The Vibration Problem Studying in Micro Actuator System Using the Differential Transformation Method

Abstract:

The aim of this study is to derive the governing equation of an electrostatically actuated micro system by use of the Hamilton principle, and then the natural frequencies of a micro fixed-fixed beam are derived as the solutions to a boundary value problem with prescribed boundary conditions through the differential transformation method (D.T.M.). The differential transformation employed is a transformed function based on the Taylor series that is effective in solving nonlinear problems with fast convergence. The numerical results of the calculated natural frequencies are compared with the analytical data and were found to be in good agreement. Hence, the differential transformation method is one of the most efficient methods of simulating the electrostatic behavior of a micro-structure system, and it has a great potential for use in the analysis of the micro fixed-fixed beam.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 1966-1970
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.1966
• Online since: January 2013
• Authors: Chin Chia Liu, Ming Fei Chen
• Keywords: Differential Transformation, MEMS, Micro Fixed-Fixed Beam, Natural Frequency

References

[1] J. M. Bosc, Y. Guo, V. Sarihan and T. Lee: Accelerated Life Testing for Micro-Machined Chemical Sensors, IEEE TRANSACTIONS ON RELIABILITY, 47(2) (1998), p.135–141.

DOI: 10.1109/24.722276

[2] Y. Zhu and H. D. Espinosa: Effect of temperature on capacitive RF MEMS switch performance—a coupled-field analysis, J. Micromech. Microeng., 14 (2004), p.1270–1279.

DOI: 10.1088/0960-1317/14/8/021

[3] N. I. Maluf, R. J. Reay and G.T.A. Kovacs: High-voltage devices and circuits fabricated using foundry CMOS for use with electrostatic MEM actuators, Sensors and Actuators A, 52 (1996), p.187–192.

DOI: 10.1016/0924-4247(96)80147-6

[4] R. Luharuka, S. LeBlanc, J. S. Bintoro, Y. H. Berthelot and P. J. Hesketh: Simulated and experimental dynamic response characterization of an electromagnetic microvalve, Sensors and Actuators A, 143 (2008), p.399–408.

DOI: 10.1016/j.sna.2007.10.084

[5] G. Rezazadeh, A. Tahmasebi and M. Zubstov: Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage, Microsyst Technol, 12 (2006), p.1163–1170.

DOI: 10.1007/s00542-006-0245-5

[6] J. D. Zook and D. W. Burns: Characteristics of polysilicon resonant micro beams, Sensors Actuators A, 35 (1992), p.51–9.

[7] D. J. Ijntema and H. A. C. Tilmans: Static and dynamic aspects of an air-gap capacitor, Sensors Actuators A, 35 (1992), p.121–8.

DOI: 10.1016/0924-4247(92)80150-2

[8] C. K. Chen and S. H. Ho: Free vibration analysis of non-uniform timoshenko beams using differential transform, Applied mathematical modeling, 22 (4-5) (1998), p.219–234.

DOI: 10.1016/s0307-904x(98)10002-1

[9] C. K. Chen, H. Y. Lai and C. C. Liu: Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam, Microsyst Technol, 15 (2009), p.813–820.

DOI: 10.1007/s00542-009-0834-1

[10] C. K. Chen, H. Y. Lai and C. C. Liu: Nonlinear Micro Circular Plate Analysis Using Hybrid Differential Transformation / Finite Difference Method, CMES: Computer Modeling in Engineering & Sciences, 40 (2) (2009), p.155–174.

[11] C. C. Liu, S. C. Yang and C. K. Chen: Nonlinear dynamic analysis of Micro Cantilever Beam Under Electrostatic Loading, Journal of Mechanics, 28 (2012), pp: 559–566.

DOI: 10.1017/jmech.2012.6

[12] C. K. Chen, H. Y. Lai and C. C. Liu: Numerical analysis of entropy generation in mixed convection flow with viscous dissipation effects in vertical channel, International Communications in Heat and Mass Transfer, 38 (2011), p.285–290.

DOI: 10.1016/j.icheatmasstransfer.2010.12.016

[13] C. T. Chiu: Mechanical Vibration (Wu-Nan Culture Enterprise, Taiwan 2005).