Sensing and Imaging

, 20:11 | Cite as

An Approach for Increasing Sensitivity of a Tunable Micro Electro Mechanical Sensor Using Electrostatic Hopping Voltage

  • Araz Rezaei Kivi
  • Saber AziziEmail author
Original Paper


The impetus of the study is to present a novel micro electro mechanical system based tunable gyroscope with the possibility of sensitivity enhancement using appropriate electrostatic hopping voltages. The proposed model is a silicon-based clamped–clamped micro beam sandwiched with two piezoelectric layers throughout the entire length. The nonlinear electrostatic forces are applied to the micro beam along its sense and drive mode directions (either lateral sides). The drive mode actuation is a combination of a direct current (DC) and an alternating current voltage; whereas the sense mode actuation is a pure DC voltage. The micro beam oscillates along the drive mode due to the harmonic drive mode excitation; as the micro beam undergoes base rotation, the Coriolis force induces another motion in the direction of the sense mode which is perpendicular to the drive mode direction. The more is the amplitude of the base rotation, the more is the sense mode amplitude. The sense mode amplitude is directly attributed to the magnitude of base rotation. The piezoelectric layers are actuated by a DC voltage which leads to an axial force proportional to the applied DC voltage. Exciting the piezoelectric layers changes the overall stiffness of the micro beam and as a result the operating frequency of the gyroscope becomes tunable. The partial differential equation of the motion is derived using Hamiltonian principle and discretized into two nonlinear ordinary differential equations along the drive and sense mode directions. The shooting method is used to capture the periodic motion orbits and accordingly the frequency response curves. By using Floquet theory the stability of the periodic orbits is determined. Due to the nonlinearity of the governing equations in the vicinity of the primary resonance, the gyroscope exhibits multi-response solution; Applying appropriate hopping voltages, the micro beam is pushed into the attraction basin of the response with higher amplitude and accordingly the sensitivity of the gyroscope is enhanced. The proposed gyroscope not only has the capability of having improved sensitivity but also its operating frequency can be tuned both in forward and backward directions by means of applying appropriate piezoelectric voltage with an appropriate polarity.


MEMS Nonlinear ODE Galerkin method Shooting method Floquet theory Hopping voltage 



  1. 1.
    Acar, C., & Shkel, A. M. (2005). An approach for increasing DRIVE-MODE bandwidth of MEMS vibratory gyroscopes. Journal of Microelectromechanical System, 14(3), 520–528.CrossRefGoogle Scholar
  2. 2.
    Zhang, Y., & Wang, W. (2009). Enhanced sensitivity of a surface acoustic wave gyroscope. Japanese Journal of Applied Physics, 48, 104502.CrossRefGoogle Scholar
  3. 3.
    Oh, H., Lee, K., Yang, S. S., & Wang, W. (2011). Enhanced sensitivity of a surface acoustic wave gyroscope using a progressive wave. Journal of Micromechanics and Microengineering, 21, 075015.CrossRefGoogle Scholar
  4. 4.
    Moon, S. J. Fabrication of micro gyroscope on the SOI substrate with enhanced sensitivity for detecting vertical motion (p. CA 94720), Department of Mechanical Engineering, University of California, Berkeley.Google Scholar
  5. 5.
    Thiruvenkatanathan, P., Yan, J., Woodhouse, J., & Seshia, A. A. (2009). Enhancing parametric sensitivity in electrically coupled MEMS resonators. Journal of Microelectromechanical System, 18(5), 1077–1086.CrossRefGoogle Scholar
  6. 6.
    Shkel, A. M., Horowitz, R., Seshia, A. A., Park, S., & Howe, R. T. (1999). Dynamics and control of micromachined gyroscopes. Proceedings of the American Control Conference, 3, 2119–2124.Google Scholar
  7. 7.
    Kawai, H., Atsuchi, K. I., Tamura, M., & Ohwada, K. (2001). High-resolution micro gyroscope using vibratory motion adjustment technology. Sensors and Actuators, A: Physical, 90, 153–159.CrossRefGoogle Scholar
  8. 8.
    Prikhodko, I. P., Zotov, S. A., Trusov, A. A., & Shkel, A. M. (2011). Sub-degree-per-hour silicon MEMS rate sensor with 1 million Q-Factor. In Solid-state sensor, actuators and microsystems conference transducers’11 (pp. 2809–2812).Google Scholar
  9. 9.
    Nitzan, S., Ahn, C. H., Su, T.-H., Li, M., Ng, E. J., Wang, S., Yang, Z. M., O’Brien, G., Boser, B. E., Kenny, T. W., & Horsley, D. A. (2013). Epitaxially-encapsulated polysilicon disk resonator gyroscope. In Proceedings of the IEEE international conference on micro electro mechanical systems (pp. 625–628).Google Scholar
  10. 10.
    Sharma, A., Zaman, M. F., Zucher, M., & Ayazi, F. (2008). A 0.1˚/hr bias drift electronically matched tuning fork micro gyroscope. In Proceeding of IEEE international conference on micor electro mechanical systems (MEMS) (pp. 6–9).Google Scholar
  11. 11.
    Handtmann, M., Aigner, R., Meckes, A., & Wachutka, G. K. M. (2002). Sensitivity enhancement of MEMS inertial sensors using negative springs and active control. Sensors and Actuators A, 97–98, 153–160.CrossRefGoogle Scholar
  12. 12.
    Sung, W. T., Lee, J. Y., Lee, J. G., & Kang, T. (2006). Design and fabrication of an automatic mode controlled vibratory gyroscope. In 16th IEEE international conference on MEMS.Google Scholar
  13. 13.
    Elsayed, M. Y., Nabki, F., & El-Gamal, M. N. (2013). A novel comb architecture for enhancing the sensitivity of bulk mode gyroscope. Journal of Sensors, 13, 16641–16656.CrossRefGoogle Scholar
  14. 14.
    Acar, C., & Shkel, A. M. (2003). Distributed-mass micromachined gyroscopes for enhanced mode-decoupling. IEEE, 1, 445–450.Google Scholar
  15. 15.
    Wang, W., Oh, H., Lee, K., Yoon, S., & Yang, S. (2009). Enhanced sensitivity of novel surface acoustic wave microelectromechanical system-interdigital Transducer Gyroscope. Japanese Journal of Applied physics, 48, 06FK09.Google Scholar
  16. 16.
    Sung, S., Sung, W. T., Kim, C., Yun, S., & Lee, Y. J. (2009). On the mode-matched control of mems vibratory gyroscope via phase-domain analysis and design. Journal of Mechatronic, 14(4), 446–455.Google Scholar
  17. 17.
    Xiao, D., Cao, S., Hou, Z., Chen, Z., Wang, X., & Wu, X. (2015). Enhanced sensitivity in a butterfly gyroscope with a hexagonal oblique beam. Applied Physics Reviews, 5, 041331.Google Scholar
  18. 18.
    Rezazadeh, G., Ghanbari, M., Mirzaee, I., & Keyvani, A. (2010). On the modeling of a piezoelectrically actuated microsensor for simultaneously measuring of fluids viscosity and density. Journal of Measurement, 43, 1516–1524.CrossRefGoogle Scholar
  19. 19.
    Mahmoodi, S. N., & Jalili, N. (2009). Piezoelectrically actuated microcantilevers: An experimental nonlinear vibration analysis. Journal of Sensors and Actuators A, 150, 131–136.CrossRefGoogle Scholar
  20. 20.
    Azizi, S., Ghazavi, M. R., Khadem, S. E., Rezazadeh, G., & Cetinkaya, C. (2013). Application of piezoelectric actuation to regularize the chaotic response of an electrostatically actuated micro-beam. Journal of Nonlinear Dynamics, 73(1–2), 853–867.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Azizi, S., Ghazavi, M. R., Rezazadeh, G., Ahmadian, I., & Cetinkaya, C. (2013). Tuning the primary resonance of a micro resonator, using piezoelectric actuation. Nonlinear Dynamics, 76(1), 839–852.CrossRefGoogle Scholar
  22. 22.
    Azizi, S., Ghazavi, M. R., Khadem, S. E., Yang, J., & Rezazadeh, G. (2012). Stability analysis of a parametrically excited functionally graded. MEM system, Current Applied Physic, 12, 456–466.CrossRefGoogle Scholar
  23. 23.
    Vahdat, A. S., Rezazadeh, G., & Ahmadi, G. (2011). Thermoelastic damping in a micro-beam resonator tunable with piezoelectric layers. Acta Mechanica Solidia Sinica, 25(1), 73–81.CrossRefGoogle Scholar
  24. 24.
    Azizi, S., Rezazadeh, G., Ghazavi, M., & Khadem, S. E. (2011). Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation. Applied Mathematical Modelling, 35, 4796–4815.CrossRefGoogle Scholar
  25. 25.
    Rezazadeh, G., Talebian, S., Yagubizade, H., & Alizadeh, Y. (2009). Piezoelectric layers application to control of pull-in voltage and natural frequency of an electrostatically actuated microplate. Journal of Mechanics and MEMS, 1(2), 445–456.Google Scholar
  26. 26.
    Rasekh, M., & Khadem, S. E. (2013). Design and performance analysis of nanogyroscope based on electrostatic actuation and capacitive sensing. Journal of Sound and Vibration, 332, 6155–6168.CrossRefGoogle Scholar
  27. 27.
    Younis, M. I. (2010). MEMS linear and nonlinear statics and dynamics (Vol. 1, p. 453). New York: Springer.Google Scholar
  28. 28.
    Nayfeh, A. H., & Mook, D. T. (1995). Nonlinear oscillations. Blacksburg: Wiley.CrossRefGoogle Scholar
  29. 29.
    Nayfeh, A. H., Younis, M. I., & Abdel-Rahman, E. (2007). Dynamic pull-in phenomenon in MEMS resonators. Journal of Nonlinear Dynamic, 48, 153–163.CrossRefGoogle Scholar
  30. 30.
    Zhang, Y., & Zhao, Y.-P. (2006). Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading. Sensors and Actuators A, 127, 366–380.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Automotive EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Mechanical Engineering DepartmentUrmia University of TechnologyUrmiaIran

Personalised recommendations