0
SPECIAL SECTION PAPERS

Bistable Cantilevers Actuated by Fringing Electrostatic Fields

[+] Author and Article Information
Naftaly Krakover

Faculty of Engineering,
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv,
Tel Aviv 69978, Israel
e-mail: Naftalyk@mail.tau.ac.il

Slava Krylov

Faculty of Engineering,
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv,
Tel Aviv 69978, Israel
e-mail: krylov@tauex.tau.ac.il

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 16, 2016; final manuscript received April 19, 2017; published online May 30, 2017. Assoc. Editor: John Judge.

J. Vib. Acoust 139(4), 040908 (May 30, 2017) (10 pages) Paper No: VIB-16-1598; doi: 10.1115/1.4036625 History: Received December 16, 2016; Revised April 19, 2017

Bistable microstructures are distinguished by their ability to stay in two different stable configurations at the same loading. They manifest rich behavior and are advantageous in applications such as switches, nonvolatile memories, and sensors. Bistability of initially curved or buckled double-clamped beams, curved plates, and shells is associated with mechanical geometric nonlinearity appearing due to coupling between bending and compressive axial/in-plane stress. The bistable behavior is achieved by using a combination of carefully tailored initial shape and constrained boundaries. However, these statically indeterminate structures suffer from high sensitivity to temperature and residual stress. In this work, we show using the model that by combining electrostatic actuation by fringing fields with direct transversal forcing by a parallel-plate electrode or piezoelectric (PZT) transducer, bistable behavior can be obtained in a simple cantilever structure distinguished by robustness and low thermal sensitivity. Reduced-order model of the cantilever was built using Galerkin decomposition, the electrostatic force was obtained by means of three-dimensional (3D) finite elements (FEs) modeling. We also demonstrate that operation of the device in the vicinity of the bistability threshold may enhance the frequency sensitivity of the cantilever to loading. This sensitivity-enhancement approach may have applications in a broad range of resonant microelectromechanical inertial, force, mass, and biosensors as well as in atomic force microscopy (AFM).

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Timoshenko, S. P. , and Gere, J. M. , 1970, Theory of Elastic Stability, McGraw-Hill, New York.
Singer, J. , Arbocz, J. , and Weller, T. , 2002, Buckling Experiments: Experimental Methods in Buckling of Thin-Walled Structures, Vol. 2, Wiley, New York, pp. 905–915.
Jones, R. M. , 2006, Buckling of Bars, Plates, and Shells, Bull Ridge, VA.
Moon, F. C. , and Holmes, P. J. , 1979, “ A Magnetoelastic Strange Attractor,” J. Sound Vib., 65(2), pp. 275–296. [CrossRef]
Ren, H. , and Gerhard, E. , 1997, “ Design and Fabrication of a Current-Pulse-Excited Bistable Magnetic Microactuator,” Sens. Actuators A, 58(3), pp. 259–264. [CrossRef]
Receveur, R. A. M. , Marxer, C. R. , Woering, R. , Larik, V. C. M. H. , and de Rooij, N.-F. , 2005, “ Laterally Moving Bistable MEMS DC Switch for Biomedical Applications,” J. Microelectromech. Syst., 14(5), pp. 1089–1098. [CrossRef]
Hichwa, B. P. , Marxer, C. , and Gale, M. , 2001, “ Bi-Stable Micro Switch,” Optical Coating Laboratory Inc., Santa Rosa, CA, U.S. Patent No. US6303885 B1.
Zhao, J. , Yang, Y. , Fan, K. , Hu, P. , and Wang, H. , 2010, “ A Bistable Threshold Accelerometer With Fully Compliant Clamped-Clamped Mechanism,” IEEE Sens. J., 10(5), pp. 1019–1024. [CrossRef]
Smith, C. G. , 1997, “ Bi-Stable Memory Element,” Cavendish Kinetics, Inc., San Jose, CA, U.S. Patent No. US5677823 A.
Charlot, B. , Sun, W. , Yamashita, K. , Fujita, H. , and Toshiyoshi, H. , 2008, “ Bistable Nanowire for Micromechanical Memory,” J. Micromech. Microeng., 18(4), p. 45005. [CrossRef]
Hafiz, M. , Kosuru, L. , Ramini, A. , Chappanda, K. , and Younis, M. , 2016, “ In-Plane MEMS Shallow Arch Beam for Mechanical Memory,” Micromachines, 7(10), p. 191. [CrossRef]
Harne, R. L. , and Wang, K. W. , 2013, “ A Review of the Recent Research on Vibration Energy Harvesting Via Bistable Systems,” Smart Mater. Struct., 22(2), p. 23001. [CrossRef]
Domínguez-Pumar, M. , Pons-Nin, J. , and Chávez-Domínguez, J. A. , 2016, “ MEMS Technologies for Energy Harvesting,” Nonlinearity in Energy Harvesting Systems, Springer, Cham, Switzerland, pp. 23–63.
Younis, M. I. , 2011, MEMS Linear and Nonlinear Statics and Dynamics, Springer Science & Business Media, New York.
Medina, L. , Gilat, R. , Robert Ilic, B. , and Krylov, S. , 2016, “ Experimental Dynamic Trapping of Electrostatically Actuated Bistable Micro-Beams,” Appl. Phys. Lett., 108(7), p. 73503. [CrossRef]
Linzon, Y. , Ilic, B. , Lulinsky, S. , and Krylov, S. , 2013, “ Efficient Parametric Excitation of Silicon-on-Insulator Microcantilever Beams by Fringing Electrostatic Fields,” J. Appl. Phys., 113(16), p. 163508. [CrossRef]
Krakover, N. , Ilic, B. R. , and Krylov, S. , 2016, “ Displacement Sensing Based on Resonant Frequency Monitoring of Electrostatically Actuated Curved Micro Beams,” J. Micromech. Microeng., 26(11), p. 115006. [CrossRef] [PubMed]
Hafiz, M. A. A. , Kosuru, L. , and Younis, M. I. , 2016, “ Microelectromechanical Reprogrammable Logic Device,” Nat. Commun., 7, p. 11137. [CrossRef] [PubMed]
Roodenburg, D. , Spronck, J. W. , van der Zant, H. S. J. , and Venstra, W. J. , 2009, “ Buckling Beam Micromechanical Memory With On-Chip Readout,” Appl. Phys. Lett., 94(18), p. 183501. [CrossRef]
Sulfridge, M. , Saif, T. , Miller, N. , and O'Hara, K. , 2002, “ Optical Actuation of a Bistable MEMS,” J. Microelectromech. Syst., 11(5), pp. 574–583. [CrossRef]
Gerson, Y. , Krylov, S. , and Ilic, B. , 2010, “ Electrothermal Bistability Tuning in a Large Displacement Micro Actuator,” J. Micromech. Microeng., 20(20), p. 112001. [CrossRef]
Medina, L. , Gilat, R. , and Krylov, S. , 2016, “ Bistable Behavior of Electrostatically Actuated Initially Curved Micro Plate,” Sens. Actuators A, 248, pp. 193–198. [CrossRef]
Ramini, A. H. , Hennawi, Q. M. , and Younis, M. I. , 2016, “ Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch,” J. Microelectromech. Syst., 25(3), pp. 570–578. [CrossRef]
Kaajakari, V. , 2009, Practical MEMS: Design of Microsystems, Accelerometers, Gyroscopes, RF MEMS, Optical MEMS, and Microfluidic Systems, Small Gear Publishing, Las Vegas, NV.
Krylov, S. , Ilic, B. R. , and Lulinsky, S. , 2011, “ Bistability of Curved Microbeams Actuated by Fringing Electrostatic Fields,” Nonlinear Dyn., 66(3), pp. 403–426. [CrossRef]
Small, J. , Irshad, W. , Fruehling, A. , Garg, A. , Liu, X. , and Peroulis, D. , 2012, “ Electrostatic Fringing-Field Actuation for Pull-In Free RF-MEMS Analogue Tunable Resonators,” J. Micromech. Microeng., 22(9), pp. 95004–95010. [CrossRef]
Ouakad, H. M. , 2014, “ Static Response and Natural Frequencies of Microbeams Actuated by Out-of-Plane Electrostatic Fringing-Fields,” Int. J. Non-Linear Mech., 63, pp. 39–48. [CrossRef]
Pallay, M. , and Towfighian, S. , 2017, “ Parametrically Excited Electrostatic MEMS Cantilever Beam With Flexible Support,” ASME J. Vib. Acoust., 139(2), p. 021002. [CrossRef]
Kambali, P. N. , and Pandey, A. K. , 2017, “ Nonlinear Coupling of Transverse Modes of a Fixed–Fixed Microbeam Under Direct and Parametric Excitation,” Nonlinear Dyn., 87(2), pp. 1271–1294. [CrossRef]
Su, J. , Yang, H. , Fay, P. , Porod, W. , and Bernstein, G. H. , 2009, “ A Surface Micromachined Offset-Drive Method to Extend the Electrostatic Travel Range,” J. Micromech. Microeng., 20(1), pp. 125–135.
Lee, K. B. , 2007, “ Non-Contact Electrostatic Microactuator Using Slit Structures: Theory and a Preliminary Test,” J. Micromech. Microeng., 17(11), pp. 2186–2196. [CrossRef]
Hah, D. , Patterson, P. R. , Nguyen, H. D. , Toshiyoshi, H. , and Wu, M. C. , 2004, “ Theory and Experiments of Angular Vertical Comb-Drive Actuators for Scanning Micromirrors,” IEEE J. Sel. Top. Quantum Electron., 10(3), pp. 505–513. [CrossRef]
Krylov, S. , and Barnea, D. I. , 2005, “ Bouncing Mode Electrostatically Actuated Scanning Micromirror for Video Applications,” Smart Mater. Struct., 14(6), pp. 1281–1296. [CrossRef]
Seleim, A. , Towfighian, S. , Delande, E. , Abdel-Rahman, E. , and Heppler, G. , 2012, “ Dynamics of a Close-Loop Controlled MEMS Resonator,” Nonlinear Dyn., 69(1–2), pp. 615–633. [CrossRef]
Adams, S. G. , Bertsch, F. M. , Shaw, K. A. , and MacDonald, N. C. , 1998, “ Independent Tuning of Linear and Nonlinear Stiffness Coefficients [Actuators],” J. Microelectromech. Syst., 7(2), pp. 172–180. [CrossRef]
Kierzenka, J. , and Shampine, L. F. , 2001, “ A BVP Solver Based on Residual Control and the Maltab PSE,” ACM Trans. Math. Software, 27(3), pp. 299–316. [CrossRef]
Hung, E. S. , and Senturia, S. D. , 1999, “ Extending the Travel Range of Analog-Tuned Electrostatic Actuators,” J. Microelectromech. Syst., 8(4), pp. 497–505. [CrossRef]
Batra, R. C. , Porfiri, M. , and Spinello, D. , 2006, “ Capacitance Estimate for Electrostatically Actuated Narrow Microbeams,” Micro Nano Lett., 1(2), p. 71. [CrossRef]
Tadmor, E. B. , and Kosa, G. , 2003, “ Electromechanical Coupling Correction for Piezoelectric Layered Beams,” J. Microelectromech. Syst., 12(6), pp. 899–906. [CrossRef]
Weinberg, M. S. , 1999, “ Working Equations for Piezoelectric Actuators and Sensors,” J. Microelectromech. Syst., 8(4), pp. 529–533. [CrossRef]
Brissaud, M. , Ledren, S. , and Gonnard, P. , 2003, “ Modelling of a Cantilever Non-Symmetric Piezoelectric Bimorph,” J. Micromech. Microeng., 13(6), pp. 832–844. [CrossRef]
Muralt, P. , Kholkin, A. , Kohli, M. , and Maeder, T. , 1996, “ Piezoelectric Actuation of PZT Thin-Film Diaphragms at Static and Resonant Conditions,” Sens. Actuators A, 53(1), pp. 398–404. [CrossRef]
Zhou, J. , McMcollough, T. , Mantell, S. C. , and Zurn, S. , 1999, “ Young's Modulus Measurement of Thin Film PZT,” IEEE 13th Biennial University/Government/Industry Microelectronics Symposium, Minneapolis, MN, June 23, pp. 153–157.
Zhang, W. , Baskaran, R. , and Turner, K. L. , 2002, “ Effect of Cubic Nonlinearity on Auto-Parametrically Amplified Resonant MEMS Mass Sensor,” Sens. Actuators A, 102(1), pp. 139–150. [CrossRef]
Turner, K. L. , Burgner, C. B. , Yie, Z. , and Holtoff, E. , 2012, “ Using Nonlinearity to Enhance Micro/Nanosensor Performance,” IEEE Sensors, Taipei, Taiwan, Oct. 28–31, pp. 1–4.
Hagleitner, C. , Hierlemann, A. , Lange, D. , Kummer, A. , Kerness, N. , Brand, O. , and Baltes, H. , 2001, “ Smart Single-Chip Gas Sensor Microsystem,” Nature, 414(6861), pp. 293–296. [CrossRef] [PubMed]
Jalili, N. , and Laxminarayana, K. , 2004, “ A Review of Atomic Force Microscopy Imaging Systems: Application to Molecular Metrology and Biological Sciences,” Mechatronics, 14(8), pp. 907–945. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematics of a cantilever actuated by fringing electrostatic fields: (a) initial undeformed configuration and (b) deformed configuration. Insets illustrate the schematic view of the electrostatic fringing fields for each case.

Grahic Jump Location
Fig. 2

Schematics of the mechanical restoring force, electrostatic fringing fields' restoring force, and the combination of both, as a function of the deflection of the beam

Grahic Jump Location
Fig. 3

Finite elements results—the electric potential for differing vertical displacements of the movable electrode (the beam) (a) undeformed configuration and (b) deformed configuration corresponding to the vertical displacement of the beam of 10 μm. Horizontal y and vertical z coordinates are shown in μm. The voltage of 1 V is applied to the side electrode.

Grahic Jump Location
Fig. 4

Force per unit length of the beam—FE results (markers) and the fit Eq. (2) (solid line). The parameters of the beam are shown in Table 1, the voltage applied to the electrode is 1 V.

Grahic Jump Location
Fig. 5

Equilibrium curves for the different values of the direct current voltage VS (numbers) applied to the side electrode. The curve corresponding to Vs = 90 V reflects bistable behavior. Solid lines correspond to the stable solution, dashed line depicts unstable branch of the equilibrium path.

Grahic Jump Location
Fig. 6

Equilibrium curves for the beam obtained using different models: single-DOF RO model (thin solid line), collocation method (dashed line), 3D FE model (markers)

Grahic Jump Location
Fig. 7

Cantilever actuated by a parallel-plate electrode in addition to the fringing field side electrode

Grahic Jump Location
Fig. 8

Model results—equilibrium curves for the beam simultaneously actuated by a parallel-plate electrode of the length Lpp = L/2 and by the side fringing fields' electrode. Different curves correspond to different voltages VS applied on the sidefringing field electrode. Solid line corresponds to stable equilibrium configurations, dashed line represents unstable equilibrium.

Grahic Jump Location
Fig. 9

Cantilever made from two layers—a passive silicon layer and an active PZT layer. Electrostatic fringing field is provided by the side electrode. Inset shows the cross section of the beam.

Grahic Jump Location
Fig. 10

Equilibrium curves—model results, piezoelectric actuation. Different curves correspond to different fringing fields' electrostatic force parameterized by VS applied to the side electrode.

Grahic Jump Location
Fig. 11

Fundamental mode frequency of the cantilever as a function of the transverse “mechanical” loading. Different curves correspond to the different values of the voltage VS (numbers) applied to the side fringing field electrode. Discontinuity can be seen on the curve corresponding to VS = 90 V, which corresponds to the bistable behavior (see Fig. 5).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In