×

Nonlinear analysis of MEMS electrostatic microactuators: primary and secondary resonances of the first mode*. (English) Zbl 1269.74099

Summary: We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler-Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM-FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM-FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abdel-Rahman, E.M., Journal of Computational and Theoretical Nanoscience 1 pp 1– (2005)
[2] Bert, C.W., Applied Mechanics Review 49 pp 1– (1996) · doi:10.1115/1.3101882
[3] Chao, P.C.P., Journal of Micromechanics and Microengineering 16 pp 986– (2006) · doi:10.1088/0960-1317/16/5/016
[4] De, S.K., Journal of Microelectromechnical Systems 15 pp 355– (2006) · doi:10.1109/JMEMS.2006.872227
[5] Kuang, J.H., Journal of Micromechanics and Microengineering 14 pp 647– (2004) · doi:10.1088/0960-1317/14/4/028
[6] Lenci, S., Journal of Micromechanics and Microengineering 16 pp 390– (2006) · doi:10.1088/0960-1317/16/2/025
[7] Mehner, J.E., Journal of Micromechanics and Microengineering 9 pp 270– (2000)
[8] Mukherjee, T., IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems 19 pp 1572– (2000) · Zbl 05449113 · doi:10.1109/43.898833
[9] Najar, F., Journal of Micromechanics and Microengineering 16 pp 2449– (2006) · doi:10.1088/0960-1317/16/11/028
[10] Najar, F., Journal of Micromechanics and Microengineering 15 pp 419– (2005) · doi:10.1088/0960-1317/15/3/001
[11] Nayfeh, A.H., Applied Nonlinear Dynamics (1995) · Zbl 0848.34001 · doi:10.1002/9783527617548
[12] Nayfeh, A.H., Nonlinear Oscillations (1979)
[13] Nayfeh, A.H., Journal of Micromechanics and Microengineering 15 pp 1840– (2005) · doi:10.1088/0960-1317/15/10/008
[14] Nayfeh, A.H., Nonlinear Dynamics 48 pp 153– (2007) · doi:10.1007/s11071-006-9079-z
[15] Shkel, A.M., Proceedings of the IEEE/Institute Of Navigation Plans
[16] Veijola, T., Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems (MSM’98)
[17] Younis, M.I., Investigation of the mechanical behavior of microbeam-based MEMS devices,” MSc Thesis (2001)
[18] Younis, M.I., Journal of Microelectromechnical Systems 12 pp 672– (2003) · doi:10.1109/JMEMS.2003.818069
[19] Zook, J.D., Sensors and Actuators A 35 pp 290– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.