Nonlinear Dynamics

, Volume 79, Issue 1, pp 673–688 | Cite as

Dynamic phenomena and analysis of MEMS capacitive power harvester subjected to low-frequency excitations

  • J. X. Zhu
  • Jie Lin
  • Nuh Sadi Yuksek
  • Mahmoud Almasri
  • Z. C. Feng
Original Paper


We study power harvesting using MEMS capacitors with single and dual air cavities that have been fabricated in our laboratory. Our goal is to achieve power harvesting from vibration sources with limited amplitude and with frequencies that are well below the resonance frequency of the fabricated device. The mathematical model includes the electrostatic forces and the forces provided by stoppers which are designed to prevent the direct contact between the capacitive plates. Global bifurcation analysis of the model illustrates the effect of the electrostatic force on the static equilibrium, the resonance frequency, and the regions of stability surrounding the equilibrium. The electrostatic forces are shown to reduce the resonance frequency at the cost of shrinking the stable domain of oscillation near the equilibrium. The inclusion of the mechanical stoppers make power harvesting still possible when the plate motion exceeds the stable domain so long as the two capacitive plates are kept at a distance to prevent the electrostatic force to dominate. Moreover, when the two plates are kept sufficiently separated, rocking instability—the instability leading to non-parallel motion between the two plates—is also prevented.


Power harvesting MEMS capacitor Charge pump Superharmonic resonance 



This work was supported in by National Science Foundation under Grant CMMI-0021330.


  1. 1.
    Meninger, S., Mur-Miranda, J.O., Amirtharajah, R., Chandrakasan, A.P., Lang, J.H.: Vibration-to-electric energy conversion. IEEE Trans. VLSI Syst. 9, 64–76 (2001)CrossRefGoogle Scholar
  2. 2.
    Umeda, M., Nakamura, K., Ueha, S.: Analysis of the transformation of mechanical impact energy to electric energy using piezoelectric vibration. Jpn. J. Appl. Phys. 35, 3267–3273 (1996)CrossRefGoogle Scholar
  3. 3.
    Gu, L.: Low-frequency piezoelectric energy harvesting prototype suitable for the MEMS implementation. Microelectr. J. 42, 277–282 (2011)CrossRefGoogle Scholar
  4. 4.
    Liu, H., Tay, C.J., Quan, C., Kobayashi, T., Lee, C.: Piezoelectric MEMS energy harvester for low-frequency vibrations with wideband operation range and steadily increased output power. J. Microelectromech. Syst. 20, 1–12 (2011)Google Scholar
  5. 5.
    Adhikari, S., Friswel, M.I., Inman, D.J.: Piezoelectric energy harvesting from broadband random vibrations. Smart Mater. Struct. 18, 115005 (2009)CrossRefGoogle Scholar
  6. 6.
    Kim, S.B., Park, H., Kim, S.H., Wikle, H.C., Park, J.H., Kim, D.J.: Comparison of MEMS PZT cantilevers based on and modes for vibration energy harvesting. J. Microelectromech. Syst. 22(1), 26–33 (2013)CrossRefGoogle Scholar
  7. 7.
    Naruse, Y., Matsubara, N., Mabuchi, K., Izumi, M., Suzuki, S.: Electrostatic micro power generation from low-frequency vibration such as human motion. J. Micromech. Microeng. 19, 1–5 (2009)CrossRefGoogle Scholar
  8. 8.
    Galchev, T., Kim, H., Najafi, K.: A parametric frequency increased power generator for scavenging low frequency ambient vibrations. Proc. Chem. 1, 1439–1442 (2009)CrossRefGoogle Scholar
  9. 9.
    Mitcheson, P.D., Miao, P., Stark, B.H., Yeatman, E.M., Holmes, A.S., Green, T.C.: MEMS electrostatic micropower generator for low frequency operation. Sens. Actuators A 115, 523–529 (2004)CrossRefGoogle Scholar
  10. 10.
    Suzuki, Y., Miki, D., Edamoto, M., Honzumi, M.: A MEMS electret generator with electrostatic levitation for vibration-driven energy-harvesting applications. J. Micromech. Microeng. 20(10), 104002 (2010)CrossRefGoogle Scholar
  11. 11.
    Kulah, H., Najafi, K.: Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sens. J. 8, 261–268 (2008)CrossRefGoogle Scholar
  12. 12.
    Wickenheiser, A.M., Garcis, E.: Broadband vibration-based energy harvesting improvement through frequency up-conversion by magnetic excitation. Smart Mater. Struct. 19, 1–11 (2010)CrossRefGoogle Scholar
  13. 13.
    Yang, B., Lee, C.: Non-resonant electromagnetic wideband energy harvesting mechanism for low frequency vibrations. Microsyst. Technol. 16, 961–966 (2010)Google Scholar
  14. 14.
    Beeby, S.P., Tudor, M.J., White, N.M.: Energy harvesting vibration sources for Microsystems applications. Meas. Sci. Technol. 17(12), R175–R195 (2006)CrossRefGoogle Scholar
  15. 15.
    Seeger, J.I., Boser, B.E.: Dynamics and control of parallel-plate actuators beyond the electrostatic instability. In: The 10th International Conference on Solid-State Sensors and Actuators, Sendai, Japan, pp. 474–477 (1999)Google Scholar
  16. 16.
    Lin, J., Zhu, J.X., Sonje, M., Chang, Y., Feng, Z.C., Almasri, M.: Two-cavity MEMS variable capacitor for power harvesting. J. Micromech. Microeng. 22, 065003 (2012)CrossRefGoogle Scholar
  17. 17.
    Seeger, J.I., Boser, B.E.: Charge control of parallel-plate, electrostatic actuators and the tip-in instability. J. Microelectromech. Syst. 12(5), 656–671 (2003)Google Scholar
  18. 18.
    Seeger, J.I., Crary, S.B.: Stabilization of electro-statically actuated mechanical devices. In: Technical Digest of the 9th International Conference on Solid-State Sensors and Actuators, pp. 1133–1136 (1997)Google Scholar
  19. 19.
    Hoffmann, D., Folkmer, B., Manoli, Y.: Fabrication, characterization and modelling of electrostatic micro-generators. J. Micromech. Microeng. 19(9), 094001 (2009)Google Scholar
  20. 20.
    Roundy, S.: On the effectiveness of vibration-based energy harvesting. J. Intell. Mater. Syst. 16(10), 809–823 (2005)CrossRefGoogle Scholar
  21. 21.
    Roundy, S., Leland, E.S., Baker, J., Carleton, E., Reilly, E.K., Lai, E., Otis, B., Rabaey, J.M., Sundararajan, V., Wright, P.K.: Improving power output for vibration-based energy scavengers. IEEE Pervasive Comput. 4(1), 28–36 (2005)CrossRefGoogle Scholar
  22. 22.
    Buren, T.V., Mitcheson, P.D., Green, T.C., Yeatman, E.M., Holmes, A.S., Troster, G.: Optimization of inertial micropower generators for human walking motion. IEEE Sens. J. 99, 1–11 (2005)Google Scholar
  23. 23.
    Sterken, T., Baert, K., Hoof, C.V., Puers, R., Borghs, G., Fiorini, P.: Comparative modeling for vibration scavengers. Proc. IEEE Sens. 3, 1249–1252 (2004)Google Scholar
  24. 24.
    Jung, S.M., Yun, K.S.: Energy-harvesting device with mechanical frequency-up conversion mechanism for increased power efficiency and wideband operation. Appl. Phys. Lett. 96, 11906–11901 (2010)CrossRefGoogle Scholar
  25. 25.
    Challa, V.R., Prasad, M.G., Shi, Y., Fisher, F.T.: A vibration energy harvesting device with bidirectional resonance frequency tenability. Smart Mater. Struct. 17, 1–10 (2008)Google Scholar
  26. 26.
    Younis, M.I., Nayfeh, A.H.: A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dyn. 31, 91–117 (2003)Google Scholar
  27. 27.
    Shirazi, F.A., Velni, J.M., Grigoriadis, K.M.: An LPV design approach for voltage control of an electrostatic MEMS actuator. J. Microelectromech. Syst. 20(1), 302–311 (2011)Google Scholar
  28. 28.
    Chan, E.K., Garikipati, K., Dutton, R.W.: Characterization of contact electro-mechanics through capacitance–voltage measurements and simulations. IEEE J. MEMS 8(2), 208–217 (1999)CrossRefGoogle Scholar
  29. 29.
    Rhoads, J.F., Shaw, S.W., Turner, K.L.: Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Control 132, 034001-1–034001-14 (2010)Google Scholar
  30. 30.
    Mol, L., Rocha, L.A., Cretu, E., Wolffenbuttel, R.F.: Squeezed film damping measurements on a parallel-plate MEMS in the free molecule regime. J. Micromech. Microeng. 19(7), 074021 (2009)Google Scholar
  31. 31.
    Peano, F., Tambosso, T.: Design and optimization of a MEMS electret-based capacitive energy scavenger. J. Microelectromech. Syst. 14(3), 429–435 (2005)CrossRefGoogle Scholar
  32. 32.
    Shaw, S.W., Holmes, P.J.: A periodically forced piecewise linear oscillator. J. Sound Vib. 90, 129–155 (1983)CrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    Rocha, L.A., Cretu, E., Wolffenbuttel, R.F.: Using dynamic voltage drive in a parallel-plate electrostatic actuator for full-gap travel range and positioning. J. Microelectromech. Syst. 15(1), 69–83(2006)Google Scholar
  34. 34.
    Chao, C.P., Chiu, C.W., Tsai, C.Y.: A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force. J. Micromech. Microeng. 16, 986–998 (2006)CrossRefGoogle Scholar
  35. 35.
    Zhu, J.X., Feng, Z.C., Lin, J., Yuksek, N.S., Almasri, M.: Dynamic study of MEMS variable capacitive device for power harvesting. In: International design engineering technical conferences and computers and information in engineering conference, pp. 253–258 (2012)Google Scholar
  36. 36.
    Feng, Z.C., Almasri, M.: Rocking instability of a capacitive vibration power harvesting MEMS device, Rome, Italy, pp. 24–29 (2011)Google Scholar
  37. 37.
    Qiu, J., Feng, Z.C.: Impact dynamics of thin plates. Comput. Struct. 75, 491–506 (2000)CrossRefGoogle Scholar
  38. 38.
    Nayfeh, A.H., Mook, D.T.: Energy transfer from high-frequency to low-frequency modes in structures transactions. ASME 117, 187 (1995)Google Scholar
  39. 39.
    Nayfeh, A.H., Younis, M.: Dynamics of MEMS resonators under superharmonic and subharmonic excitations. J. Micromech. Microeng. 15, 1840–1847 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • J. X. Zhu
    • 1
  • Jie Lin
    • 2
  • Nuh Sadi Yuksek
    • 2
  • Mahmoud Almasri
    • 2
  • Z. C. Feng
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of MissouriColumbiaUSA

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