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An electrically actuated imperfect microbeam: dynamical integrity for interpreting and predicting the device response. (English) Zbl 1293.74271
Summary: In this study we deal with a microelectromechanical system (MEMS) and develop a dynamical integrity analysis to interpret and predict the experimental response. The device consists of a clamped-clamped polysilicon microbeam, which is electrostatically and electrodynamically actuated. It has non-negligible imperfections, which are a typical consequence of the microfabrication process. A single-mode reduced-order model is derived and extensive numerical simulations are performed in a neighborhood of the first symmetric natural frequency, via frequency response diagrams and behavior chart. The typical softening behavior is observed and the overall scenario is explored, when both the frequency and the electrodynamic voltage are varied. We show that simulations based on direct numerical integration of the equation of motion in time yield satisfactory agreement with the experimental data. Nevertheless, these theoretical predictions are not completely fulfilled in some aspects. In particular, the range of existence of each attractor is smaller in practice than in the simulations. This is because these theoretical curves represent the ideal limit case where disturbances are absent, which never occurs under realistic conditions. A reliable prediction of the actual (and not only theoretical) range of existence of each attractor is essential in applications. To overcome this discrepancy and extend the results to the practical case where disturbances exist, a dynamical integrity analysis is developed. After introducing dynamical integrity concepts, integrity profiles and integrity charts are drawn. They are able to describe if each attractor is robust enough to tolerate the disturbances. Moreover, they detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable, i.e. they provide valuable information to operate the device in safe conditions according to the desired outcome and depending on the expected disturbances.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F15 Electromagnetic effects in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74M25 Micromechanics of solids
Software:
Dynamics
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[1] Senturia SD (2001) Microsystem design. Kluwer Academic, Dordrecht
[2] Younis MI (2011) MEMS linear and nonlinear statics and dynamics. Springer, Berlin
[3] Towfighian, S; Heppler, GR; Abdel Rahman, EM, Low-voltage closed loop MEMS actuators, Nonlinear Dyn, 69, 565-575, (2012)
[4] Krylov, S; Ilic, BR; Schreiber, D; Seretensky, S; Craighead, H, The pull-in behavior of electrostatically actuated bistable microbeams, J Micromech Microeng, 18, 55026, (2008)
[5] Mestrom, RMC; Fey, RHB; Beek, JTM; Phan, KL; Nijmeijer, H, Modelling the dynamics of a MEMS resonator: simulations and experiments, Sens Actuators A, 142, 306-315, (2008)
[6] Rhoads, JF; Shaw, SW; Turner, KL; Moehlis, J; DeMartini, BE, Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators, J Sound Vib, 296, 797-829, (2006)
[7] Gottlieb, O; Champneys, A; Rega, G (ed.); Vestroni, F (ed.), Global bifurcations of nonlinear thermoelastic microbeams subject to electrodynamic actuation, No. 122, 117-126, (2005), Berlin
[8] Alsaleem, FM; Younis, MI; Ouakad, HM, On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators, J Micromech Microeng, 19, (2009)
[9] Hornstein, S; Gottlieb, O, Nonlinear multimode dynamics and internal resonances of the scan process in noncontacting atomic force microscopy, J Appl Phys, 112, (2012) · Zbl 1178.74122
[10] DeMartini, BE; Butterfield, HE; Moehlis, J; Turner, KL, Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation, J Microelectromech Syst, 16, 1314-1323, (2007)
[11] De, SK; Aluru, NR, Complex nonlinear oscillations in electrostatically actuated microstructures, J Microelectromech Syst, 15, 355-369, (2006)
[12] Chavarette, FR; Balthazar, JM; Felix, JLP; Rafikov, M, A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design, Commun Nonlinear Sci Numer Simul, 14, 1844-1853, (2009)
[13] Kniffka, TJ; Welte, J; Ecker, H, Stability analysis of a time-periodic 2-dof MEMS structure, No. 1493, 559-566, (2012)
[14] Dick, AJ; Balachandran, B; Mote, CD, Intrinsic localized modes in microresonator arrays and their relationship to nonlinear vibration modes, Nonlinear Dyn, 54, 13-29, (2008) · Zbl 1178.74078
[15] Cho, H; Jeong, B; Yu, MF; Vakakis, AF; McFarland, DM; Bergman, LA, Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities, Int J Solids Struct, 49, 2059-2065, (2012)
[16] Kozinsky, I; Postma, HWC; Kogan, O; Husain, A; Roukes, ML, Basins of attraction of a nonlinear nanomechanical resonator, Phys Rev Lett, 99, 201-207, (2007)
[17] Virgin LN (2000) Introduction to experimental nonlinear dynamics: a case study in mechanical vibration. Cambridge University Press, Cambridge
[18] Thompson, JMT, Chaotic behavior triggering the escape from a potential well, Proc R Soc Lond Ser A, 421, 195-225, (1989) · Zbl 0674.70035
[19] Soliman, MS; Thompson, JMT, Integrity measures quantifying the erosion of smooth and fractal basins of attraction, J Sound Vib, 135, 453-475, (1989) · Zbl 1235.70106
[20] Lenci, S; Rega, G, Optimal control of nonregular dynamics in a Duffing oscillator, Nonlinear Dyn, 33, 71-86, (2003) · Zbl 1038.70019
[21] Lenci S, Rega G, Ruzziconi L (2013, in press) The dynamical integrity concept for interpreting/predicting experimental behavior: from macro- to nano-mechanics. Philos Trans R Soc · Zbl 1392.70035
[22] Lansbury, AN; Thompson, JMT; Stewart, HB, Basin erosion in the twin-well Duffing oscillator: two distinct bifurcation scenarios, Int J Bifurc Chaos, 2, 505-532, (1992) · Zbl 0878.34034
[23] Lenci, S; Rega, G, A dynamical systems analysis of the overturning of rigid blocks, Warsaw, Poland, August 15-21 · Zbl 1236.70050
[24] Ruzziconi, L; Lenci, S; I, YM, An imperfect microbeam under an axial load and electric excitation: nonlinear phenomena and dynamical integrity, Int J Bifurc Chaos, 23, (2013) · Zbl 1270.74115
[25] Rega, G; Lenci, S, Identifying, evaluating, and controlling dynamical integrity measures in nonlinear mechanical oscillators, Nonlinear Anal TMA, 63, 902-914, (2005) · Zbl 1153.70307
[26] Soliman, MS; Thompson, JMT, Transient and steady state analysis of capsize phenomena, Appl Ocean Res, 13, 82-92, (1991)
[27] Infeld, E; Lenkowska, T; Thompson, JMT, Erosion of the basin of stability of a floating body as caused by dam breaking, Phys Fluids, 5, 2315-2316, (1993) · Zbl 0796.76010
[28] Souza, JR; Rodrigues, ML, An investigation into mechanisms of loss of safe basins in a 2 D.O.F. nonlinear oscillator, J Braz Soc Mech Sci Eng, 24, 93-98, (2002)
[29] Freitas, MST; Viana, RL; Grebogi, C, Erosion of the safe basin for the transversal oscillations of a suspension bridge, Chaos Solitons Fractals, 18, 829-841, (2003) · Zbl 1129.74317
[30] Gonçalves, PB; Silva, FMA; Rega, G; Lenci, S, Global dynamics and integrity of a two-d.o.f. model of a parametrically excited cylindrical shell, Nonlinear Dyn, 63, 61-82, (2011) · Zbl 1215.74049
[31] Ruzziconi L, Younis MI, Lenci S (submitted). Multistability in an electrically actuated carbon nanotube: a dynamical integrity perspective · Zbl 1293.74271
[32] Lenci, S; Rega, G, Experimental versus theoretical robustness of rotating solutions in a parametrically excited pendulum: a dynamical integrity perspective, Physica D, 240, 814-824, (2011) · Zbl 1218.37116
[33] Ruzziconi, L; Younis, MI; Lenci, S; Wiercigroch, M (ed.); Rega, G (ed.), Dynamical integrity for interpreting experimental data and ensuring safety in electrostatic MEMS, No. 32, 249-261, (2013), Berlin
[34] Alsaleem, F; Younis, MI; Ruzziconi, L, An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically, J Microelectromech Syst, 19, 794-806, (2010)
[35] Settimi, V; Rega, G, Bifurcations, basin erosion and dynamic integrity in a single-mode model of noncontact atomic force microscopy, Marrakesh, Morocco, April 30-May 02, 2012
[36] Lenci, S; Rega, G, Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam, J Micromech Microeng, 16, 390-401, (2006)
[37] Ruzziconi L, Bataineh AM, Younis MI, Cui W, Lenci S (submitted). An electrically actuated imperfect microbeam resonator. Experimental and theoretical investigation of the nonlinear dynamic response
[38] Ruzziconi L, Younis MI, Lenci S (submitted). Parameter identification of an electrically actuated imperfect microbeam · Zbl 1293.74271
[39] Nusse HE, Yorke JA (1998) Dynamics. Numerical explorations. Springer, New York
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