Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements
DOI:
https://doi.org/10.21638/spbu01.2023.210Abstract
This work is devoted to studying the conditions and scenarios for synchronizing oscillations of weakly coupled microbeam elements of a differential resonant MEMS accelerometer operating in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained using the Galerkin method, was studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of system parameters is determined. Along with a local bifurcation analysis of the considered stationary regimes, a global analysis of the evolution and branching of limit cycles in the space of slow variables was also carried out, which made it possible to detect zones of coexistence of stable synchronization and beat regimes with their basins of attraction. The influence of the factor of the designed or technologically determined non-identity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.Keywords:
resonant accelerometer, weakly coupled systems, synchronizing oscillations, Van der Pol oscillator
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Литература
1. Hajjaj A. Z., Jaber N., Ilyas S., Alfosail F., Aramco S., Younis M. I. Linear and nonlinear dynamics of micro a nd nano-resonators: Review of recent advances. International Journal of Non-Linear Mechanics 119, 103328 (2020). https://doi.org/10.1016/j.ijnonlinmec.2019.103328
2. Fang Z.,Yin Y., Chen C., Zhang S., Liu Y., Han F. T. A sensitive micromachined resonant accelerometer for moving-base gravimetry. Sensors and Actuators A: Physical 325, 112694 (2021). https://doi.org/10.1016/j.sna.2021.112694
3. Endo D., Yabuno H., Yamamoto Y., Matsumoto S. Mass sensing in a liquid environment using nonlinear self-excited coupled-microcantilevers. Journal of Microelectromechanical Systems 99, 1-6 (2018). https://doi.org/10.1109/JMEMS.2018.2866877
4. Mustafazade A., Pandit M., Zhao C., Sobreviela G., Du Z., Steinmann P., Zou X., Howe R. T., Seshia A. A. A vibrating beam MEMS accelerometer for gravity and seismic measurements. Sci. Rep. 10, 10415 (2020). https://doi.org/10.1038/s41598-020-67046-x
5. Rand R. H., Holmes P. J. Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. International Journal of Non-Linear Mechanics 15 (4-5), 387-399 (1980).
6. Wei X., Xu L., Jian Z., Huan R. MEMS based ultra-high order frequency multiplication utilizing superharmonic synchronization effect. Sensors and Actuators A: Physical 332, 113152 (2021).
7. Chakraborty T., Rand R. H. The transition from phase locking to drift in a system of two weakly coupled van der Pol oscillators. International Journal of Non-Linear Mechanics 23 (5-6), 369-376 (1988).
8. Wirkus S., Rand R. The dynamics of two coupled van der Pol oscillators with delay coupling. Nonlinear Dynamics 30 (3), 205-221 (2002).
9. Kovaleva M. A., Manevitch L. I., Pilipchuk V. N. Non-linear beatings as non-stationary synchronization of weakly coupled autogenerators. Problems of Nonlinear Mechanics and Physics of Materials. Cham, Springer, 53-83 (2019).
10. Shiroky I. B., Gendelman O. V. Modal synchronization of coupled bistable van der Pol oscillators. Chaos, Solitons & Fractals 143, 110555 (2021)
11. Dhooge A., Govaerts W., Kuznetsov Y. A. MATCONT: a Matlab package for numerical bifurcation analysis of ODEs. ACM Transactions on Mathematical Software 29 (2), 141-164 (2003). https://doi.org/10.1145/980175.980184
12. Yang J., Zhong J., Chang H. A closed-loop mode-localized accelerometer. Journal of Microelectromechanical Systems 27 (2), 210-217 (2018).
13. Kang H., Yang J., Chang H. A closed-loop accelerometer based on three degree-of-freedom weakly coupled resonator with self-elimination of feedthrough signal. IEEE Sensors Journal 18 (10), 3960-3967 (2018).
14. Zhang H. M., Yuan W. Z., Li B. Y., Hao Y. C., Kraft M., Chang H. L. A novel resonant accelerometer based on mode localization of weakly coupled resonators. In: 18th International Conference: on Solid-State Sensors, Actuators and Microsystems. Transducers-2015. Anchorage, Alaska, USA, June 21-25, 2015, 1073-1076 (2015).
References
1. Hajjaj A. Z., Jaber N., Ilyas S., Alfosail F., Aramco S., Younis M. I. Linear and nonlinear dynamics of micro a nd nano-resonators: Review of recent advances. International Journal of Non-Linear Mechanics 119, 103328 (2020). https://doi.org/10.1016/j.ijnonlinmec.2019.103328
2. Fang Z.,Yin Y., Chen C., Zhang S., Liu Y., Han F. T. A sensitive micromachined resonant accelerometer for moving-base gravimetry. Sensors and Actuators A: Physical 325, 112694 (2021). https://doi.org/10.1016/j.sna.2021.112694
3. Endo D., Yabuno H., Yamamoto Y., Matsumoto S. Mass sensing in a liquid environment using nonlinear self-excited coupled-microcantilevers. Journal of Microelectromechanical Systems 99, 1-6 (2018). https://doi.org/10.1109/JMEMS.2018.2866877
4. Mustafazade A., Pandit M., Zhao C., Sobreviela G., Du Z., Steinmann P., Zou X., Howe R. T., Seshia A. A. A vibrating beam MEMS accelerometer for gravity and seismic measurements. Sci. Rep. 10, 10415 (2020). https://doi.org/10.1038/s41598-020-67046-x
5. Rand R. H., Holmes P. J. Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. International Journal of Non-Linear Mechanics 15 (4-5), 387-399 (1980).
6. Wei X., Xu L., Jian Z., Huan R. MEMS based ultra-high order frequency multiplication utilizing superharmonic synchronization effect. Sensors and Actuators A: Physical 332, 113152 (2021).
7. Chakraborty T., Rand R. H. The transition from phase locking to drift in a system of two weakly coupled van der Pol oscillators. International Journal of Non-Linear Mechanics 23 (5-6), 369-376 (1988).
8. Wirkus S., Rand R. The dynamics of two coupled van der Pol oscillators with delay coupling. Nonlinear Dynamics 30 (3), 205-221 (2002).
9. Kovaleva M. A., Manevitch L. I., Pilipchuk V. N. Non-linear beatings as non-stationary synchronization of weakly coupled autogenerators. Problems of Nonlinear Mechanics and Physics of Materials. Cham, Springer, 53-83 (2019).
10. Shiroky I. B., Gendelman O. V. Modal synchronization of coupled bistable van der Pol oscillators. Chaos, Solitons & Fractals 143, 110555 (2021)
11. Dhooge A., Govaerts W., Kuznetsov Y. A. MATCONT: a Matlab package for numerical bifurcation analysis of ODEs. ACM Transactions on Mathematical Software 29 (2), 141-164 (2003). https://doi.org/10.1145/980175.980184
12. Yang J., Zhong J., Chang H. A closed-loop mode-localized accelerometer. Journal of Microelectromechanical Systems 27 (2), 210-217 (2018).
13. Kang H., Yang J., Chang H. A closed-loop accelerometer based on three degree-of-freedom weakly coupled resonator with self-elimination of feedthrough signal. IEEE Sensors Journal 18 (10), 3960-3967 (2018).
14. Zhang H. M., Yuan W. Z., Li B. Y., Hao Y. C., Kraft M., Chang H. L. A novel resonant accelerometer based on mode localization of weakly coupled resonators. In: 18th International Conference: on Solid-State Sensors, Actuators and Microsystems. Transducers-2015. Anchorage, Alaska, USA, June 21-25, 2015, 1073-1076 (2015).
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Published
2023-05-10
How to Cite
Indeitsev, D. A., Igumnova, V. S., Lukin, A. V., Popov, I. A., & Shtukin, L. V. (2023). Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 289–304. https://doi.org/10.21638/spbu01.2023.210
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Mechanics
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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.
