Dynamical behaviour of electrically actuated microcantilevers

- Journal title : Coupled systems mechanics
- Volume 4, Issue 3, 2015, pp.251-262
- Publisher : Techno-Press
- DOI : 10.12989/csm.2015.4.3.251

Title & Authors

Dynamical behaviour of electrically actuated microcantilevers

Farokhi, Hamed; Ghayesh, Mergen H.;

Farokhi, Hamed; Ghayesh, Mergen H.;

Abstract

The current paper aims at investigating the nonlinear dynamical behaviour of an electrically actuated microcantilever. The microcantilever is excited by a combination of AC and DC voltages. The nonlinear equation of motion of the microcantilever is obtained by means of force and moment balances. A high-dimensional Galerkin scheme is then applied to reduce the equation of motion to a discrete model. A numerical technique, based on the pseudo-arclength continuation method, is used to solve the discretized model. The electrostatic deflection of the microcantilever and static pull-in instabilities, due to the DC voltage, are analyzed by plotting the so-called DC voltage-deflection curves. At the simultaneous presence of the DC and AC voltages, the nonlinear dynamical behaviour of the microcantilever is analyzed by plotting frequency-response and force-response curves.

Keywords

microcantilevers;electrically actuated;pull-in instability;dynamical behaviour;

Language

English

References

1.

Abdel-Rahman, E.M. and Nayfeh, A.H. (2003), "Secondary resonances of electrically actuated resonant microsensors", J. Micromech. Microeng., 13(3), 491-501.

2.

Alsaleem, F.M., Younis, M.I. and Ouakad, H.M. (2009), "On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators", J. Micromech. Microeng., 19(4), 045013.

3.

Ansari, R., Faghih Shojaei, M., Gholami, R., Mohammadi, V. and Darabi, M. (2012), "Thermal postbuckling behavior of size-dependent functionally graded timoshenko microbeams", Int. J. Nonlinear Mech., 50, 127-135.

4.

Ansari, R., Faghih Shojaei, M., Mohammadi, V., Gholami, R. and Darabi, M.A. (2013), "Buckling and postbuckling behavior of functionally graded Timoshenko microbeams based on the strain gradient theory", J. Mech. Mater. Struct., 7(10), 931-949.

5.

Baghani, M. (2012), "Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory", Int. J. Eng. Sci., 54, 99-105.

6.

Bao, M., Yang, H., Yin, H. and Shen, S. (2000), "Effects of electrostatic forces generated by the driving signal on capacitive sensing devices", Sensor. Actuat. - A, 84(3), 213-219.

7.

Farokhi, H., Ghayesh, M. and Amabili, M. (2013), "Nonlinear resonant behavior of microbeams over the buckled state", Appl. Phys. A, 1-11.

8.

Farokhi, H., Ghayesh, M.H. and Amabili, M. (2013), "Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory", Int. J. Eng. Sci., 68, 11-23.

9.

Ghayesh, M. (2012a), "Stability and bifurcations of an axially moving beam with an intermediate spring support", Nonlinear Dyn., 69(1-2), 193-210.

10.

Ghayesh, M. (2012b), "Subharmonic dynamics of an axially accelerating beam", Arch. Appl. Mech., 82(9), 1169-1181.

11.

Ghayesh, M., Farokhi, H. and Amabili, M. (2013), "Coupled nonlinear size-dependent behaviour of microbeams", Appl. Phys. A, 112(2), 329-338.

12.

Ghayesh, M.H. and Amabili, M. (2014), "Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam", Compos. Part B: Eng., 60, 371-377.

13.

Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013a), "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", Int. J. Eng. Sci., 63(0), 52-60.

14.

Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013b), "Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams", Int. J. Eng. Sci., 71, 1-14.

15.

Ghayesh, M.H., Farokhi, H. and Amabili, M. (2013c), "Nonlinear behaviour of electrically actuated MEMS resonators", Int. J. Eng. Sci., 71, 137-155.

16.

Ghayesh, M.H., Kazemirad, S. and Amabili, M. (2012), "Coupled longitudinal-transverse dynamics of an axially moving beam with an internal resonance", Mech. Mach. Theory, 52, 18-34.

17.

Ghayesh, M.H., Kazemirad, S. and Darabi, M.A. (2011), "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.

18.

Ghayesh, M.H., Kazemirad, S. and Reid, T. (2012), "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.

19.

Hu, Y.J., Yang, J. and Kitipornchai, S. (2010), "Pull-in analysis of electrostatically actuated curved micro-beams with large deformation", Smart Mater. Struct., 19(6), 065030.

20.

Ibrahimbegovic, A. and Al Mikdad, M. (2000), "Quadratically convergent direct calculation of critical points for 3d structures undergoing finite rotations", Comput. Method. Appl. M., 189(1), 107-120.

21.

Ibrahimbegovic, A., Hajdo, E. and Dolarevic, S. (2013), "Linear instability or buckling problems for mechanical and coupled thermomechanical extreme conditions", Coupled Syst. Mech., 2(4), 349-374

22.

Jia, X.L., Yang, J., Kitipornchai, S. and Lim, C.W. (2012), "Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation", J. Sound Vib., 331(14), 3397-3411.

23.

Kim, P., Bae, S. and Seok, J. (2012), "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.

24.

Ngo, V.M., Ibrahimbegovic, A. and Hajdo, E. (2014), "Nonlinear instability problems including localized plastic failure and large deformations for extreme thermo-mechanical loads", Coupled Syst. Mech., 3(1), 89-110.

25.

Pamidighantam, S., Puers, R., Baert, K. and Tilmans, H.A.C. (2002), "Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions", J Micromech. Microeng, 12(4), 458.

26.

Saif, M.T.A., Alaca, B.E. and Sehitoglu, H. (1999), "Analytical modeling of electrostatic membrane actuator for micro pumps", J. Microelectromech. Syst., 8(3), 335-345.

27.

Wang, Y.G., Lin, W.H., Feng, Z.J. and Li, X.M. (2012), "Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations", Int. J. Mech. Sci., 54(1), 225-233.

28.

Younis, M.I. (2011), MEMS Linear and Nonlinear Statics and Dynamics, Springer

29.

Younis, M.I., Abdel-Rahman, E.M. and Nayfeh, A. (2003), "A reduced-order model for electrically actuated microbeam-based MEMS", J. Microelectromech. Syst., 12(5), 672-680.

30.

Zengerle, R., Richter, A. and Sandmaier, H. (1992), "A micro membrane pump with electrostatic actuation", Micro Electro Mechanical Systems, 1992, MEMS '92, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robot. IEEE, 4-7 Feb 1992.