JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Brief and accurate analytical approximations to nonlinear static response of curled cantilever micro beams
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Brief and accurate analytical approximations to nonlinear static response of curled cantilever micro beams
Sun, Youhong; Yu, Yongping; Liu, Baochang;
 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;
 Language
English
 Cited by
 References
1.
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. crossref(new window)

2.
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. crossref(new window)

3.
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. crossref(new window)

4.
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. crossref(new window)

5.
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. crossref(new window)

6.
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. crossref(new window)

7.
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. crossref(new window)

8.
Fang, W. and Wickert, J.A. (1994), "Post buckling of micromachined beams", J. Micromech. Microeng., 4, 116-122. crossref(new window)

9.
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. crossref(new window)

10.
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.

11.
Gutschmidt, S. (2010), "The Influence of higher-order mode shapes for reduced-order models of electrostatically actuated microbeams", ASME J. Appl. Mech., 77, 041007. crossref(new window)

12.
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. crossref(new window)

13.
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. crossref(new window)

14.
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. crossref(new window)

15.
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. crossref(new window)

16.
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. crossref(new window)

17.
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. crossref(new window)

18.
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. crossref(new window)

19.
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. crossref(new window)

20.
Nayfeh, A.H., Younis, M.I. and Abdel-Rahman, E.M. (2005), "Reduced-order models for mems applications", Nonlin. Dyn., 41, 211-236. crossref(new window)

21.
Osterberg, P.M. (1995), "Electrostatically actuated microelectromechancial test structures for material property measurements", Ph.D. Dissertation, Massachusetts Institute of Technology.

22.
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. crossref(new window)

23.
Petersen, K.E. (1978), "Dynamic micromechanics on silicon techniques and devices", IEEE T. Electron Dev., 25(10), 1241-1250. crossref(new window)

24.
Rebeiz, G.M. (2003), RF MEMS: Theory, Design, and Technology, Wiley.

25.
Senturia, S.D. (2001), Microsystem Design, Kluwer, Boston, MA.

26.
Shames, I.H. and Dym, C.L. (1985), Energy and Finite Element Methods in Structural Mechanics, McGraw-Hill.

27.
Wang, W. and Soper, S.A. (2007), Bio-MEMS: Technologies and Applications, CRC/Taylor & Francis.

28.
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. crossref(new window)

29.
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. crossref(new window)

30.
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. crossref(new window)

31.
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. crossref(new window)

32.
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. crossref(new window)

33.
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. crossref(new window)

34.
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. crossref(new window)