Federation
  • Vasilisa S. Igumnova Peter the Great St. Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St. Petersburg, 195251, Russian Federation
  • Alexei V. Lukin Peter the Great St. Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St. Petersburg, 195251, Russian Federation
  • Ivan A. Popov Peter the Great St. Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St. Petersburg, 195251, Russian Federation
  • Lev V. Shtukin Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, V.O., Bolshoi pr., St. Petersburg, 199178, Russian Federation; Peter the Great St. Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St. Petersburg, 195251, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2021.204

Abstract

In the presented work, a model of a microelectromechanical accelerometer with two movable beam elements located between two fixed electrodes is proposed. The action of the transfer forces of inertia in the longitudinal direction leads to a change in the spectral properties of the system, which is a useful output signal of the sensor. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of inphase and antiphase oscillations with small changes in the measured component of the acceleration vector of the moving object. Diagrams of equilibrium positions are plotted for varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is shown that the sensitivity of a sensor based on modal localization can be orders of magnitude higher than the sensitivity of known systems based on measuring the shift of natural frequencies. A nonlinear dynamic model of an accelerometer with external harmonic electrostatic excitation of oscillations is constructed. Resonance characteristics are obtained, a comparison is made between the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear factors.

Keywords:

resonant accelerometer, weakly coupled system, modal localization, resonance curves

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References

Литература

1. Zhao Ch., Montaseri M.H., Wood G. S., Pu S.H., Seshia A.A., Kraft M. A Review on MEMS Coupled Resonators for Sensing Applications Utilizing Mode Localization. Sensors and Actuators A:Physical 249, 93–111 (2016). https://doi.org/10.1016/j.sna.2016.07.015

2. Hajjaj A. Z., Jaber N., Ilyas S., Alfosail F.K., Younis M.I. Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances. International Journal of Non-Linear Mechanics 119, 103328 (2019). https://doi.org/10.1016/j.ijnonlinmec.2019.103328

3. Pierre C., Dowell E.H. Localization of vibrations by structural irregularity. Journal of Sound and Vibration 114, 549–564 (1987). https://doi.org/10.1016/S0022-460X(87)80023-8

4. Pierre C. Mode localization and eigenvalue loci veering phenomena in disordered structures. Journal of Sound and Vibration 126, 485–502 (1988). https://doi.org/10.1016/0022-460X(88)90226-X

5. Zhang H. Ambient pressure drift rejection of mode-localized resonant sensors. 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS), 1095–1098 (2017). https://doi.org/10.1109/MEMSYS.2017.7863604

6. Zhao C., Pandit M., Sun B., Sobreviela G., Zou X., Seshia A. A Closed-Loop Readout Configuration for Mode-Localized Resonant MEMS Sensors. Journal of Microelectromechanical Systems 26 (3), 501–503. https://doi.org/10.1109/JMEMS.2017.2690942

7. Wang C., Chen F., Wang Y., Sadeghpour S., Wang C., Baijot M., Esteves R., Zhao C., Bai J., Liu H., Kraft M. Micromachined Accelerometers with Sub-mug/rHz Noise Floor: A Review. Sensors 20 (14), 4054 (2020). https://doi.org/10.3390/s20144054

8. Zhang H.M., Yuan W. Z., B.Y. Li, Hao Y.C., Kraft M., Chang H. L. A novel resonant accelerometer based on mode localization of weakly coupled resonators. 2015 Transducers - 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 1073–1076 (2015). https://doi.org/10.1109/TRANSDUCERS.2015.7181112

9. Zhang H., Li B., Yuan W., Kraft M., Chang H. An Acceleration Sensing Method Based on the Mode Localization of Weakly Coupled Resonators. Journal of Microelectromechanical Systems 25 (2), 286–296. https://doi.org/10.1109/JMEMS.2015.2514092

10. Manav M., Phani A. S., Cretu E. Mode Localization and Sensitivity in Weakly Coupled Resonators. IEEE Sensors Journal 19 (8), 2999–3007 (2019). https://doi.org/10.1109/JSEN.2018.2889646

11. Морозов Н.Ф., Индейцев Д.А., Игумнова В.С., Беляев Я.В., Лукин А.В., Попов И.А., Штукин Л.В. Модель микромеханического акселерометра, основанного на явлении модальной локализации. Доклады Российской академии наук. Физика, технические науки 494 (1), 51–56 (2020). https://doi.org/10.31857/S2686740020050132

References

1. Zhao Ch., Montaseri M.H., Wood G. S., Pu S.H., Seshia A.A., Kraft M. A Review on MEMS Coupled Resonators for Sensing Applications Utilizing Mode Localization. Sensors and Actuators A: Physical 249, 93–111 (2016). https://doi.org/10.1016/j.sna.2016.07.015

2. Hajjaj A. Z., Jaber N., Ilyas S., Alfosail F.K., Younis M. I. Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances. International Journal of Non-Linear Mechanics 119, 103328 (2019). https://doi.org/10.1016/j.ijnonlinmec.2019.103328

3. Pierre C., Dowell E.H. Localization of vibrations by structural irregularity. Journal of Sound and Vibration 114, 549–564 (1987). https://doi.org/10.1016/S0022-460X(87)80023-8

4. Pierre C. Mode localization and eigenvalue loci veering phenomena in disordered structures. Journal of Sound and Vibration 126, 485–502 (1988). https://doi.org/10.1016/0022-460X(88)90226-X

5. Zhang H. Ambient pressure drift rejection of mode-localized resonant sensors. 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS), 1095–1098 (2017). https://doi.org/10.1109/MEMSYS.2017.7863604

6. Zhao C., Pandit M., Sun B., Sobreviela G., Zou X., Seshia A. A Closed-Loop Readout Configuration for Mode-Localized Resonant MEMS Sensors. Journal of Microelectromechanical Systems 26 (3), 501–503. https://doi.org/10.1109/JMEMS.2017.2690942

7. Wang C., Chen F., Wang Y., Sadeghpour S., Wang C., Baijot M., Esteves R., Zhao C., Bai J., Liu H., Kraft M. Micromachined Accelerometers with Sub-mug/rHz Noise Floor: A Review. Sensors 20 (14), 4054 (2020). https://doi.org/10.3390/s20144054

8. Zhang H.M., Yuan W. Z., B.Y. Li, Hao Y.C., Kraft M., Chang H. L. A novel resonant accelerometer based on mode localization of weakly coupled resonators. 2015 Transducers - 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 1073–1076 (2015). https://doi.org/10.1109/TRANSDUCERS.2015.7181112

9. Zhang H., Li B., Yuan W., Kraft M., Chang H. An Acceleration Sensing Method Based on the Mode Localization of Weakly Coupled Resonators. Journal of Microelectromechanical Systems 25 (2), 286–296. https://doi.org/10.1109/JMEMS.2015.2514092

10. Manav M., Phani A. S., Cretu E. Mode Localization and Sensitivity in Weakly Coupled Resonators. IEEE Sensors Journal 19 (8), 2999–3007 (2019). https://doi.org/10.1109/JSEN.2018.2889646

11. Morozov N.F., Indeitsev D.A., Igumnova V. S., Belyaev Ya.V., Lukin A.V., Popov I.A., Shtukin L.V. A Novel Model of a Mode-Localized MEMS Accelerometer. Doklady Rossiiskoi Akademii Nauk. Fizika, Tekhnicheskie Nauki 494 (1), 51–56 (2020). https://doi.org/10.31857/S2686740020050132 (In Russian)

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Published

2021-07-21

How to Cite

Morozov, N. F., Indeitsev, D. A., Igumnova, V. S., Lukin, A. V., Popov, I. A., & Shtukin, L. V. (2021). Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(2), 233–246. https://doi.org/10.21638/spbu01.2021.204

Issue

Vol. 8 No. 2 (2021)

Section

In memoriam of P. E. Tovstik

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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