Browse > Article
http://dx.doi.org/10.12989/sem.2015.56.3.461

Brief and accurate analytical approximations to nonlinear static response of curled cantilever micro beams  

Sun, Youhong (College of Construction Engineering, Jilin University)
Yu, Yongping (College of Construction Engineering, Jilin University)
Liu, Baochang (College of Construction Engineering, Jilin University)
Publication Information
Structural Engineering and Mechanics / v.56, no.3, 2015 , pp. 461-472 More about this Journal
Abstract
In this paper, the nonlinear static response of curled cantilever beam actuators subjected to the one-sided electrostatic field is focused on. By assuming the deflection function of electrostatically actuated beam, analytical approximate solutions are established via using Galerkin method to solve the equilibrium equation. The Pull-In voltages which determine the stability of the curled beam actuators are also obtained. These approximate solutions show excellent agreements with numerical solutions obtained by the shooting method and the experimental data for a wide range of beam length. Expressions of these analytical approximate solutions are brief and could easily be used to derive the effects of various physical parameters on MEMS structures.
Keywords
MEMS; Galerkin method; large deformation; analytical approximation;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Senturia, S.D. (2001), Microsystem Design, Kluwer, Boston, MA.
2 Shames, I.H. and Dym, C.L. (1985), Energy and Finite Element Methods in Structural Mechanics, McGraw-Hill.
3 Wang, W. and Soper, S.A. (2007), Bio-MEMS: Technologies and Applications, CRC/Taylor & Francis.
4 Wu, B.S., Yu, Y.P., Li, Z.G. and Xu, Z.H. (2013), "An analytical approximation method for predicting static responses of electrostatically actuated microbeams", Int. J. Nonlin. Mech., 54, 99-104.   DOI
5 Younis, M.I., Abdel-Rahman, E.M. and Nayfeh, A.H. (2003), "A reduced-order model for electrically actuated microbeam-based mems", J. Microelectromech. S., 12, 672-680.   DOI
6 Yu, Y.P. and Sun, Y.H. (2012), "Analytical approximate solutions for Large post-buckling response of a hygrothermal beam", Struct. Eng. Mech., 43(2), 211-223.   DOI
7 Yu, Y.P., Wu, B.S. and Lim, C.W. (2012), "Numerical and analytical approximations to large post-buckling deformation of MEMS", Int. J. Mech. Sci., 55, 95-103.   DOI
8 Zamanian, M. and Hosseini, S.A.A. (2012), "Secondary resonances of a microresonator under AC-DC electrostatic and DC piezoelectric actuations", Struct. Eng. Mech., 42(5), 677-699.   DOI
9 Zamanian, M., Khadem, S.E. and Mahmoodi, S.N. (2010), "Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation", Struct. Eng. Mech., 35(4), 387-407.   DOI
10 Zhang, Y. and Zhao, Y.P. (2006), "Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading", Sens. Actuat. A-Phys., 127, 366-380.   DOI
11 Abbasnejad, B., Rezazadeh, G. and Shabani, R. (2013), "Stability analysis of a capacitive FGM micro-beam using modified couple stress theory", Acta Mechanica Solida Sinica, 26(4), 427-438.   DOI
12 Al-Sadder, S.Z. (2006), "Large deflection behavior of a flexible circular cantilever arc device subjected to inward or outward polar force", Struct. Eng. Mech., 22(4), 433-447.   DOI
13 Chen, W.C., Yeh, P.I., Hu, C.F. and Fang, W.L. (2008), "Design and characterization of single-layer step-bridge structure for out-of-plane thermal actuator", J. Microelectromech. S., 17, 70-77.   DOI
14 Cheng, J., Zhe, J. and Wu, X. (2004), "Analytical and finite element model pull-in study of rigid and deformable electrostatic microactuators", J. Micromech. Microeng., 14, 57-68.   DOI
15 Chowdhery, S., Ahmadi, M. and Miller, W.C. (2005), "A closedform model for the pull-in voltage of electrostatically actuated cantilever beams", J. Micromech. Microeng. 15, 756-763.   DOI
16 Chuang, W.C., Lee, H.L., Chang, P.Z. and Hu, Y.C. (2010), "Review on the modeling of electrostatic MEMS", Sensors, 10, 6149-6171.   DOI
17 Elata, D. and Abu-Salih, S. (2005), "Analysis of a novel method for measuring residual stress in micro-systems", J. Micromech. Microeng. 15, 921-927.   DOI
18 Fang, W. and Wickert, J.A. (1994), "Post buckling of micromachined beams", J. Micromech. Microeng., 4, 116-122.   DOI
19 Gabbay, L.D. and Senturia, S.D. (2000), "Computer-aided generation of nonlinear reduced-order dynamic macromodels. I: Non-stress-stiffened case", J. Microelectromech. S. 9, 262-269.   DOI
20 Gupta, R.K. (1997), "Electrostatic Pull-In test structure design for in-situ mechanical property measurements of microelectromechanical systems (MEMS)", Ph.D. Dissertation, Massachusetts Institute of Technology.
21 Gutschmidt, S. (2010), "The Influence of higher-order mode shapes for reduced-order models of electrostatically actuated microbeams", ASME J. Appl. Mech., 77, 041007.   DOI
22 Hess, A.E. and et al. (2011), "Development of a stimuli-responsive polymer nanocomposite toward biologically optimized, MEMS-based neural probes", J. Micromech. Microeng., 21, 054009.   DOI
23 Hu, Y.C. (2006), "Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads", J. Micromech. Microeng., 16, 648-655.   DOI
24 Hu, Y.C. and Wei, C.S. (2007), "An analytical model considering the fringing fields for calculating the pull-in voltage of micro curled cantilever beams", J. Micromech. Microeng., 17, 61-67.   DOI
25 Miyashita, Y., Iwasaka, M. and Kimura, T. (2014), "Microcrystal-like cellulose fibrils as the diamagnetic director for microfluidic systems", J. Appl. Phys., 115(17), 17B519.   DOI
26 Kazama, A., Aono, T. and Okada, R. (2013), "Stress relaxation mechanism with a ring-shaped beam for a piezoresistive three-axis accelerometer", J. Microelectromech. S., 22, 386-394.   DOI
27 Krylov, S. (2007), "Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures", Int. J. Nonlin. Mech., 42, 626-642.   DOI
28 Lee, B.C. and Kim, E.S. (2000), "Analysis of partly corrugated rectangular diaphragms using the Rayleigh-Ritz method", J. Microelectromech. S., 9, 399-406.   DOI
29 Mobki, H., Rezazadeh, G., Sadeghi, M., Vakili-Tahami, F. and Seyyed-Fakhrabadi, M. (2013), "A comprehensive study of stability in an electro-statically actuated micro-beam", Int. J. Nonlin. Mech., 48, 78-85.   DOI   ScienceOn
30 Nayfeh, A.H., Younis, M.I. and Abdel-Rahman, E.M. (2005), "Reduced-order models for mems applications", Nonlin. Dyn., 41, 211-236.   DOI
31 Osterberg, P.M. (1995), "Electrostatically actuated microelectromechancial test structures for material property measurements", Ph.D. Dissertation, Massachusetts Institute of Technology.
32 Pamidighantam, S. and et al. (2002), "Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions", J. Micromech. Microeng., 12, 458-464.   DOI
33 Petersen, K.E. (1978), "Dynamic micromechanics on silicon techniques and devices", IEEE T. Electron Dev., 25(10), 1241-1250.   DOI
34 Rebeiz, G.M. (2003), RF MEMS: Theory, Design, and Technology, Wiley.