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Nonlinear Dynamic Analysis of Micro Cantilever Beam Under Electrostatic Loading

Published online by Cambridge University Press:  22 March 2012

C.-C. Liu ,
S.-C. Yang  and
C.-K. Chen
C.-C. Liu
Affiliation:
Department of Industrial Education and Technology, National Changhua University of Education, Changhua, Taiwan 50007, R.O.C.
S.-C. Yang
Affiliation:
Graduate Institute of Vehicle Engineering, National Changhua University of Education, Changhua, Taiwan 50007, R.O.C.
C.-K. Chen*
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Corresponding author ([email protected])
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Abstract

A hybrid differential transformation / finite difference scheme is used to analyze the complex nonlinear behavior of an electrostatically-actuated micro cantilever beam which high aspect ratios (length/width). The validity of the proposed method is confirmed by comparing the numerical results obtained for the tip displacement and pull-in voltage of the cantilever beam with the analytical and experimental results presented in the literature. The hybrid scheme is then applied to analyze both the steady-state and the dynamic deflection behavior of the cantilever beam as a function of the applied voltage. Overall, the results confirm that the hybrid method provides an accurate and computationally-efficient means of analyzing the complex nonlinear behavior of both the current micro cantilever beam system and other micro-scale electrostatically-actuated structures.

Keywords

Pull-in voltageMicro cantilever beamElectrostatic actuatorMEMSHybrid methodDifferential transformation
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 63 - 70
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. http://www.freescale.com/Google Scholar
2. http://www.ti.com/Google Scholar
3. Yeh, J. A., Huang, J. Y., Chen, C. N. and Hui, C. Y., “Design of an Electrostatic Rotary Comb Actuator,” Journal of Microlithography Microfabrication and Microsystems, 5, 023008–1 (2006).Google Scholar
4. Younis, M. I., Alsaleem, F. and Jordy, D., “The Response of Clamped-Clamped Microbeams Under Mechanical Shock,” International Journal of Non-Linear Mechanics, 42, pp. 643–657 (2007).Google Scholar
5. Luharuka, R., LeBlancet, S., Bintoro, J. S., Berthelot, Y. H. and Hesketh, P. J., “Simulated and Experimental Dynamic Response Characterization of an Electromagnetic Microvalve,” Sensors and Actuators A, 143, pp. 399–408 (2008).CrossRefGoogle Scholar
6. Mahmoodi, S. N. and Jalili, N., “Non-Linear Vibrations and Frequency Response Analysis of Piezoelectrically Driven Microcantilevers,” International Journal of Non-Linear Mechanics, 42, pp. 577–587 (2007).Google Scholar
7. Osterberg, P. M. and Senturia, S. D., “M-Test: Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures,” Journal of Microelectromechanical Systems, 6, pp. 107–118 (1997).Google Scholar
8. Wong, J. E., Lang, J. H. and Schmidt, M. A., “An Electrostatically Actuated MEMS Switch for Power Applications,” Proceedings of the IEEE MEMS 2000 Conference, Miyazaki, Japan, 23–27, pp. 633–638 (2000).Google Scholar
9. Osterberg, P., Yie, H., White, C. J. and Senturia, S., “Self-consistent Simulation and Modeling of Electrostatically Deformed Diaphragms,” IEEE MEMS'94 Workshop, Oiso, Japan, 25–28, pp. 28–32 (1994).Google Scholar
10. Legtenberg, R., Gilbert, J. and Senturia, S. D., “Electrostatic Curved Electrode Actuators,” Journal of Microelectromechanical Systems, 6, pp. 257–265 (1997).Google Scholar
11. Gretillat, M. A., Yang, Y. J., Hung, E. S., Rabinvich, V., Ananthasuresh, G. K., Rooij, N. F. and Senturia, S. D., “Nonlinear Electromechanical Behavior of an Electrostatic Microrelay,” Proc. of the International Conf. on Solid-State and Actuators, (Transducers ′97), Chicago, 16–19, pp. 1141–1144 (1997).Google Scholar
12. Hung, E. S. and Senturia, S. D., “Extending the Travel Range of Analog-Tuned Electrostatic Actuators,” Journal of Microelectromechanical Systems,, 8, pp. 497–505 (1999).Google Scholar
13. Chan, E. K., Garikipati, K. and Dutton, R. W., “Characterization of Contact Electromechanics Through Capacitance-Voltage Measurements and Simulations,” Journal of Microelectromechanical Systems,, 8, pp. 208–217 (1999).Google Scholar
14. Nemirovsky, Y., “A Methodology and Model for the Pull-In Parameters of Electrostatic Actuators,” Journal of Microelectromechanical Systems, 10, pp. 601–615 (2001).CrossRefGoogle Scholar
15. Zhou, X., Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China (1986).Google Scholar
16. Chiou, J. S. and Tzeng, J. R., “Application of the Taylor Transform to Nonlinear Vibration Problems,” Journal of Vibration and Acoustics, Transactions of the ASME, 118, pp. 83–87 (1996).Google Scholar
17. Chen, C. L. and Liu, Y. C., “Solution of Two-Boundary-Value Problems Using the Differential Transformation Method,” Journal of Optimization Theory and Application, 99, pp. 23–35 (1998).Google Scholar
18. Chen, C. K. and Ho, S. H., “Application of Differential Transformation to Eigenvalue Problem,” Applied Mathematics and Computation, 79, pp. 173–188 (1996).CrossRefGoogle Scholar
19. Chen, C. K. and Ho, S. H., “Free Vibration Analysis of Non-Uniform Timoshenko Beams Using Differential Transform,” Applied Mathematical Modeling, 22, pp. 219–234 (1998a).Google Scholar
20. Yu, L. T. and Chen, C. K., “The Solution of the Blasius Equation by the Differential Transformation Method,” Mathematical and Computer Modelling, 28, pp. 101–111 (1998).Google Scholar
21. Yu, L. T. and Chen, C. K., “Application of the Hybrid Method to the Transient Thermal Stresses Response in Isotropic Annular Fins,” Journal of Applied Mechanics, ASME, 66, pp. 340–346 (1999).Google Scholar
22. Kuo, B. L. and Chen, C. K., “Application of the Hybrid Method to the Solution of the Nonlinear Burgers' Equation,” Journal of Applied Mechanics, ASME, 70, pp. 926–929 (2003).Google Scholar
23. Hu, Y. C., Chang, C. M. and Huang, S. C., “Some Design Considerations on the Electrostatically Actuated Microstructures,” Sensors and Actuators A, 112, pp. 155–161 (2004).CrossRefGoogle Scholar
24. Chowdhury, S., Ahmadi, M. and Miller, C. W., “A Closed-Form Model for the Pull-In Voltage of Electrostatically Actuated Cantilever Beams,” Journal of Micromechanics and Microengineering, 15, pp. 756–763 (2005).Google Scholar
25. Krylov, S., “Lyapunov Exponents as a Criterion for the Dynamic Pull-In Instability of Electrostatically Actuated Microstructures,” International Journal of Non-Linear Mechanics, 42, pp. 626–642 (2007).CrossRefGoogle Scholar