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Forecasting bifurcation morphing: application to cantilever-based sensing

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Abstract

Two novel techniques are proposed to enhance the bifurcation morphing method as applied to cantilever-based sensors. First, nonlinear feedback excitations with added time delay are employed to minimize the sensitivity of the sensors to small variations in the unavoidable time delay. Second, a novel approach to forecast bifurcations is applied to the sensors. This approach significantly reduces the time required to obtain bifurcation diagrams. Both techniques are demonstrated experimentally in detecting mass variations of a test cantilever beam. This cantilever-based sensor operating based on the bifurcation morphing method is shown to be accurate, quick and robust when these techniques are utilized.

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References

  1. Bagowski, C.P., Ferrell, J.E. Jr: Bistability in the JNK cascade. Curr. Biol. 11(15), 1176–1182 (2001)

    Article  Google Scholar 

  2. Berglund, N., Gentz, B.: Metastability in simple climate models: pathwise analysis of slowly driven Langevin equations. Stoch. Dyn. 2, 327–356 (2001)

    Article  MathSciNet  Google Scholar 

  3. Binnig, G., Quate, C.F., Gerber, C.: Atomic force microscope. Phys. Rev. Lett. 56(9), 930–933 (1986)

    Article  Google Scholar 

  4. Burg, T.P., Godin, M., Knudsen, S.M., Shen, W., Carlson, G., Foster, J.S., Babcock, K., Manalis, S.R.: Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446(7139), 1066–1069 (2007)

    Article  Google Scholar 

  5. Carpenter, S., Brock, W.: Rising variance: a leading indicator of ecological transition. Ecol. Lett. 9(3), 308–315 (2006)

    Google Scholar 

  6. Carpenter, S.R., Brock, W.A., Cole, J.J., Kitchell, J.F., Pace, M.L.: Leading indicators of trophic cascades. Ecol. Lett. 11(2), 128–138 (2008)

    Google Scholar 

  7. Chisholm, R.A., Filotas, E.: Critical slowing down as an indicator of transitions in two-species models. J. Theor. Biol. 257(1), 142–149 (2009)

    Article  Google Scholar 

  8. Dakos, V., Scheffer, M., van Nes, E.H., Brovkin, V., Petoukhov, V., Held, H.: Slowing down as an early warning signal for abrupt climate change. Proc. Natl. Acad. Sci. USA 105(38), 14,308–14,312 (2008)

    Article  Google Scholar 

  9. D’Souza, K., Epureanu, B.I.: Nonlinear feedback auxiliary signals for system interrogation and damage detection. Proc. R. Soc., Math. Phys. Eng. Sci. 464(2100), 3129–3148 (2008)

    Article  MATH  Google Scholar 

  10. Gupta, A., Akin, D., Bashir, R.: Single virus particle mass detection using microresonators with nanoscale thickness. Appl. Phys. Lett. 84(11), 1976–1978 (2004)

    Article  Google Scholar 

  11. Guttal, V., Jayaprakash, C.: Changing skewness: an early warning signal of regime shifts in ecosystems. Ecol. Lett. 11(5), 450–460 (2008)

    Article  Google Scholar 

  12. Ilic, B., Craighead, H.G., Krylov, S., Senaratne, W., Ober, C., Neuzil, P.: Attogram detection using nanoelectromechanical oscillators. J. Appl. Phys. 95(7), 3694–3703 (2004)

    Article  Google Scholar 

  13. Ilic, B., Yang, Y., Craighead, H.G.: Virus detection using nanoelectromechanical devices. Appl. Phys. Lett. 85(13), 2604–2606 (2004)

    Article  Google Scholar 

  14. Jeffries, C., Wiesenfeld, K.: Observation of noisy precursors of dynamical instabilities. Phys. Rev. A 31(2), 1077–1084 (1985)

    Article  Google Scholar 

  15. Kleinen, T., Held, H., Petschel-Held, G.: The potential role of spectral properties in detecting thresholds in the earth system: application to the thermohaline circulation. Ocean Dyn. 53, 53 (2003)

    Article  Google Scholar 

  16. Lange, D., Hagleitner, C., Hierlemann, A., Brand, O., Baltes, H.: Complementary metal oxide semiconductor cantilever arrays on a single chip: mass-sensitive detection of volatile organic compounds. Anal. Chem. 74(13), 3084–3095 (2002)

    Article  Google Scholar 

  17. Lavrik, N.V., Datskos, P.G.: Femtogram mass detection using photothermally actuated nanomechanical resonators. Appl. Phys. Lett. 82(16), 2697–2699 (2003)

    Article  Google Scholar 

  18. Li, M., Tang, H.X., Roukes, M.L.: Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. Nat. Nanotechnol. 2(2), 114–120 (2007)

    Article  Google Scholar 

  19. Lim, J., Epureanu, B.I.: Exploiting delayed nonlinear feedback for sensing based on bifurcation morphing. Int. J. Struct. Stab. Dyn. 11(4), 621–640 (2011)

    Article  Google Scholar 

  20. Lim, J., Epureanu, B.I.: Forecasting a class of bifurcations: theory and experiment. Phys. Rev. E 83(1), 016,203 (2011). doi:10.1103/PhysRevE.83.016203

    Article  MathSciNet  Google Scholar 

  21. Narducci, M., Figueras, E., Lopez, M.J., Gracia, I., Santander, J., Ivanov, P., Fonseca, L., Cane, C.: Sensitivity improvement of a microcantilever based mass sensor. Microelectron. Eng. 86(4–6), 1187–1189 (2009)

    Article  Google Scholar 

  22. van Nes, E.H., Scheffer, M.: Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169(6), 738–47 (2007)

    Article  Google Scholar 

  23. Rhoads, J.F., Shaw, S.W., Turner, K.L.: Nonlinear dynamics and its applications in micro- and nanoresonators. In: Proceedings of the ASME Dynamic Systems and Control Conference 2008, pp. 543–572 (2009). Pts A and B

    Google Scholar 

  24. Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., van Nes, E.H., Rietkerk, M., Sugihara, G.: Early-warning signals for critical transitions. Nature 461(7260), 53–59 (2009)

    Article  Google Scholar 

  25. Strogatz, S.H.: Nonlinear Dynamics and Chaos—With Applications to Physics, Biology, Chemistry, and Engineering, 1st edn. Westview Press, Boulder (2001)

    Google Scholar 

  26. Thundat, T., Wachter, E.A., Sharp, S.L., Warmack, R.J.: Detection of mercury-vapor using resonating microcantilevers. Appl. Phys. Lett. 66(13), 1695–1697 (1995)

    Article  Google Scholar 

  27. Vyas, A., Peroulis, D., Bajaj, A.K.: A microresonator design based on nonlinear 1:2 internal resonance in flexural structural modes. J. Microelectromech. Syst. 18(3), 744–762 (2009)

    Article  Google Scholar 

  28. Wiesenfeld, K.: Virtual Hopf phenomenon—a new precursor of period-doubling bifurcations. Phys. Rev. A 32(3), 1744–1751 (1985)

    Article  MathSciNet  Google Scholar 

  29. Wissel, C.: A universal law of the characteristic return time near thresholds. Oecologia 65(1), 101–107 (1984)

    Article  Google Scholar 

  30. Yin, S.H., Epureanu, B.I.: Enhanced nonlinear dynamics and monitoring bifurcation morphing for the identification of parameter variations. J. Fluids Struct. 21(5–7), 543–559 (2005)

    Google Scholar 

  31. Younis, M.I., Alsaleem, F.: Exploration of new concepts for mass detection in electrostatically-actuated structures based on nonlinear phenomena. J. Comput. Nonlinear Dyn. 4(2), 021,010 (2009)

    Article  Google Scholar 

  32. Zhang, W.H., Turner, K.L.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sens. Actuators A, Phys. 122(1), 23–30 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI, 48109, USA

    Joosup Lim & Bogdan I. Epureanu

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  1. Joosup Lim
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  2. Bogdan I. Epureanu
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Correspondence to Bogdan I. Epureanu.

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Lim, J., Epureanu, B.I. Forecasting bifurcation morphing: application to cantilever-based sensing. Nonlinear Dyn 67, 2291–2298 (2012). https://doi.org/10.1007/s11071-011-0146-8

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  • DOI: https://doi.org/10.1007/s11071-011-0146-8

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