Free vibration of axially loaded microbeam in MEMS based on sinusoidal shear deformation theory

Cong Ich Le; Dinh Kien Nguyen

doi:10.15625/2525-2518/16957

Author affiliations

Authors

Cong Ich Le Department of Machinery Design, Le Quy Don Technical University, 236 Hoang Quoc Viet, Bac Tu Liem, Ha Noi, Viet Nam
Dinh Kien Nguyen Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Ha Noi, Viet Nam

DOI:

https://doi.org/10.15625/2525-2518/16957

Keywords:

Microbeam, Sinusoidal theory, MCST, MEMS, Free Vibration

Abstract

Free vibration of an axially loaded silicon microbeam in MEMS under electrostatic actuation is studied on the basis of a sinusoidal shear deformation theory. Based on the modified couple stress theory (MCST) and von Kármán geometric nonlinearity, a nonlinear finite element formulation is derived and employed to construct the discrete nonlinear governing equations for the microbeam. The deflection of the microbeam at a given DC voltage is firstly calculated using the Newton Raphson based iterative procedure, and used to evaluate the tangent stiffness matrix. The natural frequencies of the microbeam corresponding the DC voltage are then computed. The influence of the applied voltage, the axial force as well as the material length scale parameter on the frequencies of the microbeam is studied in detail and highlighted. The dependence of the pull-in voltage upon the material length scale and the axial force is also examined and discussed.

Downloads

Download data is not yet available.

References

Choi B. and Lovell E. G. - Improved analysis of microbeams under mechanical and electrostatic loads, Journal of Micromechanics and Microengineering 7 (1) (1997) 24-29. DOI: https://doi.org/10.1088/0960-1317/7/1/005

Abdel-Rahman E. M., Younis M. I. and Nayfeh A. H. - Characterization of the mechanical behavior of an electrically actuated microbeam, Journal of Micromechanics and Microengineering 12 (6) (2002) 759-766. DOI: https://doi.org/10.1088/0960-1317/12/6/306

Younis M. I., Abdel-Rahman E. M., and Nayfeh A. - A reduced-order model for electrically actuated microbeam-based MEMS, Journal of Microelectromechanical systems 12 (5) (2003) 672-680. DOI: https://doi.org/10.1109/JMEMS.2003.818069

Younis M. I. and Nayfeh A. H. - A study of the nonlinear response of a resonant microbeam to an electric actuation, Nonlinear Dynamics 31 (1) (2003) 91-117. DOI: https://doi.org/10.1023/A:1022103118330

Abdel-Rahman E. M. and Nayfeh A. H. - Secondary resonances of electrically actuated resonant microsensors, Journal of Micromechanics and Microengineering 13 (3) (2003) 491-501. DOI: https://doi.org/10.1088/0960-1317/13/3/320

Chaterjee S. and Pohit G. - A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams, Journal of sound and vibration. 322 (4-5), (2009) 969-986. DOI: https://doi.org/10.1016/j.jsv.2008.11.046

Ghazavi M. R., Rezazadeh G., and Azizi S. - Finite element analysis of static and dynamic pull-in instability of a fixed-fixed micro beam considering damping effects, Sensors & Transducers 103 (4), (2009) 132-143.

Rezazadeh G., Sadeghian H., Hosseinzadeh I. and Toloei A. - Investigation of pull-in phenomenon on extensible micro beam subjected to electrostatic pressure, Sensors & Transducers Journal. 79 (5) (2007) 1173-1179.

Kaneria A. J., Sharma D. S. and Trivedi R. R. - Static analysis of electrostatically actuated micro cantilever beam, Procedia Engineering 51 (2013) 776-780. DOI: https://doi.org/10.1016/j.proeng.2013.01.111

Farokhi H. and Ghayesh M. H. - Size-dependent behaviour of electrically actuated microcantilever-based MEMS, International Journal of Mechanics and Materials in Design 12 (3) (2016) 301-315. DOI: https://doi.org/10.1007/s10999-015-9295-0

Ghayesh M. H. and Farokhi H. - Nonlinear behaviour of electrically actuated microplate-based MEMS resonators, Mechanical Systems and Signal Processing. 109 (2018) 220-234. DOI: https://doi.org/10.1016/j.ymssp.2017.11.043

Baghani M. - Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory, International Journal of Engineering Science 54, (2012), 99-105. DOI: https://doi.org/10.1016/j.ijengsci.2012.01.001

Ghayesh M. H., Farokhi H., and Amabili M. - Nonlinear behaviour of electrically actuated MEMS resonators, International Journal of Engineering Science 71 (2013) 137-155. DOI: https://doi.org/10.1016/j.ijengsci.2013.05.006

Yang F. A. C. M., Chong A. C. M., Lam D. C. C., and Tong P. - Couple stress based strain gradient theory for elasticity, International journal of solids and structures 39 (10) (2002) 2731-2743. DOI: https://doi.org/10.1016/S0020-7683(02)00152-X

Thai H. T. and Vo T. P. - A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates, Applied Mathematical Modelling. 37 (5), (2013) 3269-3281. DOI: https://doi.org/10.1016/j.apm.2012.08.008

Géradin M. and Rixen D. - Mechanical vibrations, Theory and Application to Structural Dynamics. John Wiley & Són, Chichester, 1997.

Younis M. I. - MEMS linear and nonlinear statics and dynamics (Vol. 20). Springer Science & Business Media, 2011. DOI: https://doi.org/10.1007/978-1-4419-6020-7

Osterberg P. M. and Senturia S. D. - M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelec-tromechanical systems 6 (2) (1997) 107-118. DOI: https://doi.org/10.1109/84.585788

Przemieniecki J. S. - Theory of Matrix Structural Analysis, McGraw-Hill Book Company, New York, 1985.