Abstract
Nonlinear dynamic investigation of electrostatically actuated micro-electro-mechanical-system (MEMS) microcantilever structures is presented. The nonlinear analysis aims to better quantify, than the linear model, the instability threshold associated with electrostatically actuated MEMS structures, where the pull-in voltage of the microcantilever is determined using a phase portrait analysis of the microsystem. The microcantilever is modeled as a lumped mass-spring system. The nonlinear electrostatic force is incorporated into the lumped microsystem through an equivalent area of the microcantilever for a given electrostatic potential. Electro-mechanical force balance plots are obtained for various electrostatic potentials from which the static equilibrium positions of the microcantilever are obtained and the respective conservative energy values are determined. Subsequently, phase portrait plots are obtained for the corresponding energy values from which the pull-in voltage is estimated for the microsystem. This pull-in voltage value is in good agreement with the previously published results for the same geometric and material parameters. The results obtained for linear electrostatic models are also presented for comparison.
Similar content being viewed by others
References
Abdel-Rahman EM, Younis MI, Nayfeh AH (2002) Characterization of the mechanical behavior of an electrically actuated microbeam. J Micromech Microeng 12:759–766
Chen X, Fox CHJ, Mcwilliam S (2004) Optimization of a cantilever microswitch with piezoelectric actuation. J Intell Mater Syst Struct 15:823–834
Chu PB, Pister KSJ (1994) Analysis of closed-loop control of parallel-plate electrostatic microgrippers. In: Proceedings of the international conference on robotics and automation, pp 820–825
Hagedorn P, Stadler W (1982) Non-linear oscillations, 2nd edn. Clarendon Press, Oxford
Hu YC, Chang CM, Huang SC (2003) Some design considerations on the electrostatically actuated microstructures. Sens Actuators A 112:155–161
Brüel & Kjær S. & V. (1998) Lecture note, BA 7676–7712
Lai Y, McDonald J, Kujath M, Hubbard T (2004) Force, deflection and power measurements of toggled microthermal actuators. J Micromech Microeng 14:49–56
Luo ACJ, Wang FY (2004) Nonlinear dynamics of a micro-electro-mechanical system with time-varying capacitors. J Vib Acoust 126:77–83
Micralyne Inc., Canadian Microelectronics Corporation, MicraGeM (2004) A silicon-on-insulator based micromachining process, V3.0 (beta version)
MikroMasch Technical Data Sheet (2002) CSC38/AlBS/15
Nathanson HC, Newell WE, Wickstrom RA, Davis J (1967) The resonant gate transistor. Trans Electron Devices 14:117–133
Piekarski B, Dubey M, DeVoe D, Zakar E, Zeto R, Conrad J, Piekarz R, Ervin M (1999) Fabrication of suspended piezoelectric microresonators. Integr Ferroelectr 24:147–154
Rinaldi G, Packirisamy M, Stiharu I (2004a) An improved method for predicting microfabrication influence in atomic force microscopy performances. Int J Nanotechnol 1:292–306
Rinaldi G, Packirisamy M, Stiharu I (2004b) Electrostatic boundary conditioning of MEMS devices. In: Proceedings of the 8th international Cairo University MDP, conference on current advances in mechanical design and production VIII, Cairo–Egypt, 4–6 January 2004
Rinaldi G, Packirisamy M, Stiharu I (2006) Dynamic testing of micromechanical structures under thermo-electro-mechanical influences. Measurement 40:563–574
Rinaldi G, Packirisamy M, Stiharu I (2007) Boundary characterization of MEMS structures through electro-mechanical testing. Sens Actuators 143(2):415–422
Taschini S, Baltes H, Korvink JG (2000) Non linear analysis of electrostatic actuation in MEMS with arbitrary geometry. In: Proceedings of the international conference on modeling and simulation of microsystems, pp 485–488
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kalyanaraman, R., Rinaldi, G., Packirisamy, M. et al. Equivalent area nonlinear static and dynamic analysis of electrostatically actuated microstructures. Microsyst Technol 19, 61–70 (2013). https://doi.org/10.1007/s00542-012-1621-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-012-1621-y