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Nonlinear performance analysis of forced carbon nanotube-based bio-mass sensors

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Abstract

In this effort, an analytical solution is proposed for the large amplitude nonlinear vibrations of doubly clamped carbon nanotube (CNT)-based nano-scale bio-mass sensors. The single walled CNT is modeled as an elastic Euler–Bernoulli nano-scale beam and the size effects are introduced into the mathematical model of the system through Eringen’s nonlocal elastic field theory. The nonlinearity arises due to mid-plane stretching of the bridged CNT, and is accounted for as the von Kármán nonlinearity. The impacts of deposited nano-scale bio-object, its geometrical properties, and its landing position along the longitudinal axis of the CNT-based resonator are considered. The nonlinear equations of motion are derived based on Hamilton’s principle and then the Method of Multiple Scales is employed to derive an analytical approximate solution for the system’s response. To verify the analytical solution and show its limits of applicability, the equations of motion are discretized by multi-mode Galerkin’s method and then the obtained set of equations are numerically solved by Runge–Kutta method and compared with those obtained by analytical solution. The potential applications of the CNT-based resonators for both of nonlinear frequency-/amplitude-based mass sensing are investigated and discussed. The obtained results show that the amplitude-based mass sensing has higher performance than frequency-based one in high quality-factor environments, such as in vitro biological mass sensing in the air or vacuum and inversely the frequency-based mass sensing method has higher mass sensibility in low quality factor environments, such as in vivo biological mass sensing in the liquid solution samples.

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References

  • Adhikari, S., Chowdhury, R.: The calibration of carbon nanotube based bionanosensors. J. Appl. Phys. 107, 124322 (2010)

    Article  Google Scholar 

  • Ali-Akbari, H.R., Shaat, M., Abdelkefi, A.: Bridged single-walled carbon nanotube-based atomic-scale mass sensors. Appl. Phys. A 122, 762 (2016)

    Article  Google Scholar 

  • Ali-Akbari, H.R., Ceballes, S., Abdelkefi, A.: Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors. Phys. E 94, 31–46 (2017)

    Article  Google Scholar 

  • Ansari, R., Hemmatnezhad, M., Ramezannezhad, H.: Application of HPM to the nonlinear vibrations of multiwalled carbon nanotubes. Numer. Methods Partial Differ. Equ. 26, 490–500 (2010)

    MathSciNet  MATH  Google Scholar 

  • Arash, B., Wang, Q.: A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput. Mater. Sci. 51, 303–313 (2012)

    Article  Google Scholar 

  • Aydogdu, M., Arda, M.: Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity. Int. J. Mech. Mater. Des. 12, 71–84 (2016)

    Article  Google Scholar 

  • Bağdatli, S.M.: Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory. Compos. B 80, 43–52 (2015)

    Article  Google Scholar 

  • Balthazar, J.M., Bassinello, D.G., Tusset, A.M., Bueno, A.M., de Pontes Junior, B.R.: Nonlinear control in an electromechanical transducer with chaotic behavior. Meccanica 49, 1859–1867 (2014)

    MathSciNet  MATH  Google Scholar 

  • Biedermann, L.B., Tung, R.C., Raman, A., Reifenberger, R.G., Yazdanpanah, M.M., Cohn, R.W.: Charactrerization of silver-gallium nano-wires for force and mass sensing applications. Nanotechnology 21, 305701 (2010)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: On the parameters which govern the symmetric snap-through buckling behavior of an initially curved microbeam. Int. J. Solids Struct. 66, 77–87 (2015)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: Dynamic behavior of micro-resonator under alternating current voltage. Int. J. Mech. Mater. Des. 13, 481–497 (2017a)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Chiu, H., Hung, P., Postma, H.W.C., Bockrath, M.: Atomic-scale mass sensing using carbon nanotubes resonators. Nano Lett. 8(12), 4342–4346 (2008)

    Article  Google Scholar 

  • Cho, H.N., Yu, M.F., Vakakis, A.F., Bergman, L.A., McFarland, D.M.: Tunable, broadband nonlinear nanomechanical resonator. Nano Lett. 10, 1793–1798 (2010)

    Article  Google Scholar 

  • Chowdhury, R., Adhikari, S., Mitchell, J.: Vibrating carbon nanotube based bio-sensors. Phys. E 42, 104–109 (2009)

    Article  Google Scholar 

  • Cigeroglu, E., Samandari, H.: Nonlinear free vibrations of curved double walled carbon Nanotubes using differential quadrature method. Phys. E 64, 95–105 (2014)

    Article  Google Scholar 

  • Dai, M.D., Eom, K., Kim, C.-W.: Nanomechanical mass detection using nonlinear oscillations. Appl. Phys. Lett. 95, 203104 (2009)

    Article  Google Scholar 

  • Dai, H.L., Ceballes, S., Abdelkefi, A., Hong, Y.Z., Wang, L.: Exact modes for post-buckling characteristics of nonlocal nanobeams in a longitudinal magnetic field. Appl. Math. Model. 55, 758–775 (2018)

    Article  MathSciNet  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 (2016b)

    Article  Google Scholar 

  • Eltaher, M.A., Khater, M.E., Samir, A.: Emam, A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nano-scale beams. Appl. Math. Model. 40(5–6), 4109–4128 (2016a)

    Article  MathSciNet  Google Scholar 

  • Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703 (1983)

    Article  Google Scholar 

  • Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)

    MATH  Google Scholar 

  • Fang, B., Zhen, Y.X., Zhang, C.P., Tang, Y.: Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory. Appl. Math. Model. 37, 1096–1107 (2013)

    Article  MathSciNet  MATH  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 

  • Firouz-Abadi, R.D., Hojjati, M., Rahmanian, M.: Free vibrations of single-walled carbon peapods. Phys. E 56, 410–413 (2014)

    Article  Google Scholar 

  • Fu, Y.M., Hong, J.W., Wang, X.Q.: Analysis of nonlinear vibration for embedded carbon nanotubes. J. Sound Vib. 296, 746–756 (2006)

    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. 14, 127–140 (2018)

    Article  MATH  Google Scholar 

  • Ghommem, M., Abdelkefi, A.: Nonlinear Reduced-Order Modeling and Effectiveness of Electrically-Actuated Microbeams for Bio-mass Sensing Applications. J. Mech. Mater. Des, Int (2018). https://doi.org/10.1007/s10999-018-9402-0

    Google Scholar 

  • Ghorbanpour Arani, A., Kolahchi, R., Mortazavi, S.A.: Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems. Int. J. Mech. Mater. Des. 10, 179–191 (2014)

    Article  Google Scholar 

  • Guo, S.-Q., Yang, S.-P.: Axial vibration analysis of nanocones based on nonlocal elasticity theory. Acta. Mech. Sin. 28, 801–807 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Hawwa, M.A., Al-Qahtani, H.M.: Nonlinear oscillations of a double-walled carbon nanotube. Comput. Mater. Sci. 48, 140–143 (2010)

    Article  Google Scholar 

  • Huttel, A.K., Steele, G.A., Witkamp, B., Poot, M., Kouwenhoven, L.P., van derZant, H.S.J.: Carbon nanotubes as ultrahigh quality factor mechanical resonators. Nano Lett. 9, 2547–2552 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Joshi, A.Y., Sharma, S.C., Harsha, S.P.: Nonlinear dynamic analysis of single-walled carbon nanotube based mass sensor. J. Nanotechnol. Eng. Med. 2, 041008 (2012)

    Article  Google Scholar 

  • Ke, L.L., Xiang, Y., Yang, J., Kitipornchai, S.: Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Comput. Mater. Sci. 47, 409–417 (2009)

    Article  Google Scholar 

  • Kiani, K., Ghaffari, H., Mehri, B.: Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects. Curr. Appl. Phys. 13, 107–120 (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 

  • Kozinsky, I., Postma, H.W.C., Bargatin, I., Roukes, M.L.: Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators. Appl. Phys. Lett. 88, 253101 (2006)

    Article  Google Scholar 

  • Kuang, Y.D., He, X.Q., Chen, C.Y., Li, G.Q.: Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid. Comput. Mater. Sci. 45, 875–880 (2009)

    Article  Google Scholar 

  • Lassagne, B., Garcia-Sanchez, D., Aguasca, A., Bachtold, A.: Ultrasenseitive mass sensing with a nanotube electromechanical resonator. Nano Lett. 8(11), 3735–3738 (2008)

    Article  Google Scholar 

  • Li, C., Chou, T.-W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)

    Article  MATH  Google Scholar 

  • Li, X.-F., Tang, G.-J., Shen, Z.-B., Lee, K.Y.: Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55, 75–84 (2015)

    Article  Google Scholar 

  • Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Dynamic properties of flexural beams using a nonlocal elasticity model. J. Appl. Phys. 99, 073510 (2006)

    Article  Google Scholar 

  • Mahdavi, M.H., Jiang, L.Y., Sun, X.: Nonlinear vibration of a single-walled carbon nanotube embedded in a polymer matrix aroused by interfacial van der Waals forces. J. Appl. Phys. 106, 114309 (2009)

    Article  Google Scholar 

  • Mehdipour, I., Barari, A.: Why the center-point of bridged carbon nanotube length is the most mass sensitive location for mass attachment. Comput. Mater. Sci. 55, 136–141 (2012)

    Article  Google Scholar 

  • Mehdipour, I., Erfani-Moghadam, A., Mehdipour, C.: Application of an electrostatically actuated cantilevered carbon nanotube with an attached mass as a bio-mass sensor. Curr. Appl. Phys. 13, 1463–1469 (2013)

    Article  Google Scholar 

  • Natsuki, T., Matsuyama, N., Shi, J.-X., Ni, Q.-Q.: Vibration analysis of nanomechanical mass sensor using carbon nanotubes under axial tensile loads. Appl. Phys. A 116, 1001–1007 (2014)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Ouakad, H.M., Younis, M.I.: Nonlinear dynamics of electrically actuated carbon nanotube resonators. J. Comput. Nonlinear Dyn. 5, 1–13 (2010)

    Article  Google Scholar 

  • Peddieson, J., Buchanan, G.R., McNitt, R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci. 41, 305–312 (2003)

    Article  Google Scholar 

  • Rafiee, M., Mareishi, S., Mohammadi, M.: An investigation on primary resonance phenomena of elastic medium based single walled carbon nanotubes. Mech. Res. Commun. 44, 51–56 (2012)

    Article  Google Scholar 

  • Reagan, M., Najm, H.N., Ghanem, R.G., Mnio, O.M.: Uncertainty quantification in reacting flow simulations through nonintrusive spectral projection. Combust. Flame 132, 545–555 (2003)

    Article  Google Scholar 

  • Shaat, M., Abdelkefi, A.: Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force. Int. J. Eng. Sci. 90, 58–75 (2015a)

    Article  MathSciNet  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 (2015b)

    Article  Google Scholar 

  • Shaat, M., Abdelkefi, A.: Reporting the sensitivities and resolutions of CNT-based resonators for mass sensing. Mater. Des. 114, 591–598 (2017)

    Article  Google Scholar 

  • Shaat, M., Abdelkefi, A.: Buckling characteristics of nanocrystalline nano-beams. Int. J. Mech. Mater. Des. 14, 71–89 (2018)

    Article  Google Scholar 

  • Shen, H.S., Zhang, C.L.: Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates. Comput. Mater. Sci. 50, 1022–1029 (2011)

    Article  Google Scholar 

  • Shen, Z.-B., Tang, G.-J., Zhang, L., Li, X.-F.: Vibration of double-walled carbon nanotube based nanomechanical sensor with initial axial stress. Comput. Mater. Sci. 58, 51–58 (2012)

    Article  Google Scholar 

  • Shirazi, M.J., Vatankhah, R., Boroushaki, M., Salarieh, H., Alasty, A.: Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty. Commun. Nonlinear Sci. Numer. Simul. 17, 742–753 (2014)

    Article  MathSciNet  Google Scholar 

  • Sneha Rupa, N., Ray, M.C.: Analysis of flexoelectric response in nanobeams using nonlocal theory of elasticity. Int. J. Mech. Mater. Des. 13, 453–467 (2017)

    Article  Google Scholar 

  • Souayeh, S., Kacem, N.: Computational models for large amplitude nonlinear vibrations of electrostatically actuated carbon nanotube-based mass sensors. Sens. Actuators, A 208, 10–20 (2014)

    Article  Google Scholar 

  • Togun, N.: Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory. Microsyst. Technol. 22, 2349–2359 (2016)

    Article  Google Scholar 

  • Waggoner, P.S., Varshney, M., Craighead, H.G.: Detection of prostate specific antigen with nanomechanical resonators. Lab Chip 9, 3095–3099 (2009)

    Article  Google Scholar 

  • Wang, Q.: Wave propagation in carbon nanotube via nonlocal continuum mechanics. J. Appl. Phys. 98, 124301 (2005)

    Article  Google Scholar 

  • Wang, Y.-Z., Li, F.-M.: Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix. Mech. Res. Commun. 60, 45–51 (2014)

    Article  Google Scholar 

  • Wang, K., Wang, B.: Vibration modeling of carbon-nanotube-based biosensors incorporating thermal and nonlocal effects. J. Vib. Control 22, 1405–1414 (2016)

    Article  MathSciNet  Google Scholar 

  • Xu, K.Y., Guo, X.N., Ru, C.Q.: Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces. J. Appl. Phys. 99, 1–7 (2006)

    Google Scholar 

  • Yan, Y., Wang, W.Q., Zhang, L.X.: Applied multiscale method to analysis of nonlinear vibration for double-walled carbon nanotubes. Appl. Math. Model. 35, 2279–2289 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, New York (2010)

    Google Scholar 

  • Zhang, D., Lei, Y., Shen, Z.: Effect of longitudinal magnetic field on vibration response of double-walled carbon nanotubes embedded in viscoelastic medium. Acta Mech. Solida Sin. 31, 187–206 (2018)

    Article  Google Scholar 

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Acknowledgements

The authors, S. Ceballes and A. Abdelkefi, would like to acknowledge the New Mexico Consortium and Los Alamos National Laboratory for funding support.

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Authors and Affiliations

  1. Sharif Technology Services Complex, Sharif University of Technology, Tehran, Iran

    H. R. Ali-Akbari

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

    S. Ceballes & A. Abdelkefi

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  1. H. R. Ali-Akbari
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  3. A. Abdelkefi
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Correspondence to A. Abdelkefi.

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Ali-Akbari, H.R., Ceballes, S. & Abdelkefi, A. Nonlinear performance analysis of forced carbon nanotube-based bio-mass sensors. Int J Mech Mater Des 15, 291–315 (2019). https://doi.org/10.1007/s10999-018-9414-9

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