Size-dependent behaviour of electrically actuated microcantilever-based MEMS
Tóm tắt
In this paper, the nonlinear size-dependent static and dynamic behaviours of a microelectromechanical system under an electric excitation are investigated. A microcantilever is considered for the modelling of the deformable electrode of the MEMS. The governing equation of motion is derived based on the modified couple stress theory (MCST), a non-classical model capable of capturing small-size effects. With the aid of a high-dimensional Galerkin scheme, the nonlinear partial differential equation governing the motion of the deformable electrode is converted into a reduced-order model of the system. Then, the pseudo-arclength continuation technique is used to solve the governing equations. In order to investigate the static behaviour and static pull-in instabilities, the system is excited only by the electrostatic actuation (i.e., a DC voltage). The results obtained for the static pull-in instability predicted by both the classical theory and MCST are compared. In the second stage of analysis, the nonlinear dynamic behaviour of the deformable electrode due to the AC harmonic actuation is investigated around the deflected configuration, incorporating size dependence.
Tài liệu tham khảo
Abdel-Rahman, E.M., Nayfeh, A.H.: Secondary resonances of electrically actuated resonant microsensors. J. Micromech. Microeng. 13(3), 491–501 (2003)
Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95(1–4), 299–314 (1999)
Ansari, R., Gholami, R., Darabi, M.: Thermal buckling analysis of embedded single-walled carbon nanotubes with arbitrary boundary conditions using the nonlocal Timoshenko beam theory. J. Therm. Stresses 34(12), 1271–1281 (2011)
Ansari, R., Gholami, R., Darabi, M.: Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditions. Acta Mech. 223(12), 2523–2536 (2012a)
Ansari, R., Gholami, R., Darabi, M.A.: A nonlinear Timoshenko beam formulation based on strain gradient theory. J. Mech. Mater. Struct. 7(2), 195–211 (2012b)
Ansari, R., Gholami, R., Shojaei, M.F., Mohammadi, V., Darabi, M.: Surface stress effect on the pull-in instability of hydrostatically and electrostatically actuated rectangular nanoplates with various edge supports. J. Eng. Mater. Technol. 134, 041013 (2012c)
Asghari, M., Kahrobaiyan, M.H., Nikfar, M., Ahmadian, M.T.: A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory. Acta Mech. 223(6), 1233–1249 (2012)
Baghani, M.: Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory. Int. J. Eng. Sci. 54, 99–105 (2012)
Doedel, E., Paffenroth, R., Champneys, A., Fairgrieve, T., Kuznetsov, Y.A., Oldeman, B., Sandstede, B., Wang, X.: AUTO-07P: continuation and bifurcation software for ordinary differential equations (2007)
Farokhi, H., Ghayesh, M.H.: Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory. Int. J. Mech. Sci. 90, 133–144 (2015)
Farokhi, H., Ghayesh, M., Amabili, M.: Nonlinear resonant behavior of microbeams over the buckled state. Appl. Phys. 113(2), 297–307 (2013a)
Farokhi, H., Ghayesh, M.H., Amabili, M.: In-plane and out-of-plane nonlinear dynamics of an axially moving beam. Chaos Solitons Fractals 54, 101–121 (2013b)
Farokhi, H., Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. Int. J. Eng. Sci. 68, 11–23 (2013c)
Ghayesh, M.H.: Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation. Int. J. Non-Linear Mech. 45(4), 382–394 (2010)
Ghayesh, M.: Stability and bifurcations of an axially moving beam with an intermediate spring support. Nonlinear Dyn. 69(1), 193–210 (2012a)
Ghayesh, M.: Subharmonic dynamics of an axially accelerating beam. Arch. Appl. Mech. 82(9), 1169–1181 (2012b)
Ghayesh, M.H.: Coupled longitudinal–transverse dynamics of an axially accelerating beam. J. Sound Vib. 331(23), 5107–5124 (2012c)
Ghayesh, M.H.: Nonlinear dynamic response of a simply-supported Kelvin–Voigt viscoelastic beam, additionally supported by a nonlinear spring. Nonlinear Anal. Real World Appl. 13(3), 1319–1333 (2012d)
Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of axially moving viscoelastic beams over the buckled state. Comput. Struct. 112–113, 406–421 (2012a)
Ghayesh, M.H., Amabili, M.: Three-dimensional nonlinear planar dynamics of an axially moving Timoshenko beam. Arch. Appl. Mech. 83(4), 591–604 (2012b)
Ghayesh, M.H., Amabili, M.: Non-linear global dynamics of an axially moving plate. Int. J. Non-Linear Mech. 57, 16–30 (2013a)
Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of an axially moving Timoshenko beam with an internal resonance. Nonlinear Dyn. 73, 39–52 (2013b)
Ghayesh, M.H., Amabili, M.: Post-buckling bifurcations and stability of high-speed axially moving beams. Int. J. Mech. Sci. 68, 76–91 (2013c)
Ghayesh, M.H., Amabili, M.: Steady-state transverse response of an axially moving beam with time-dependent axial speed. Int. J. Non-Linear Mech. 49, 40–49 (2013d)
Ghayesh, M.H., Amabili, M.: Coupled longitudinal–transverse behaviour of a geometrically imperfect microbeam. Compos. B Eng. 60, 371–377 (2014)
Ghayesh, M.H., Farokhi, H.: Nonlinear dynamics of a microscale beam based on the modified couple stress theory. Compos. B Eng. 50, 318–324 (2013)
Ghayesh, M.H., Farokhi, H.: Nonlinear dynamics of microplates. Int. J. Eng. Sci. 86, 60–73 (2015)
Ghayesh, M.H., Kazemirad, S., Darabi, M.A.: A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions. J. Sound Vib. 330(22), 5382–5400 (2011)
Ghayesh, M.H., Kazemirad, S., Amabili, M.: Coupled longitudinal–transverse dynamics of an axially moving beam with an internal resonance. Mech. Mach. Theory 52, 18–34 (2012a)
Ghayesh, M.H., Kazemirad, S., Reid, T.: Nonlinear vibrations and stability of parametrically exited systems with cubic nonlinearities and internal boundary conditions: a general solution procedure. Appl. Math. Model. 36(7), 3299–3311 (2012b)
Ghayesh, M., Farokhi, H., Amabili, M.: Coupled nonlinear size-dependent behaviour of microbeams. Appl. Phys. A 112(2), 329–338 (2013a)
Ghayesh, M.H., Amabili, M., Farokhi, H.: Coupled global dynamics of an axially moving viscoelastic beam. Int. J. Non-Linear Mech. 51, 54–74 (2013b)
Ghayesh, M.H., Amabili, M., Farokhi, H.: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. Int. J. Eng. Sci. 63, 52–60 (2013c)
Ghayesh, M.H., Amabili, M., Farokhi, H.: Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams. Int. J. Eng. Sci. 71, 1–14 (2013d)
Ghayesh, M.H., Farokhi, H., Amabili, M.: Nonlinear behaviour of electrically actuated MEMS resonators. Int. J. Eng. Sci. 71, 137–155 (2013e)
Ghayesh, M.H., Farokhi, H., Amabili, M.: In-plane and out-of-plane motion characteristics of microbeams with modal interactions. Compos. B Eng. 60, 423–439 (2014)
Gholipour, A., Farokhi, H., Ghayesh, M.: In-plane and out-of-plane nonlinear size-dependent dynamics of microplates. Nonlinear Dyn. 79(3), 1771–1785 (2014)
Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14(6), 431–440 (1978)
Jia, X.L., Yang, J., Kitipornchai, S., Lim, C.W.: Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation. J. Sound Vib. 331(14), 3397–3411 (2012)
Kazemirad, S., Ghayesh, M., Amabili, M.: Thermo-mechanical nonlinear dynamics of a buckled axially moving beam. Arch. Appl. Mech. 83(1), 25–42 (2013)
Kim, P., Bae, S., Seok, J.: Resonant behaviors of a nonlinear cantilever beam with tip mass subject to an axial force and electrostatic excitation. Int. J. Mech. Sci. 64(1), 232–257 (2012)
Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003)
Li, Y., Meguid, S.A., Fu, Y., Xu, D.: Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 470(2162), 20130473 (2013a)
Li, Y., Meguid, S.A., Fu, Y., Xu, D.: Unified nonlinear quasistatic and dynamic analysis of RF-MEMS switches. Acta Mech. 224(8), 1741–1755 (2013b)
Mestrom, R.M.C., Fey, R.H.B., van Beek, J.T.M., Phan, K.L., Nijmeijer, H.: Modelling the dynamics of a MEMS resonator: simulations and experiments. Sens. Actuators A 142(1), 306–315 (2008)
Nayfeh, A.H., Younis, M.I.: Dynamics of MEMS resonators under superharmonic and subharmonic excitations. J. Micromech. Microeng. 15(10), 1840–1847 (2005)
Ouakad, H.M., Younis, M.I.: On using the dynamic snap-through motion of MEMS initially curved microbeams for filtering applications. J. Sound Vib. 333(2), 555–568 (2014)
Rao, S.S.: Vibration of Continuous Systems. Wiley, Hoboken (2007)
Reddy, J.N., Kim, J.: A nonlinear modified couple stress-based third-order theory of functionally graded plates. Compos. Struct. 94(3), 1128–1143 (2012)
Rokni, H., Seethaler, R.J., Milani, A.S., Hosseini-Hashemi, S., Li, X.-F.: Analytical closed-form solutions for size-dependent static pull-in behavior in electrostatic micro-actuators via Fredholm integral equation. Sens. Actuators A 190, 32–43 (2013)
Timoshenko, S., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, Singapore (1970)
Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)
Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, New York (2011)
Younis, M.I., Nayfeh, A.H.: A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dyn. 31(1), 91–117 (2003)
Younis, M.I., Abdel-Rahman, E.M., Nayfeh, A.: A reduced-order model for electrically actuated microbeam-based MEMS. J. Microelectromech. Syst. 12(5), 672–680 (2003)