Nonlinear Dynamics

, Volume 92, Issue 2, pp 287–304 | Cite as

A micromechanical mass sensing method based on amplitude tracking within an ultra-wide broadband resonance

  • Randi Potekin
  • Seok Kim
  • D. Michael McFarland
  • Lawrence A. Bergman
  • Hanna Cho
  • Alexander F. Vakakis
Original Paper
  • 177 Downloads

Abstract

We propose a mass sensing scheme in which amplitude shifts within a nonlinear ultra-wide broadband resonance serve as indicators for mass detection. To achieve the broad resonance bandwidth, we considered a nonlinear design of the resonator comprised of a doubly clamped beam with a concentrated mass at its center. A reduced-order model of the beam system was constructed in the form of a discrete spring-mass system that contains cubic stiffness due to axial stretching of the beam in addition to linear stiffness (Duffing equation). The cubic nonlinearity has a stiffening effect on the frequency response causing nonlinear bending of the frequency response toward higher frequencies. Interestingly, we found that the presence of the concentrated mass broadens the resonant bandwidth significantly, allowing for an ultra-wide operational range of frequencies and response amplitudes in the proposed mass sensing scheme. A secondary effect of the cubic nonlinearity is strong amplification of the third harmonic in the beam’s response. We computationally study the sensitivity of the first and third harmonic amplitudes to mass addition and find that both metrics are more sensitive than the linearized natural frequency and that in particular, the third harmonic amplitude is most sensitive. This type of open-loop mass sensing avoids complex feedback control and time-consuming frequency sweeping. Moreover, the mass resolution is within a functional range, and the design parameters of the resonator are reasonable from a manufacturing perspective.

Keywords

Broadband nonlinear resonator Mass sensor Third harmonic 

Notes

Acknowledgements

This work was financially supported in part by the National Science Foundation, Grant NSF CMMI 14-638558 at the University of Illinois at Urbana-Champaign, and Grants CMMI-1619801 at The Ohio State University. This support is gratefully acknowledged.

References

  1. 1.
    Albrecht, T.R., Grütter, P., Horne, D., Rugar, D.: Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity. J. Appl. Phys. 69(2), 668–673 (1991)CrossRefGoogle Scholar
  2. 2.
    Aldridge, J.S., Cleland, A.N.: Noise-enabled precision measurements of a duffing nanomechanical resonator. Phys. Rev. Lett. 94(15), 5–8 (2005)CrossRefGoogle Scholar
  3. 3.
    Alsaleem, F.M., Younis, M.I.: Stabilization of electrostatic MEMS resonators duffing nanomechanical resonator. Phys. Rev. Lett. 94(15), 5–8 (2010)Google Scholar
  4. 4.
    Antonio, D., Zanette, D.H., López, D.: Frequency stabilization in nonlinear micromechanical oscillators. Nat. Commun. 3, 806 (2012)CrossRefGoogle Scholar
  5. 5.
    Arlett, J.L., Myers, E.B., RoukesM, L.: Comparative advantages of mechanical biosensors. Nature Nanotech. 6, 203–215 (2011). Feedback. Journal of Microelectromechanical Systems, 25(1): 2–10CrossRefGoogle Scholar
  6. 6.
    Askari, H., Jamshidifar, H., Fidan, B.: High resolution mass identification using nonlinear vibrations of a nanoplate. Measurement 101, 166–174 (2017)CrossRefGoogle Scholar
  7. 7.
    Bajaj, N., Sabater, A.B., Hickey, J.N., Chiu, G.T.C., Rhoads, J.F.J.: Design and implementation of a tunable, Duffing-like electronic resonator via nonlinear. J. Microelectromech. Syst. 25(1), 2–10 (2016)CrossRefGoogle Scholar
  8. 8.
    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(6), 758 (2016)CrossRefGoogle Scholar
  9. 9.
    Butt, H.-J., Jaschke, M.: Calculation of thermal noise in atomic force microscopy. Nanotechnology 6, 1–7 (1995)CrossRefGoogle Scholar
  10. 10.
    Chaste, J., Eichler, A., Moser, J., Ceballos, G., Rurali, R., Bachtold, A.: A nanomechanical mass sensor with yoctogram resolution. Nat. Nanotechnol. 7(5), 301–304 (2012)CrossRefGoogle Scholar
  11. 11.
    Chiu, H.-Y., Hung, H., Postma, H., Bockrath, M.: Atomic-scale mass sensing using carbon nanotube resonators. Nano Lett. 8(12), 4342–4346 (2008)CrossRefGoogle Scholar
  12. 12.
    Cho, H., Yu, M.-F., Vakakis, A., Bergman, L., McFarland, D.M.: Tunable, broadband nonlinear nanomechanical resonator. Nano Lett. 10(5), 1793–1798 (2010)CrossRefGoogle Scholar
  13. 13.
    Cho, H., Jeong, B., Yu, M.F., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities. Int. J. Solids Str. 49, 2059–2065 (2012)CrossRefGoogle Scholar
  14. 14.
    Cleland, A.N.: Thermomechanical noise limits on parametric sensing with nanomechanical resonators. New J. Phys. 7, 235 (2005)CrossRefGoogle Scholar
  15. 15.
    Cleland, A.N., Roukes, M.L.: Noise processes in nanomechanical resonators. J. Appl. Phys. 92(5), 2758–2769 (2002)CrossRefGoogle Scholar
  16. 16.
    Dai, M.D., Eom, K., Kim, C.-W.: Nanomechanical mass detection using nonlinear oscillations. Appl. Phys. Lett. 95(203104), 1–3 (2009)Google Scholar
  17. 17.
    de Oteyza, D.G., Gorman, P., Chen, Y.-C., Wickenburg, S., Riss, A., Mowbray, D.J., Etkin, G., Pedramrazi, Z., Tsai, H.-Z., Rubio, A., Crommie, M.F., Fischer, F.R.: Direct imaging of covalent bond structure in single-molecule chemical reactions. Science 340, 1434–1437 (2013)CrossRefGoogle Scholar
  18. 18.
    Dohn, S., Schmid, S., Amiot, F., Boisen, A.: Position and mass determination of multiple particles using cantilever based mass sensors. Appl. Phys. Lett. 97, 044103 (2010)CrossRefGoogle Scholar
  19. 19.
    Duo, S., Jensen, S.: Optimization of nonlinear structural resonance using the incremental harmonic balancing method. J. Sound Vib. 334, 239–254 (2015)CrossRefGoogle Scholar
  20. 20.
    Ekinci, K.L., Yang, Y.T., Roukes, M.L.: Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95(5), 2682–2689 (2004)CrossRefGoogle Scholar
  21. 21.
    Garcia, R., Perez, R.: Dynamic atomic force microscopy methods. Surf. Sci. 47, 197–301 (2002)CrossRefGoogle Scholar
  22. 22.
    Grüter, R.R., Khan, Z., Paxman, R., Ndieyira, J.W., Dueck, B., Bircher, B.A., Yang, J.L., Drechsler, U., Despont, M., McKendry, R.A., Hoogenboom’, B.W.: Disentangling mechanical and mass effects on nanomechanical resonators. Appl. Phys. Lett. 96(023113), 1–3 (2010)Google Scholar
  23. 23.
    Gupta, A.K., Nair, P.R., Ladisch, M.R., Broyles, S., Alam, M.A., Bashir, R.: Anamalous resonance in a nanomechanical biosensor. PNAS 103(36), 13362–13367 (2006)CrossRefGoogle Scholar
  24. 24.
    Hanay, M.S., Kelber, S., Naik, A.K., Chi, D., Hentz, S., Bullard, E.C., Colinet, E., Duraffourg, L., Roukes, M.L.: Single protein nanomechanical mass spectrometry in real time. Nat. Nanotechnol. 7(9), 602–608 (2012)CrossRefGoogle Scholar
  25. 25.
    Heer, C.V.: Statistical Mechanics, Kinetic Theory and Stochastic Processes. Academic Press Inc, London (1972)Google Scholar
  26. 26.
    Hiller, T., Li, L.L., Holthoff, E.L., Bamieh, B., Turner, K.L.: System identification, design, and implementation of amplitude feedback control on a nonlinear parametric MEM resonator for trace nerve agent sensing. J. Microelectromech. Syst. 24(5), 1275–1284 (2015)CrossRefGoogle Scholar
  27. 27.
    Ilic, B., Czaplewski, D., Zalautdinov, M., Craighead, H.G., Neuzil, P., Campagnolo, C., Batt, C.: Single cell detection with micromechanical oscillators. J. Vac. Sci. Technol. B. 19, 2825–2828 (2001)CrossRefGoogle Scholar
  28. 28.
    Ilic, B., Yang, Y., Aubin, K., Reichenbach, R., Krylov, S., Craighead, H.G.: Enumeration of DNA molecules bound to a nanomechanical oscillator. Nano Lett. 5(5), 925–929 (2005)CrossRefGoogle Scholar
  29. 29.
    Ilic, B., Krylov, S., Craighead, H.G.: Young’s modulus and density measurements of thin atomic layer deposited films using resonant nanomechanics. J. Appl. Phys. 108(044317), 1–11 (2010)Google Scholar
  30. 30.
    Jain, A., Nair, P.R., Alam, M.A.: Flexure-FET biosensor to break the fundamental sensitivity limits of nanobiosensors using nonlinear electromechanical coupling. PNAS 109(24), 9304–9308 (2012)CrossRefGoogle Scholar
  31. 31.
    Jensen, K., Kwanpyo, K., Zettl, A.: An atomic-resolution nanomechanical mass sensor. Nat. Nanotechnol. 3, 533–537 (2008)CrossRefGoogle Scholar
  32. 32.
    Johnson, B.N., Mutharasan, R.: Biosensing using dynamic-mode cantilever sensors: a review. Biosens. Bioelectr. 32, 1–18 (2012)CrossRefGoogle Scholar
  33. 33.
    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(4), 45023 (2010)CrossRefGoogle Scholar
  34. 34.
    Karabalin, R.B., Feng, X.L., Roukes, M.L.: Parametric nanomechanical amplification at very high frequency. Nanolett. 9(9), 3116–3123 (2009)CrossRefGoogle Scholar
  35. 35.
    Keum, H., Yang, Z., Han, K., Handler, D.E., Nguyen, T.N., Schutt-Aine, J., Bahl, G., Kim, S.: Microassembly of heterogenous materials using transfer printing and thermal processing. Sci. Rep. 6(29925), 1–9 (2016)Google Scholar
  36. 36.
    Kharrat, C., Colinet, E., Voda, A.: H\(\infty \) loop shaping control for PLL-based mechanical resonance tracking in NEMS resonant mass sensors. In: Proceedings of IEEE Sensors, pp. 1135–1138 (2008)Google Scholar
  37. 37.
    Kozinsky, I., Postma, H.W.C., Kogan, O., Husain, A., Roukes, M.L.: Basins of attraction of a nonlinear nanomechanical resonator. Phys. Rev. Lett. 99(20), 8–11 (2007)CrossRefGoogle Scholar
  38. 38.
    Kumar, V., Boley, J.W., Yang, Y., Ekowaluyo, H., Miller, J.K., Chiu, T.-C., Rhoads, J.F.: Bifurcation-based mass sensing using piezoelectrically-actuated microcantilevers. Appl. Phys. Lett. 98(153510), 1–3 (2011)Google Scholar
  39. 39.
    Kumar, V., Yang, Y., Boley, J.W., Chiu, T.-C., Rhoads, J.F.: Modeling, analysis, and experimental validation of a bifurcation-based microsensor. J. Microelectromech. Syst. 21(3), 549–558 (2012)CrossRefGoogle Scholar
  40. 40.
    Li, L., Hiller, T., Bamieh, B., Turner, K.: Amplitude control of parametric resonances for mass sensing. Proc. IEEE Sens. 2014(December), 198–201 (2014)Google Scholar
  41. 41.
    Li, L., Polunin, P.M., Duo, S., Shoshani, O., Strachan, B.S., Jensen, J.S., Shaw, S.W., Turner, K.L.: Tailoring the nonlinear response of MEMS resonators using shape optimization. Appl. Phys. Lett. 110(081902), 1–5 (2017)Google Scholar
  42. 42.
    Ma, S., Huang, H., Lu, M., Veidt, M.: A simple resonant method that can simultaneously measure elastic modulus and density of thin films. Surf. Coat. Tech. 209, 208–211 (2012)CrossRefGoogle Scholar
  43. 43.
    Mahmoud, M.A.: Validity and accuracy of resonance shift prediction formulas for microcantilevers: a review and comparative study. Crit. Rev. Solid State Mater. Sci. 41(5), 386–429 (2016)CrossRefGoogle Scholar
  44. 44.
    Olcum, S., Cermak, N., Wasserman, S.C., Manalis, S.R.: High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions. Nat. Commun. 6, 7070 (2015)CrossRefGoogle Scholar
  45. 45.
    Rhoads, J., Shaw, S., Turner, K., Baskaran, R.: Tunable microelectromechanical filters that exploit parametric resonance. J. Vib. Acoust. 127, 423–430 (2005)CrossRefGoogle Scholar
  46. 46.
    Rhoads, J.F., Shaw, S.W., Turner, K.L.: Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Control. 132(3), 034001: 1-14 (2010)CrossRefGoogle Scholar
  47. 47.
    Turner, K., Miller, S., Hartwell, P., MacDonald, N., Strogatz, S.: Five parametric resonances in a microelectromechanical system. Nature 396(6707), 149–152 (1998)CrossRefGoogle Scholar
  48. 48.
    Unterreithmeier, Q.P., Faust, T., Kotthaus, J.P.: Nonlinear switching dynamics in a nanomechanical resonator. Phys. Rev. B Condens. Matter Mater. Phys. 81(24), 1–4 (2010)CrossRefGoogle Scholar
  49. 49.
    Yang, Y.T., Callegari, C., Feng, X.L., Ekinici, K.L., Roukes, M.L.: Zemptogram-scale nanomechanical mass sensing. Nanoletters 6(4), 583–586 (2006)CrossRefGoogle Scholar
  50. 50.
    Yang, Y.T., Callegari, C., Feng, X.L., Roukes, M.L.: Surface absorbate fluctuations and noise in nanoelectromechanical systems. Nanoletters 11, 1753–1759 (2011)CrossRefGoogle Scholar
  51. 51.
    Younis, M.I., Alsaleem, F.: Electrostatically-actuated structures based on nonlinear phenomena. J. Comput. Nonlinear Dyn. 4(021010), 1–15 (2009)Google Scholar
  52. 52.
    Yu, M., Wagner, G., Ruoff, R., Dyer, M.: Realization of parametric resonances in a nanowire mechanical system with nanomanipulation inside a scanning electron microscope. Phys. Rev. B. 66(073406), 1–4 (2002)Google Scholar
  53. 53.
    Zhang, Y.: Detecting the stiffness of biochemical absorbates. Sens. Actuators B 202, 286–293 (2014)CrossRefGoogle Scholar
  54. 54.
    Zhang, W., Turner, K.L.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sens. Actuators A 122, 23–30 (2005)CrossRefGoogle Scholar
  55. 55.
    Zhang, W., Baskaran, R., Turner, K.L.: Effect of cubic nonlinearity on auto- parametrically amplified resonant MEMS mass sensor. Sens. Actuators A 102(1–2), 139–150 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Randi Potekin
    • 1
  • Seok Kim
    • 1
  • D. Michael McFarland
    • 2
  • Lawrence A. Bergman
    • 2
  • Hanna Cho
    • 3
  • Alexander F. Vakakis
    • 1
  1. 1.Department of Mechanical Science and EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of Aerospace EngineeringUniversity of IllinoisUrbanaUSA
  3. 3.Department of Mechanical and Aerospace EngineeringOhio State UniversityColumbusUSA

Personalised recommendations