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Investigation of the Photothermal Excited Microcantilevers Based on Modified Couple Stress Theory

  • Y. Q. SongEmail author
  • B. Cretin
  • D. M. Todorovic
  • P. Vairac
Article
  • 37 Downloads

Abstract

In microscale and sub-micron scale, scale effect highlights and the classical continuum mechanics cannot describe microstructure-dependent size effects. So many non-classical theories were put forward. The modified couple stress theory was established by introducing a material parameter to characterize the scale effect. In this paper, the dynamic responses of microcantilever under photothermal excitation are studied using the modified couple stress theory. The microcantilever deflection governing equation was given, and deflections were obtained numerically using relaxation method. Comparison was made between numerical results with that obtained with experimental measurement and showed a good agreement. According to the numerical results, the scale effect becomes remarkable as the ratio of thickness to the material parameter changes from zero to one. Also, the results showed that this ratio has prominent effect on the resonant frequency of microcantilever.

Keywords

Microcantilever vibration Modified couple stress theory Photothermal Relaxation method 

Notes

Acknowledgments

The work was supported by the National Natural Science Foundation of China (Grants Nos. 11672224 and 11272243), the Fundamental Research Funds for the Central Universities and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 13JS103).

References

  1. 1.
    X.D. Yan, Y.J. Tang, H.F. Ji, Y. Lvov, T. Thundat, Detection of organophosphates using an acetyl cholinesterase (AChE) coated microcantilever. Instrum. Sci. Technol. 32, 175–183 (2004)CrossRefGoogle Scholar
  2. 2.
    S.Q. Li, Z.M. Orona, Z.M. Li, Z.Y. Cheng, Biosensor based on magnetostrictive microcantilever. Appl. Phys. Lett. 88, 073507 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    C. Karnati, H. Du, H.F. Ji, X. Xu, Y.A. Lvov, P. Mulchandani, W. Chen, Organophosphorus hydrolase multilayer modified microcantilevers for organophosphorus detection. Biosens. Bioelectron. 22, 2636–2642 (2007)CrossRefGoogle Scholar
  4. 4.
    M.K. Ghatkesar, T. Braun, V. Barwich, J. Ramseyer, C. Gerber, M. Hegner, H.P. Lang, Resonating modes of vibrating microcantilevers in liquid. Appl. Phys. Lett. 92, 043106 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    J.O. Liu, S. Somnath, W.P. King, Heated atomic force microscope cantilever with high resistivity for improved temperature sensitivity. Sens. Actuators A Phys. 201, 141–147 (2013)CrossRefGoogle Scholar
  6. 6.
    K. Lakshmoji, K. Prabakar, S. Tripura, J. Jayapandian, A.K. Tyagi, C.S. Sunda, Origin of bending in uncoated microcantilever-surface topography? Appl. Phys. Lett. 104, 041602 1-4 (2014)CrossRefGoogle Scholar
  7. 7.
    F. Huber, H.P. Lang, J. Zhang, D. Rimoldi, C. Gerber, Nanosensors for cancer detection. Swiss Med. Wkly. 145, w14092 (2015)Google Scholar
  8. 8.
    J. Tamayo, D. Ramos, J. Mertens, Effect of the adsorbate stiffness on the resonance response of microcantilever sensors. Appl. Phys. Lett. 89, 224104 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    S. Chaterjee, G. Pohit, A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams. J. Sound Vib. 322, 969–986 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    J. Tamayo, J. Ruz, V. Pini, P. Kosaka, M. Calleja, Quantification of the surface stress in microcantilever biosensors: revisiting Stoney’s equation. Nanotechnology 47, 475702 (2012)CrossRefGoogle Scholar
  11. 11.
    J.S. Peng, W. Feng, H.Y. Lin, C.H. Hsueh, S. Lee, Measurements of residual stresses in the Parylene C film/silicon substrate using a microcantilever beam. J. Micromech. Microeng. 23, 095001 1-7 (2013)Google Scholar
  12. 12.
    U. Andreaus, L. Placidi, G. Rega, Microcantilever dynamics in tapping mode atomic force microscopy via higher eigenmodes analysis. J. Appl. Phys. 113, 224302 1-14 (2013)CrossRefGoogle Scholar
  13. 13.
    I. Dufour, E. Lemaire, B. Caillard, H. Debeda, C. Lucat, S.M. Heinrich, F. Josse, O. Brand, Effect of hydro-dynamic force on microcantilever vibrations; applications to liquid-phase chemical sensing. Sens. Actuators B Chem. 192, 664–672 (2014)CrossRefGoogle Scholar
  14. 14.
    A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors (Elsevier Science Publishing Company, North Holland, 1987)Google Scholar
  15. 15.
    D.M. Todorović, P.M. Nikolić, A.I. Bojičić, K.T. Radulovic, Thermoelastic and electronic strain contributions to the frequency transmission photoacoustic effect in semiconductors. Phys. Rev. B 55, 15631–15642 (1997)ADSCrossRefGoogle Scholar
  16. 16.
    D.M. Todorović, P.M. Nikolić, A.I. Bojičić, Photoacoustic frequency transmission technique: electronic deformation mechanism in semiconductor. J. Appl. Phys. 85, 7716–7726 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    Y.Q. Song, J.T. Bai, Z. Zhao, Y.F. Kang, Study on the vibration of optically excited microcantilevers under fractional-order thermoelastic theory. Int. J. Thermophys. 36, 733–746 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    D.M. Todorović, P.M. Nikolić, Carrier transport contribution to thermoelastic and electronic deformation in semiconductor, in Semiconductors and Electronic Materials, ed. by A. Mandelis, P. Hess (SPIE Optical Engineering Press, Belingham, 2000), pp. 273–318Google Scholar
  19. 19.
    D.M. Todorović, Plasma, thermal and elastic waves in semiconductors. Rev. Sci. Instrum. 74, 582–585 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Y.Q. Song, B. Cretin, D.M. Todorovic, P. Vairac, Study of laser excited vibration of silicon cantilever. J. Appl. Phys. 104, 104909 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Y.Q. Song, B. Cretin, D.M. Todorovic, P. Vairac, Study of photothermal vibrations of semiconductor cantilevers near the resonant frequency. J. Phys. D Appl. Phys. 41, 155106 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    N.A. Fleck, J.W. Hutchinson, Phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825–1827 (1993)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    N.A. Fleck, G.M. Muller, M.F. Ashby, J.W. Hutchinson, Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475–487 (1994)CrossRefGoogle Scholar
  24. 24.
    J.S. Stolken, A.G. Evans, A microbend test method for measuring the plasticity length scale. J. Acta Mater. 46, 5109–5115 (1998)CrossRefGoogle Scholar
  25. 25.
    D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    A.W. Mcfarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J. Micromech. Microeng. 15, 1060–1067 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    W.T. Koiter, Couple-stresses in the theory of elasticity: I and II. Proc. K. Neder. Akad. Weterschappen Ser. B 67, 17–44 (1964)MathSciNetzbMATHGoogle Scholar
  28. 28.
    R.D. Mindlin, H.F. Tiersten, Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. 11, 415–448 (1962)MathSciNetCrossRefGoogle Scholar
  29. 29.
    U.B.C.O. Ejike, The plane circular crack problem in the linearized couple-stress theory. Int. J. Eng. Sci. 7, 947–961 (1969)CrossRefGoogle Scholar
  30. 30.
    M. Kishida, K. Sasaki, Torsion of a circular bar with annular groove in couple-stress theory. Int. J. Eng. Sci. 28, 773–781 (1990)CrossRefGoogle Scholar
  31. 31.
    F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Coupled stress based strain gradient theory for elasticity. Int. J. Solid Struct. 39, 2731–2743 (2002)CrossRefGoogle Scholar
  32. 32.
    S.K. Park, X.L. Gao, Bernoulli-Euler beam model based on a modified couple stress theory. J. Micromech. Microeng. 16, 2355–2359 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    S. Kong, S. Zhou, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli–Euler micro-beams. Int. J. Eng. Sci. 46, 427–437 (2008)CrossRefGoogle Scholar
  34. 34.
    L. Wang, Size-dependent vibration characteristics of fluid-conveying microtubes. J. Fluids Struct. 26, 675–684 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    E. Taati, M. Molaei Najafabadi, Size-dependent generalized thermoelasticity model for Timoshenko microbeams. Acta Mech. 225, 1823–1842 (2014)MathSciNetCrossRefGoogle Scholar
  36. 36.
    M.H. Kahrobaiyan, M. Asghari, M.T. Ahmadian, A Timoshenko beam element based on the modified couple stress theory. Int. J. Eng. Sci. 79, 75–83 (2014)zbMATHGoogle Scholar
  37. 37.
    M. Rahaeifard, M.T. Ahmadian, K. Firoozbakhsh, Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage. Proc. IMechE C J. Mech. Eng. Sci. 228, 896–906 (2014)CrossRefGoogle Scholar
  38. 38.
    M. Rahaeifard, M.T. Ahmadian, K. Firoozbakhsh, Vibration analysis of electrostatically actuated nonlinear microbridges based on the modified couple stress theory. Appl. Math. Model. 39, 6694–6704 (2015)MathSciNetCrossRefGoogle Scholar
  39. 39.
    M. Rahaeifard, M.H. Kahrobaiyan, M.T. Ahmadian, K. Firoozbakhsh, Size-dependent pull-in phenomena in nonlinear microbridges. Int. J. Mech. Sci. 54, 306–310 (2012)CrossRefGoogle Scholar
  40. 40.
    M.H. Kahrobaiyan, M. Asghari, M. Rahaeifard, M.T. Ahmadian, Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1985–1994 (2010)CrossRefGoogle Scholar
  41. 41.
    M.H. Kahrobaiyan, M. Rahaeifard, M.T. Ahmadian, A size-dependent yield criterion. Int. J. Eng. Sci. 74, 151–161 (2014)CrossRefGoogle Scholar
  42. 42.
    E. Jomehzadeh, H.R. Noori, A.R. Saidi, The size-dependent vibration analysis of micro-plates based on a modified couple stress theory. Physica E 43, 877–883 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    Y.G. Wang, W.H. Lin, N. Liu, Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory. Appl. Math. Model. 39, 117–127 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Y. Q. Song
    • 1
    Email author
  • B. Cretin
    • 2
  • D. M. Todorovic
    • 3
  • P. Vairac
    • 2
  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace EngineeringXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.Femto-ST, Université, de Franche-Comté, CNRS, ENSMM, UTBMBesanҫonFrance
  3. 3.Institute for Multidisciplinary Research, University of BelgradeBelgradeSerbia

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