Skip to main content
SpringerLink
Log in

Dynamic analysis of a novel wide-tunable microbeam resonator with a sliding free-of-charge electrode

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, a MEMS-based resonator with a novel effective stiffness tunability is presented. The performance of the proposed resonator is based on the transversal vibration of the two porous cantilever microbeams with a rectangular microplate at the end of the structure. The microplate as a free-of-charge slider electrode is in contact with two other fixed substrate electrodes via the thin layer of dielectric material. Applying a constant DC voltage to the two fixed electrodes leads to the movement of free electrons in the slider and eventually to the formation of two series capacitors. As a result, the slider meets a nonlinear electrostatic force proportional to the square of the applied DC voltage. It will act as a nonlinear spring with a tunable stiffness during the oscillation of the resonator. The coupled nonlinear equations governing the longitudinal and transversal vibration of the resonator are extracted in the presence of the nonlinear voltage-sliding spring. Its steady-state solution is obtained based on a physically based learning method that makes it possible to obtain frequency response for the first harmony as well as for the higher harmonies and to predict primary and secondary resonances in different harmonies of the response. The effect of the applied tuning DC voltage, the geometrical parameters of the resonator, and the cantilever's porosity on the dynamic response of the resonator are investigated. It is shown that the tuning stiffness of this voltage-sliding spring provides a highly effective solution to realize an extreme tunable range. In the end, a modified tunable structure is introduced in which the folded beams are replaced with common ones. The modified resonator by making the nonlinear behavior of the resonator least can improve its performance significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Ghanbari, M., Rezazadeh, G.: A liquid-state high sensitive accelerometer based on a micro-scale liquid marble. Microsyst. Technol. 26(3), 617–623 (2019)

    Google Scholar 

  2. Jin, L., Qin, S.Y., Zhang, R., Li, M.W.: High sensitivity tunneling magneto-resistive micro-gyroscope with immunity to external magnetic interference. Sci. Rep. 10, 16441 (2020)

    Article  Google Scholar 

  3. Sravani, V., Venkata, S.K.: An improved capacitance pressure sensor with a novel electrode design. Sens. Actuators A Phys. 332, 113–112 (2021)

    Article  Google Scholar 

  4. Luo, A., Zhang, Y., Quo, X., Lu, Y., Lee, C., Wang, F.: Optimization of MEMS vibration energy harvester with perforated electrode. J. Microelectromech. Syst. 30(2), 299–308 (2021)

    Article  Google Scholar 

  5. Ghanbari, M., Rezazadeh, G.: An electrostatically actuated microsensor for determination of micropolar fluid physical properties. Meccanica 55, 2091–2106 (2020)

    Article  MathSciNet  Google Scholar 

  6. Ghanbari, M., Rezazadeh, G.: A MEMS-based methodology for measurement of effective density and viscosity of nanofluids. Eur. J. Mech. B 86, 67–77 (2021)

    Article  MathSciNet  Google Scholar 

  7. Basu, A.K., Basu, A., Bhattacharya, S.: Micro/Nano fabricated cantilever based biosensor platform: A review and recent progress. Enzyme Microb. Technol. 139, 109558 (2020)

    Article  Google Scholar 

  8. Ghanbari, M, Rezazadeh, G, Mirzaee, I.:. Simultaneous measurement of fluids viscosity and density using microbeam. In: 5th International Conference on Perspective Technologies and Methods in MEMS Design, vol. 36, p. 44 (2009)

  9. Zengerle, T., Joppich, J., Lensch, H., Ababneh, A., Seidel, H.: Equivalent circuit model for the damping of micro-oscillators from molecular to viscous flow regime. J. Micromachines Microengineering 31(9), 095010 (2021)

    Article  Google Scholar 

  10. Ghanbari, M., Rezazadeh, G.: Estimating the effective quality factor of a rotary comb-drive microresonator based on a non-classical theory. Microsyst. Technol. 27, 3533–3543 (2021)

    Article  Google Scholar 

  11. Uranga, A., Verd, J., Barniol, N.: CMOS-MEMS resonators: from devices to applications. Microelectron. Eng. 132, 58–73 (2015)

    Article  Google Scholar 

  12. Li, Y., Wang, J., Luo, Z., Chen, D., Chen, J.: A resonant pressure microsensor capable of self-temperature compensation. Sensors 15(5), 10048–10058 (2015)

    Article  Google Scholar 

  13. Zhang, S., Zheng, Y., Lu, Y., Xie, B., Chen, D., Wang, J., Chen, J.: A micromachined resonant micro-pressure sensor. IEEE Sens. J. 21(18), 19789–19796 (2021)

    Article  Google Scholar 

  14. Lu, Y., Yan, P., Xiang, C., Chen, D., Wang, J., Xie, B., Chen, J.: A resonant pressure microsensor with the measurement range of 1MPa based on sensitivities balanced dual resonators. Sensors 19(10), 2272 (2019)

    Article  Google Scholar 

  15. Xiang, C., Lu, Y., Cheng, C., Wang, J., Chen, D., Chen, J.: A resonant pressure microsensor with a wide pressure measurement range. Micromachines 12(4), 382 (2021)

    Article  Google Scholar 

  16. Fang, Z., Yin, Y., Chen, C., Zhang, S., Liu, Y., Han, F.: A sensitive micromachined resonant accelerometer for moving-base gravimetry. Sens. Actuators A Phys. 325, 112694 (2021)

    Article  Google Scholar 

  17. Li, Y., Jin, B., Zhao, M., Yang, F.: Design and optimization of the resonator in a resonant accelerometer based on mode and frequency analyses. Micromachines 12(5), 530 (2021)

    Article  Google Scholar 

  18. Matsu, A., Kadokura, M., Yamazaki, H., Nishiyama, M., Watanabe, K.: Cantilever type accelerometer based on a mirror-terminated hetero-core optical fiber. IEEE Sens. J. 21(20), 22464–22471 (2021)

    Article  Google Scholar 

  19. Rao, K., Liu, H., Wei, X., Wu, W., Hu, C., Fan, J., Liu, J., Tu, L.: A high-resolution area-change-based capacitive MEMS tilt sensor. Sens. Actuators A Phys. 313, 112191 (2020)

    Article  Google Scholar 

  20. Yang, J., Zhang, M., Si, C., Han, G., Ning, J., Yang, F.: A T-shape aluminum nitride thin-film piezoelectric MEMS resonant accelerometer. J. Microelectromech. Syst. 28(5), 776–781 (2019)

    Article  Google Scholar 

  21. Mansoorzare, H., Todi, A., Moradian, S., A bdolvand R,: A piezo-capacitive high-frequency resonant accelerometer. IEEE International Ultrasonics Symposium, USA (2020)

    Book  Google Scholar 

  22. Halevy, O., Krakover, N., Krylov, S.: Feasibility study of a resonant accelerometer with bistable electrostatically actuated cantilever as a sensing element. Int. J. Nonlinear Mech. 118, 103255 (2020)

    Article  Google Scholar 

  23. Bradai, S., Naifar, S., Keutel, T., Kanoun, O.: Electrodynamic resonant energy harvester for low frequencies and amplitudes. In: IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings (2014)

  24. Masara, D.O., Gamal, H.E., Mokhiamar, O.: Split cantilever multi-resonant piezoelectric energy harvester for low-frequency application. Energies 14(16), 5077 (2021)

    Article  Google Scholar 

  25. Dhakar, L., Liu, H., Tay, F.E.H., Lee, C.: A new energy harvester design for high power output at low frequencies. Sens. Actuators A Phys. 199, 344–352 (2013)

    Article  Google Scholar 

  26. Qin, Y., Wang, S., Wei, T., Chen, R.: A wide band nonlinear dual piezoelectric cantilever energy harvester coupled by origami. Smart Mater. Struct. 30, 025025 (2021)

    Article  Google Scholar 

  27. Su, W.J., Lin, J.H., Li, W.C.: Analysis of a cantilevered piezoelectric energy harvester in different orientations for rotational motion. Sensors 20(4), 1206 (2020)

    Article  Google Scholar 

  28. Huang, D., Zhou, S., Litak, G.: Analytical analysis of the vibrational tristable energy harvester with a Rl resonant circuit. Nonlinear Dyn. 97, 663–677 (2019)

    Article  MATH  Google Scholar 

  29. Seo, M.H., Choi, D.H., Kim, I.H., Jung, H.J., Yoon, J.B.: Multi resonant energy harvester exploiting high-mode resonances frequency down-shifted by a flexible body beam. Appl. Phys. Lett. 101, 123903 (2012)

    Article  Google Scholar 

  30. Garg, A., Dwivedy, S.K.: Piezoelectric energy harvester under parametric excitation: A theoretical and experimental investigation. J. Intell. Mater. Syst. Struct. 31(4), 612–631 (2019)

    Article  Google Scholar 

  31. Pyo, D., Yang, T.H., Ryu, S., Kwon, D.S.: Novel linear impact-resonant actuator for mobile applications. Sens. Actuators A Phys. 233, 460–471 (2015)

    Article  Google Scholar 

  32. Shen, D., Wen, J., Ma, J., Hu, Y., Wang, R., Li, J.: A novel linear inertial piezoelectric actuator based on asymmetric clamping materials. Sens. Actuators A Phys. 303, 111746 (2020)

    Article  Google Scholar 

  33. Dong, H., Li, T., Wang, Z., Ning, Y.: Design and experiment of a piezoelectric actuator based on inchworm working principle. Sens. Actuators A Phys. 306, 111950 (2020)

    Article  Google Scholar 

  34. Deng, J., Chen, W., Li, K., Wang, L., Liu, Y.: A sandwich piezoelectric actuator with long stroke and nanometer resolution by the hybrid of two actuation modes. Sens. Actuators A Phys. 296, 121–131 (2019)

    Article  Google Scholar 

  35. Chen, S.H., Michael, A., Kwok, C.Y.: Design and modeling of piezoelectrically driven micro-actuator with large out-of-plane and low driving voltage for micro-optics. J. Microelectromech. Syst. 28(5), 919–932 (2019)

    Article  Google Scholar 

  36. Kazmi, S.N.R., Hafiz, M.A.A., Chappanda, K.N., Ilyas, N., Holguin, J., Costa, P.M.F.J., Younis, M.I.: Tunable nanoelectromechanical resonator for logic computations. Nanoscale 9, 3449–3457 (2017)

    Article  Google Scholar 

  37. Piazza, G., Abdolvand, R., Ho, G.K., Ayazi, F.: Voltage-tunable piezoelectrically -transduced single-crystal silicon micromechanical resonators. Sens. Actuators A Phys. 111, 71–78 (2004)

    Article  Google Scholar 

  38. Chen, C., Lee, S., Deshpande, V.V., Lee, G.H., Lekas, M., Shepard, K., Hone, J.: Graphene mechanical oscillators with tunable frequency. Nat. Nanotechnol. 8, 923–927 (2013)

    Article  Google Scholar 

  39. Vissers, M.R., Hubmayr, J., Sandberg, M., Chaudhuri, S., Bockstiegel, C., Gao, J.: Frequency-tunable superconducting resonators via nonlinear kinetic inductance. Appl. Phys. Lett. 107, 062601 (2015)

    Article  Google Scholar 

  40. Daeichin, M., Ozdogan, M., Towfighian, S., Miles, R.: Dynamic response of a tunable MEMS accelerometer, based on repulsive force. Sens. Actuators A Phys. 289, 34–43 (2019)

    Article  Google Scholar 

  41. Lee, K.B., Lin, L., Cho, Y.H.: A closed-form approach for frequency tunable comb resonators with curved finger contour. Sens. Actuators A Phys. 141, 523–529 (2008)

    Article  Google Scholar 

  42. Bouhedma, S., Rao, Y., Schutz, A., Yuan, C., Hu, S., Lange, F., Bechtold, T., Hohlfeld, D.: System-level model and simulation of a frequency-tunable vibration energy harvester. Micromachines 11, 91 (2020)

    Article  Google Scholar 

  43. Li, M., Jing, X.: Novel tunable broadband piezoelectric harvesters for ultra-low-frequency bridge vibration energy harvesting. Appl. Energy 225, 113829 (2019)

    Article  Google Scholar 

  44. Russillo, A.F., Failla, G., Alotta, G.: Ultra-wide low-frequency band gap in locally-resonant plates with tunable inerter-based resonators. Appl. Math. Model. 106, 682–695 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wu, Q., Qi, G.: Quantum dynamics for Al-doped graphene composite sheet under hydrogen atom impact. Appl. Math. Model. 90, 1120–1129 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  46. Aliev, G.N., Goller, B., Snow, P.A.: Elastic properties of porous silicon studied by acoustic transmission spectroscopy. J. Appl. Phys. 110, 043534 (2011)

    Article  Google Scholar 

  47. Mescheder, U.M., Kovacs, A., Kronast, W., Barsony, I., Adam, M., Ducso, C.: Porous Silicon as multifunctional material in MEMS. In: Proceeding of 1st IEEE conference in Nanotechnology, Maui, USA (2001)

  48. Bert, C.W.: Prediction of elastic moduli of solids with oriented porosity. J. Mater. Sci. 20, 2220–2224 (1985)

    Article  Google Scholar 

  49. Rice, R.W.: Use of normalized porosity in models for the porosity dependence of mechanical properties. J. Mater. Sci. 40, 983–989 (2005)

    Article  Google Scholar 

  50. Barla, K., Herino, R., Bomchil, G., Pfister, C.J., Freund, A.: Determination of lattice parameter and elastic properties of porous silicon by X-ray diffraction. J. Cryst. Growth 68, 727–732 (1984)

    Article  Google Scholar 

  51. Da Fonseca, R.J.M., Saurel, J.M., Despaux, G., et al.: Elastic characterization of porous silicon by acoustic microscopy. Superlattices Microstruct. 16(1), 21–23 (1994)

    Article  Google Scholar 

  52. Martini, R., Depauw, V., Gonzalez, M., Vanstreels, K., Nieuwenhuysen, K.V., Gordon, I., Poortmans, J.: Mechanical properties of sintered meso-porous silicon: a numerical model. Nanoscale Res. Lett. 7, 597 (2012)

    Article  Google Scholar 

  53. Rezazadeh, G., Tahmasebi, A.M.: Electromechanical behavior of microbeams with piezoelectric and electrostatic actuation. Sens. Imaging 10, 15–30 (2009)

    Article  Google Scholar 

  54. Ghanbari, M., Hossainpour, S., Rezazadeh, G.: Studying thin film damping in a micro-beam resonator based on non-classical theories. Acta. Mech. Sin. 32(3), 369–379 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  55. Ghanbari, M., Hossainpour, S., Rezazadeh, G.: Study of squeeze film damping in a micro-beam resonator based on micropolar theory. Latin Am. J. Solids Struct. 12(1), 77–91 (2015)

    Article  Google Scholar 

  56. Ghanbari, M., Hossainpour, S., Rezazadeh, G.: Studying torsional vibration of a microshaft in a micro-scale fluid media based on nonclassical theories. Latin Am. J. Solids Struct. 16(1), e138 (2019)

    Article  Google Scholar 

  57. Ghanbari, M., Hossainpour, S., Rezazadeh, G.: On the modeling of a piezoellectrically actuated micro-sensor for measurement of microscale fluid physical properties. Appl. Phys. A 12, 651–663 (2015)

    Article  Google Scholar 

  58. Wu, Q., Yao, M., Niu, Y.: Nonplanar free and forced vibrations of an imperfect nanobeam employing nonlocal strain gradient theory. Commun. Nonlinear Sci. Numer. Simul. 114, 106692 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  59. Wu, Q., Yao, M., Li, M., Cao, D., Bai, B.: Nonlinear coupling vibrations of graphene composite laminated sheets impacted by particles. Appl. Math. Model. 93, 75–88 (2021)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran

    Mina Ghanbari

  2. Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran

    Ghader Rezazadeh

  3. South Ural State University, Chelyabinsk, Russian Federation

    Ghader Rezazadeh

  4. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Vahid Moloudpour-Tolkani

  5. Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Ardabil, Iran

    Mehrdad Sheikhlou

Authors
  1. Mina Ghanbari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghader Rezazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vahid Moloudpour-Tolkani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mehrdad Sheikhlou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mina Ghanbari.

Ethics declarations

Conflict of interest

The authors have no conflict of interest to declare.

Data availability statement

The datasets generated during the current study are not publicly available due to the university policy but are available from the corresponding author upon reasonable request.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghanbari, M., Rezazadeh, G., Moloudpour-Tolkani, V. et al. Dynamic analysis of a novel wide-tunable microbeam resonator with a sliding free-of-charge electrode. Nonlinear Dyn 111, 8039–8060 (2023). https://doi.org/10.1007/s11071-023-08286-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08286-0

Keywords

Search

Navigation