Abstract
This chapter discusses the nonlinear dynamics of an electrically actuated resonator as a case study in some depth. Several experimental data of the static and dynamic responses will be shown. After that, we discuss several modeling and simulation techniques to explain the measurements, particularly, the measured pull-in data. A shooting technique to find periodic motion and a basin-of-attraction technique will be illustrated and demonstrated. These are used to shed light on the fractal or chaotic-like nature of the dynamic behavior near the pull-in regime. Bifurcation analysis will be conducted based on the so-called Dover-Cliff integrity curves, which help justify the experimental measurements. This complicated behavior of the resonator will be then proposed to realize a new class of devices that combines the functionality of a mass detector and a switch. Finally, delayed-feedback control technique will be demonstrated as a powerful method to enhance the stability of the resonator.
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Alsaleem F, Younis M I, Ouakad H (2009) On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators. Journal of Micromechanics and Microengineering, 19:045013(1–14)
Alsaleem F M, Younis M I, and Ruzziconi L (2010) An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically. Journal of Microelectromechanical Systems. 19-4:794–806
Nayfeh A and Balachandran B (1995) Applied nonlinear dynamics. Wiley, New York
Thompson J and Stewart H (2001) Nonlinear dynamics and chaos. Wiley, New York
Lenci S and Rega G (2003) Optimal control of non-regular dynamics in a Duffing oscillator. Nonlinear Dynamics. 33:71–86
Lenci S and Rega, G (2006) Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam. Journal of Micromechanics and Microengineering. 16:390–401
Lenci S and Rega G (2008) Dynamical integrity and control of nonlinear mechanical oscillators. Journal of Vibration and Control. 159–179: doi:10.1177/1077546307079403
Ruzziconi L, Younis M I, and Lenci S (2010) Dynamical integrity for interpreting experimental data and ensuring safety in electrostatic MEMS. Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, Aberdeen, Scotland, UK, pp: 27–30
Nayfeh A H, Ouakad H M, Najar F, Choura S and Abdel-Rahman E M (2010) Nonlinear dynamics of a resonant gas sensor. Nonlinear Dynamics. 59–4:607–618
Nayfeh A, Younis M I, and Abdel-Rahman E (2007) Dynamic pull-in phenomenon in MEMS resonator. Nonlinear Dynamics. 48:153–163
Nayfeh A H and Younis M I (2005) Dynamics of MEMS resonators under superharmonic and subharmonic excitations. Journal of Micromechanics and Microengineering. 15:1840–1847
Younis M I and Al-saleem F M (2009) Exploration of new concepts for mass detection in electrostatically-actuated structures based on nonlinear phenomena. Nonlinear Dynamics. 4–2:doi:10.1115/1.3079785, 15 pages
Lange D, Brand O, and Baltes H (2002) CMOS cantilever sensor systems: atomic-force microscopy and gas sensing applications. Springer, Berlin
Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Physics Letters A. 170:421–428
Nakajima H and Ueda Y (1998) Half-period delayed feedback control for dynamical systems with symmetries. Physical Review E. 58:1757–1763
Yamasue K and Hikihara T (2006) Persistence of chaos in a time-delayed-feedback controlled duffing system. Physical Review E. 73:036209–16
Yamasue K and Hikihara T (2006) Control of microcantilevers in dynamic force microscopy using time delayed feedback. Review of Scientific Instruments. 77:53703–16
Alsaleem F M and Younis M I (2010) Stabilization of electrostatic MEMS resonators using delayed feedback controller. Smart Materials and Structures. 19:035016
Alsaleem F M and Younis M I (2011) Integrity analysis of electrostatically actuated resonators with delayed feedback controller. Dynamic Systems, Measurements, and Control.133:019101JD
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Younis, M.I. (2011). Nonlinear Dynamics of an Electrically Actuated Resonator. In: MEMS Linear and Nonlinear Statics and Dynamics. Microsystems, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6020-7_7
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DOI: https://doi.org/10.1007/978-1-4419-6020-7_7
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