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Nonlinear reduced-order modeling and effectiveness of electrically-actuated microbeams for bio-mass sensing applications

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Abstract

We apply perturbation techniques to develop a reduced-order model of an electrically-actuated microcantilever beam with a tip mass deployed as resonant sensor for bio-mass detection and sensing. This analytical model is validated against numerical model obtained by combining the differential quadrature method for space discretization and Runge–Kutta for time marching. The model is then employed to analyze the nonlinear dynamics and effectiveness of the bio-mass sensor under varying electric loading and explore novel concepts to quantify the mass of biological entities. The working principle of the present bio-mass sensor is based on inspecting the attenuation in the microbeam vibrations resulting from the biological element being deposited on its tip and then extracting the corresponding mass. The output parameter of the present bio-mass sensor is considered as the change in the maximum beam deflections at the tip with and without added mass. Calibration curves, showing the variations of the output parameter with the added mass, are generated to demonstrate the feasibility of the proposed sensing approach for mass detection of biological elements, particularly the Escherichia coli. Reducing the AC voltage when exciting the microbeam is observed to enhance the sensitivity of the output parameter for specific mass threshold. However, the operational range of the bio-mass sensor can be extended when applying higher DC and AC voltages.

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References

  • Abbasnejad, B., Rezazadeh, G.: Mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure. Int. J. Mech. Mater. Des. 8, 381–392 (2012)

    Article  Google Scholar 

  • Aboelkassem, Y., Nayfeh, A., Ghommem, M.: Bio-mass sensor using an electrostatically-actuated microcantilever in a vacuum microchannel. Microsyst. Technol. 16, 1749–1755 (2010)

    Article  Google Scholar 

  • Bouchaala, A., Jaber, N., Yassine, O., Shekhah, O., Chernikova, V., Eddaoudi, M., Younis, M.I.: Nonlinear-based MEMS sensors and active switches for gas detection. Sensors 16, 758 (2016a)

    Article  Google Scholar 

  • Bouchaala, A., Nayfeh, A.H., Younis, M.: Frequency shifts of micro and nano cantilever beam resonators due to added masses. J. Dyn. Syst. Meas. Control 138, 1–9 (2016b)

    Article  Google Scholar 

  • Bouchaala, A., Nayfeh, A.H., Jaber, N., Younis, M.: Mass and position determination in MEMS mass sensors: a theoretical and an experimental investigation. J. Micromech. Microeng. 26, 1–10 (2016c)

    Article  Google Scholar 

  • Bouchaala, A., Nayfeh, A.H., Younis, M.: Analytical study of the frequency shifts of micro and nano clamped–clamped beam resonators due to an added mass. Meccanica 52, 333–348 (2017)

    Article  MATH  Google Scholar 

  • Chen, X., Meguid, S.A.: Asymmetric bifurcation of initially curved nanobeam. J. Appl. Mech. 82, 091003 (2015a)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: Snap-through buckling of initially curved microbeam subject to an electrostatic force. Proc. R. Soc. A 471, 20150072 (2015b)

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, X., Meguid, S.A.: Dynamic behavior of micro-resonator under alternating current voltage. Int. J. Mech. Mater. Des. 13(4), 1–17 (2016). https://doi.org/10.1007/s10999-016-9354-1

  • Chen, X., Meguid, S.A.: Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam. Proc. R. Soc. A 472, 20150597 (2017)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: Nonlinear vibration analysis of a microbeam subject to electrostatic force. Acta Mech. 228, 1343–1361 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Cooper, M.A.: Label-Free Biosensors: Techniques and Applications. Cambridge University Press, New York (2009)

    Book  Google Scholar 

  • Elishakoff, I., Versaci, C., Maugeri, N., Muscolino, G.: Clamped-free single-walled carbon nanotube-based mass sensor treated as Bernoulli–Euler beam. J. Nanotechnol. Eng. Med. 2, 1–8 (2011)

    MATH  Google Scholar 

  • Eltaher, M.A., Agwa, M.A., Mahmoud, F.F.: Nanobeam sensor for measuring a zeptogram mass. Int. J. Mech. Mater. Des. 12, 211–221 (2016)

    Article  Google Scholar 

  • Farokhi, H., Ghayesh, M.H.: Size-dependent behaviour of electrically actuated microcantilever-based MEMS. Int. J. Mech. Mater. Des. 12, 301–315 (2016)

    Article  Google Scholar 

  • Ghaderi, R.: Dynamic modeling and vibration analysis of piezoelectric microcantilever in AFM application. Int. J. Mech. Mater. Des. 12, 413–425 (2016)

    Article  Google Scholar 

  • Ghayesh, M.H., Farokhi, H.: Size-dependent internal resonances and modal interactions in nonlinear dynamics of microcantilevers. Int. J. Mech. Mater. Des. 1–14 (2017). https://doi.org/10.1007/s10999-017-9365-6

  • Ghommem, M., Abdelkefi, A.: Novel design of microgyroscopes employing electrostatic actuation and resistance-change based sensing. J. Sound Vib. 411, 278–288 (2017a)

    Article  Google Scholar 

  • Ghommem, M., Abdelkefi, A.: Nonlinear analysis of rotating nanocrystalline silicon microbeams for microgyroscope applications. Microsyst. Technol. 23, 5931–5946 (2017b)

    Article  Google Scholar 

  • Ghommem, M., Nayfeh, A., Choura, S.: Model reduction and analysis of a vibrating beam microgyroscope. J. Vib. Control 19, 1240–1249 (2013)

    Article  MathSciNet  Google Scholar 

  • Ibrahim, M., Younis, M.I.: The dynamic response of electrostatically driven resonators under mechanical shock. J. Micromech. Microeng. 20, 025006 (2009)

    Article  Google Scholar 

  • Johnson, B.N., Mutharasan, R.: Biosensing using dynamic-mode cantilever sensors: a review. Biosens. Bioelectron. 32, 118 (2012)

    Article  Google Scholar 

  • Jrad, M., Younis, M.I., Najar, F.: Modeling and design of an electrically actuated resonant microswitch. J. Vib. Control 22, 559–569 (2016)

    Article  MathSciNet  Google Scholar 

  • Kacem, N., Arcamone, J., Perez-Murano, F., Hentz, S.: Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications. J. Micromech. Microeng. 20, 1–9 (2010)

    Article  Google Scholar 

  • Kim, D., Hong, S., Jang, J., Park, J.: Simultaneous determination of position and mass in the cantilever sensor using transfer function method. Appl. Phys. Lett. 103, 033108 (2013)

    Article  Google Scholar 

  • Kivi, A.R., Azizi, S., Khalkhali, A.: Sensitivity enhancement of a MEMS sensor in nonlinear regime. Int. J. Mech. Mater. Des. 12, 337–351 (2016)

    Article  Google Scholar 

  • Li, X., Yu, H., Gan, X., Xia, X., Xu, P., Li, J., Liu, M., Li, Y.: Integrated MEMS/NEMS resonant cantilevers for ultrasensitive biological detection. J. Sens. 1–10 (2009). https://www.hindawi.com/journals/js/2009/637874/

  • Maraldo, D., Mutharasan, R.: Mass-change sensitivity of high-order mode of piezoelectric-excited millimeter-sized cantilever (PEMC) sensors: theory and experiments. Sens. Actuators B Chem. 143, 731–739 (2010)

    Article  Google Scholar 

  • Michael, A., Kwok, C.Y.: Design criteria for bi-stable behavior in a buckled multi-layered MEMS bridge. J. Micromech. Microeng. 16, 2034 (2006)

    Article  Google Scholar 

  • Najar, F., Choura, S., El-Borgi, S., Abdel-Rahman, E.M., Nayfeh, A.H.: Modeling and design of variable-geometry electrostatic microactuators. J. Micromech. Microeng. 15, 419–429 (2005)

    Article  MATH  Google Scholar 

  • Najar, F., Choura, S., Abdel-Rahman, E.M., El-Borgi, S., Nayfeh, A.H.: Dynamic analysis of variable-geometry electrostatic microactuators. J. Micromech. Microeng. 16, 2449–2457 (2006)

    Article  MATH  Google Scholar 

  • Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (2011)

    MATH  Google Scholar 

  • Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. Wiley, New York (1995)

    Book  MATH  Google Scholar 

  • Shaat, M., Abdelkefi, A.: Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications. Int. J. Mech. Sci. 101–102, 280–291 (2015)

    Article  Google Scholar 

  • Shaat, M., Abdelkefi, A.: Buckling characteristics of nanocrystalline nano-beams. Int. J. Mech. Mater. Des. 1–19 (2016). https://doi.org/10.1007/s10999-016-9361-2

  • Singh, S.S., Pal, P., Pandey, A.K.: Mass sensitivity of nonuniform microcantilever beams. J. Vib. Acoust. 138, 1–7 (2016)

    Google Scholar 

  • Wu, G., Datar, R.H., Hansen, K.M., Thundat, T., Cote, R.J., Majumdar, A.: Bioassay of prostate-specific antigen (PSA) using microcantilevers. Nat. Biotechnol. 19, 856–860 (2001)

    Article  Google Scholar 

  • Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, Berlin (2011)

    Book  Google Scholar 

  • Younis, M., Alsaleem, F.: Exploration of new concepts for mass detection in electrostatically-actuated structures based on nonlinear phenomena. J. Comput. Nonlinear Dyn. 4, 033108 (2009)

    Article  Google Scholar 

  • Younis, M., Alsaleem, F., Jordy, D.: The response of clamped–clamped microbeams under mechanical shock. Int. J. Nonlinear Mech. 42, 643–657 (2007)

    Article  Google Scholar 

  • Yu, Y., Wu, B., Lim, C.W.: Numerical and analytical approximations to large post-buckling deformation of MEMS. Int. J. Mech. Sci. 55, 95–103 (2012)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering, American University of Sharjah, 26666, Sharjah, UAE

    M. Ghommem

  2. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, 88003, USA

    A. Abdelkefi

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  1. M. Ghommem
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  2. A. Abdelkefi
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Correspondence to M. Ghommem.

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Ghommem, M., Abdelkefi, A. Nonlinear reduced-order modeling and effectiveness of electrically-actuated microbeams for bio-mass sensing applications. Int J Mech Mater Des 15, 125–143 (2019). https://doi.org/10.1007/s10999-018-9402-0

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  • DOI: https://doi.org/10.1007/s10999-018-9402-0

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