Structural Engineering and Mechanics

  • 제61권2호
  • /
  • Pages.193-207
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear vibration analysis of an electrostatically excited micro cantilever beam coated by viscoelastic layer with the aim of finding the modified configuration

  • Poloei, E. (Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University) ;
  • Zamanian, M. (Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University) ;
  • Hosseini, S.A.A. (Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University)
  • 투고 : 2016.05.21
  • 심사 : 2016.08.09
  • 발행 : 2017.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

키워드

참고문헌

  1. Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H. (2002), "Characterization of the mechanical behavior of an electrically actuated microbeam", Micromech. Microeng., 12(6), 759-766. https://doi.org/10.1088/0960-1317/12/6/306
  2. Aboelkassem, Y., Nayfeh, A.H. and Ghommem, M. (2010), "Biomass sensor using an electrostatically actuated microcantilever in a vacuum microchannel", Microsyst. Technol., 16(10), 1749-1755. https://doi.org/10.1007/s00542-010-1087-8
  3. Bataineh, A.M. and Younis, M.I. 2015, "Dynamics of a clampedclamped microbeam resonator considering fabrication imperfections", Microsyst. Technol., 21(11), 2425-2434. https://doi.org/10.1007/s00542-014-2349-7
  4. Beeby, S., Ensell, G., Kraft, M. and White, N. (2004), MEMS Mechanical Sensors, Artech House, Inc, Boston, London.
  5. Boudjiet, M.T., Bertrand, J., Mathieu, F., Nicu, L., Mazenq, L., Leichle, T., Heinrich, S. M., Pellet, C. and Dufour, I. (2015), "Geometry optimization of uncoated silicon microcantileverbased gas density sensors", Sens. Actuat. B: Chem., 208, 600-607 https://doi.org/10.1016/j.snb.2014.11.067
  6. Chaterjee, S. and Pohit, G.A. (2009), "Large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams", J. Sound Vib., 322(4-5), 969-986. https://doi.org/10.1016/j.jsv.2008.11.046
  7. Chitsaz Yazdi, F. and Jalali, A. (2015), "Vibration behavior of a viscoelastic composite microbeam under simultaneous electrostatic and piezoelectric actuation", Mech. Time-Depend. Mater., 19(3), 277-304.
  8. Dufour, I., Lochon, F., Heinrich, S.M., Josse, F. and Rebiere, D. (2007), "Effect of coating viscoelasticity on quality factor and limit of detection of microcantilever chemical sensors", Sens. J., 7(2), 230-236. https://doi.org/10.1109/JSEN.2006.888600
  9. Fu, Y.M., Zhang, J. and Bi, R.G. (2009), "Analysis of the nonlinear dynamic stability for an electrically actuated viscoelastic microbeam", Microsyst. Technol., 15(5), 763-769. https://doi.org/10.1007/s00542-009-0791-8
  10. Ghayesh, M.H., Farokhi, H. and Alici, G. (2015), "Size-dependent electro-elasto-mechanics of MEMS with initially curved deformable electrodes", Int. J. Mech. Sci., 103, 247-264. https://doi.org/10.1016/j.ijmecsci.2015.09.011
  11. Hoseini, S.M., Shooshtari, A., Kalhori, H. and Mahmoodi, S.M. (2014), "Nonlinear-forced vibrations of piezoelectrically actuated viscoelastic cantilevers", Nonlin. Dyn., 78(1), 571-583. https://doi.org/10.1007/s11071-014-1461-7
  12. Huang, Y.T., Chen, H.L. and Hsu, W. (2014), "An analytical model for calculating the pull-in voltage of micro cantilever beams subjected to tilted and curled effects", Microelec. Eng., 125, 73-77. https://doi.org/10.1016/j.mee.2013.12.030
  13. Kim, I.K. and Lee, S.I. (2015), "Nonlinear resonances of a singlewall carbon nanotube cantilever", Physica E: Low-dimens. Syst. Nanostruct., 67, 159-167. https://doi.org/10.1016/j.physe.2014.11.022
  14. Lizhoung, X. and Xiaoli, J. (2007), "Electromechanical coupled nonlinear dynamics for microbeams", Arch. Appl. Mech., 77(7), 485-502. https://doi.org/10.1007/s00419-007-0110-8
  15. Mahmoodi, S.N., Afshari, M. and Jalili, N. (2008), "Nonlinear vibrations of piezoelectric microcantilevers for biologicallyinduced surface stress sensing", Commun. Nonlin. Sci. Numer. Simul., 13(9), 1964-1977. https://doi.org/10.1016/j.cnsns.2007.03.030
  16. Mahmoodi, S.N., Khadem, S.E. and Kokabi, M. (2007), "Nonlinear free vibrations of Kelvin-Voigt visco-elastic beams", Int. J. Mech. Sci., 49(6), 722-732. https://doi.org/10.1016/j.ijmecsci.2006.10.005
  17. Masri, K.M. and Younis, M.I. (2015), "Investigation of the dynamics of a clamped-clamped microbeam near symmetric higher order modes using partial electrodes", Int. J. Dyn. Control, 3(2), 173-182. https://doi.org/10.1007/s40435-014-0137-y
  18. Najar, F., El-Borgi, S., Reddy, J.N. and Mrabet, K. (2015), "Nonlinear nonlocal analysis of electrostatic nanoactuators", Compos. Struct., 120, 117-128. https://doi.org/10.1016/j.compstruct.2014.09.058
  19. Nayfeh, A.H. and Pai, P.F. (2004), Linear and Nonlinear Structural Mechanics, Wiley, New York.
  20. Nayfeh, A.H. and Younis, M.I. (2005), "Dynamics of MEMS resonators under superharmonic and subharmonic excitations", Micromech. Microeng., 15(10), 1840-1847. https://doi.org/10.1088/0960-1317/15/10/008
  21. Nayfeh, A.H., Younis, M.I. and Abdel-Rahman, E.M. (2007), "Dynamic pull-in phenomenon in MEMS resonators", Nonlin. Dyn., 48(1), 153-163. https://doi.org/10.1007/s11071-006-9079-z
  22. Nie, M., Huang, Q. and Li, W. (2006), "Measurement of material properties of individual layers for composite films by a pull-in method", J. Phys. Conf. Ser., 34(34), 516-521. https://doi.org/10.1088/1742-6596/34/1/085
  23. Poloei, E., Zamanian, M. and Hosseini, S.A.A. (2015), "Static deflection and natural frequency analysis of two-layered electrostatically actuated microcantilever for finding the optimum configuration", Mod. Mech. Eng., 15(5), 245-253.
  24. Raeisifard, H., Zamanian, M., Nikkhah Bahrami, M., Yousefi-Koma, A. and Raeisi Fard, H. (2014), "On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage", J. Sound Vib., 333(21), 5494-5510. https://doi.org/10.1016/j.jsv.2014.05.050
  25. Rahaeifard, M. and Ahmadian, M.T. (2015), "On pull-in instabilities of microcantilevers", Int. J. Eng. Sci., 87, 23-31. https://doi.org/10.1016/j.ijengsci.2014.11.002
  26. Rasekh, M. and Khadem, S.E. (2011), "Pull-in analysis of an electrostatically actuated nano-cantilever beam with nonlinearity in curvature and inertia", Int. J. Mech. Sci., 53(2), 108-115. https://doi.org/10.1016/j.ijmecsci.2010.11.007
  27. Rasekh, M. and Khadem, S.E. (2013), "Design and performance analysis of a nanogyroscope based on electrostatic actuation and capacitive sensing", J. Sound Vib., 332(23), 6155-6168. https://doi.org/10.1016/j.jsv.2013.06.024
  28. Rezazadeh, G. (2008), "A comprehensive model to study nonlinear behavior of multilayered micro beam switches", Microsyst. Technol., 14(1), 135-141. https://doi.org/10.1007/s00542-007-0398-x
  29. Rezazadeh, G., Keyvani, A. and Jafarmadar, S. (2012), "On a MEMS based dynamic remote temperature sensor using transverse vibration of a bi-layer micro-cantilever", Measur., 45(3), 580-589. https://doi.org/10.1016/j.measurement.2011.10.004
  30. Shooshtari, A., Hoseini, S.M., Mahmoodi, S.N. and Kalhori, H. (2012), "Analytical solution for nonlinear free vibrations of viscoelastic microcantilevers covered with a piezoelectric layer", Smart Mater. Struct., 21(7), 75015- 75025. https://doi.org/10.1088/0964-1726/21/7/075015
  31. Sun, W., Sun, Y., Yu, Y. and Zheng, S. (2016), "Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method", Struct. Eng. Mech., 59(1), 1-14. https://doi.org/10.12989/sem.2016.59.1.001
  32. Wang, K.F. and Wang, B.L. (2015), "A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature", Physica E: Low-dimens. Syst. Nanostruct., 66, 197-208. https://doi.org/10.1016/j.physe.2014.10.012
  33. Yang, W.D. and Wang, X. (2016), "Nonlinear pull-in instability of carbon nanotubes reinforced nano-actuator with thermally corrected Casimir force and surface effect", Int. J. Mech. Sci., 107, 34-42. https://doi.org/10.1016/j.ijmecsci.2015.12.025
  34. Younis, M. I. (2011), MEMS Linear and Nonlinear Statics and Dynamics, Springer US, New York.
  35. Younis, M.I. (2015), "Multi-mode excitation of a clampedclamped microbeam resonator", Nonlin. Dyn., 80(3), 1531-1541. https://doi.org/10.1007/s11071-015-1960-1
  36. Younis, M.I. and Alsaleem, F. (2009), "Exploration of new concepts for mass detection in electrostatically-actuated structures based on nonlinear phenomena", J. Comput. Nonlin. Dyn., 4(2), 021010-021025. https://doi.org/10.1115/1.3079785
  37. Younis, M.I. and Nayfeh, A.H. (2003), "A Study of the nonlinear response of a resonant microbeam to an electric actuation", Nonlin. Dyn., 3(1), 91-117.
  38. Zamanian, M. and Karimiyan, A. (2015), "Analysis of the mechanical behavior of a doubled microbeam configuration under electrostatic actuation", Int. J. Mech. Sci., 93, 82-92. https://doi.org/10.1016/j.ijmecsci.2015.01.011
  39. Zamanian, M. and Khadem, S.E. (2010), "Nonlinear vibration of an electrically actuated microresonator tuned by combined DC piezoelectric and electric", Smart Mater. Struct., 19(1), 15012-15031. https://doi.org/10.1088/0964-1726/19/1/015012
  40. Zamanian, M., Khadem, S.E. and Mahmoodi, S.N. (2010), "Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation", Struct. Eng. Mech., 35(4), 387-407. https://doi.org/10.12989/sem.2010.35.4.387

피인용 문헌

  1. Modeling and analysis of power harvesting by a piezoelectric layer coated on an electrostatically actuated microcantilever vol.5, pp.12, 2018, https://doi.org/10.1088/2053-1591/aadf15
  2. Vibrations of a Resonant Gas Sensor Under Multicoupled Fields vol.14, pp.4, 2019, https://doi.org/10.1115/1.4042292
  3. Effect of different viscoelastic models on free vibrations of thick cylindrical shells through FSDT under various boundary conditions vol.73, pp.3, 2020, https://doi.org/10.12989/sem.2020.73.3.319