RESEARCH OF VIBRATION OSCILLATIONS OF MEMS RESONATORS DURING THEIR OPERATION

2024;
: 76-82
Received: May 24, 2024
Revised: June 14, 2024
Accepted: August 16, 2024
1
Computer-Aided Design System Department, Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

 A mathematical model has been developed to study the amplitude-frequency characteristics of the resonator beam. Nonlinear mechanics methods were used in the modeling process. The model takes into account the influence of changes in the elastic properties of the beam material on its oscillation amplitude and frequency. To analyze the internal processes in the material, Voigt's and Bolotin's laws were applied. The modeling results showed that an increase in the elastic component of the beam material leads to a rise in the oscillation amplitude and a decrease in the oscillation frequency.

[1] Q. Shin, A. Qiu, Y. Su and R. Shi, “Nonlinear oscillation characteristics of MEMS resonator”, 2010 IEEE International Conference on Mechatronics and Automation, 2010, pp. 1250–1253, https://doi.org/10.1109/ICMA.2010.5589936.

[2] Daniel Platz, Ulrich Schmid “Vibrational modes in MEMS resonators” Journal of Micromechanics and Microengineering , vol. 29  No 12, 3001, https://doi.org/10.1088/1361-6439/ab4bad

[3] C. Comi, A. Corigliano, G. Langfelder, A. Longoni and A. Tocchio, "On the nonlinear behaviour of MEMS resonators," 2011 12th Intl. Conf. on Thermal, Mechanical & Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, 2011, pp. 1/6–6/6, https://doi.org/10.1109/ESIME.2011.5765821

[4] David A. Czaplewski, Daniel López, Oriel Shoshani Steven W. Shaw  "Nonlinear mode coupling in a MEMS resonator", Proc. SPIE 11324, Novel Patterning Technologies for Semiconductors, MEMS/NEMS and MOEMS 2020, 1132414 (23 March 2020), https://doi.org/10.1117/12.2551883

[5] Pustan, Marius, Birleanu, C., Rusu, F., Haragâş, S “Dynamic Behavior of MEMS Resonators.” Applied Mechanics and Materials, Trans Tech Publications, Ltd., 2014, vol. 658 pp. 694–699. https://doi.org/10.4028/www.scientific.net/amm.658.694

[6] Rocha, R.T., Alfosail, F., Zhao, W., Younis, M.I., Masri, S.F. “Nonparametric Identification of a Nonlinear MEMS Resonator”,  Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. 2022, рр. 405–415, https://doi.org/10.1007/978-3-030-81166-2_36

[7] Lee, J. EY. “Lamé Mode MEMS Resonators”, Encyclopedia of Nanotechnology, Springer, Dordrecht. 2016, рр. 1731–1739  https://doi.org/10.1007/978-94-017-9780-1_101001 A. Tocchio, C. Comi, G. Langfelder, A. Corigliano and A. Longoni, “Enhancing the Linear Range of MEMS Resonators for Sensing Applications”, in IEEE Sensors Journal, vol. 11, no. 12, pp. 3202-3210, Dec. 2011, https://doi.org/10.1109/JSEN.2011.2158997

[8] Saadon Salem, Wahab Yufridin. “Review on Vibration-Based  MEMS Piezoelectronic Energy Harvesters”, Journal of Science and Engineering, 2015, vol. 72 Iss. 1, pp 1–6, https://doi.org/10.13140/RG.2.1.2796.3604.

[9] J. J. M. Zaal, W. D. van Driel, S. Bendida, Q. Li, J. T. M. van Beek, G. Q.  Zhang, “Packaging influences on the reliability of MEMS resonators”, Microelectronics Reliability, 2008, vol. 48, Iss. 8–9, pp.  1567-1571, https://doi.org/10.1016/j.microrel.2008.06.041

[10] R. Mestrom, R. Fey, J. van Beek, K. Phan, H. Nijmeijer “Nonlinear oscillations in MEMS resonators” ResearchGate, 2006, https://www.researchgate.net/publication/255599539

[11] Huzyk, N.; Pukach, P.Y.; Sokil, B.; Sokil, M.; Vovk, M. “On the external and internal resonance phenomena of the elastic bodies with the complex oscillations”, Mathematical Modeling and Computing, 2022, vol. 9, No. 1, pp. 152–158, https://doi.org/10.23939/mmc2022.01.152

[12] Topilnytskyy, Volodymyr, et al. "Modeling the Dynamics of Vibratory Separator of the Drum Type with Concentric Arrangement of Sieves." Eastern-European Journal of Enterprise Technologies, vol. 2, no. 7, 2017, pp. 26-35, https://doi.org/10.15587/1729-4061.2017.95615

[13]  Andrukhiv, A.; Sokil, M.; Sokil, B.; Fedushko, S.; Syerov, Y.; Karovic, V., Jr.; Klynina, T. Influence of Impulse Disturbances on Oscillations of Nonlinearly Elastic Bodies. Mathematics, 2021, 9, 819. https://doi.org/10.3390/math9080819