Volume 19, Issue 10 (October 2019)                   Modares Mechanical Engineering 2019, 19(10): 2375-2385 | Back to browse issues page

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Akrami Nia E, Ekhteraei Toussi H. Investigating the Static Deformation and Instability Voltage of Viscoelastic Curved Microbeam. Modares Mechanical Engineering 2019; 19 (10) :2375-2385
URL: http://mme.modares.ac.ir/article-15-25008-en.html
1- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran
2- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran , ekhteraee@um.ac.ir
Abstract:   (5468 Views)
Microbeams are one of the most important members of microelectromechanical systems (MEMS) which contrast of electrical and mechanical forces in them cause pull-in instability. One of the proposed mechanisms for controlling this instability and enlarging the stable range of system are initially curved microbeams. Despite studying various pull-in instability in straight elastic or viscoelastic microbeams, the instability of curved microbeams has been investigated only within the range of elastic behavior. Therefore in the present study, assuming a clamped-clamped viscoelastic initially curved microbeam, the effect of viscoelastic behavior on the instabilities called snap-through and pull-in, was investigated. The viscoelastic behavior was simulated by the standard anelastic linear solid model. The governing differential equation was obtained based on the modified couple stress theory and by use of Hamilton’s pull-in instability principle. By using the Galerkin method, the governing equation was converted to a nonlinear ordinary differential equation and solved by MATLAB sofware. The structure behaviors are compared in two extreme situations before and after the viscoelastic relaxation by drawing diagrams. The results show when the time of structure relaxation increases, viscoelastic behavior causes more decreasing in instabilities voltage, but its effect on the position of instability will depend on the axial load. In this way, in the presence of tensile load, viscoelastic behavior increases the snap-through position and decreases the pull-in position, but in the presence of compressive load, snap-through occurs at smaller deflections and pull-in occurs at larger deflections.

Full-Text [PDF 1339 kb]   (1941 Downloads)    
Article Type: Original Research | Subject: Micro & Nano Systems
Received: 2018/09/10 | Accepted: 2019/02/22 | Published: 2019/10/22

References
1. Taylor GI. The coalescence of closely spaced drops when they are at different electric potentials. Proceedings of the Royal Society A. 1968;306(1487):19680159. [Link] [DOI:10.1098/rspa.1968.0159]
2. Nathanson HC, Newell WE, Wickstrom RA, Davis JR. The resonant gate transistor. IEEE Transactions on Electron Devices. 1967;14(3):117-133. [Link] [DOI:10.1109/T-ED.1967.15912]
3. Qiu J, Lang JH, Slocum AH. A centrally-clamped parallel-beam bistable MEMS mechanism. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090), 25-25 Jan 2001, Interlaken, Switzerland. Piscataway: IEEE; 2001. [Link]
4. Zhang Y, Wang Y, Li Z, Huang Y, Li D. Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading. Journal of Microelectromechanical Systems. 2007;16(3):684-693. [Link] [DOI:10.1109/JMEMS.2007.897090]
5. Zhang Y, Wang Y, Li Z. Analytical method of predicting the instabilities of a micro arch-shaped beam under electrostatic loading. Microsystem Technologies. 2010;16(6):909-918. [Link] [DOI:10.1007/s00542-010-1031-y]
6. Ouakad HM, Younis MI. The dynamic behavior of MEMS arch resonators actuated electrically. International Journal of Non Linear Mechanics. 2010;45(7):704-713. [Link] [DOI:10.1016/j.ijnonlinmec.2010.04.005]
7. Moghimi Zand M. The dynamic pull-in instability and snap-through behavior of initially curved microbeams. Mechanics of Advanced Materials and Structures. 2012;19(6):485-491. [Link] [DOI:10.1080/15376494.2011.556836]
8. Salehi Kolahi MR, Moeinkhah H. Non-linear vibration of curved microbeam under electrostatic actuation by using reduced order model and finite element simulation. Modares Mechanical Engineering. 2018;17(12):514-522. [Persian] [Link]
9. Bethe K, Baumgarten D, Frank J. Creep of sensor's elastic elements: Metals versus non-metals. Sensors and Actuators A Physical. 1990;23(1-3):844-849. [Link] [DOI:10.1016/0924-4247(90)87044-J]
10. Elwenspoek M, Jansen HV. Silicon micromachining. Cambridge UK: Cambridge University Press; 2004. [Link]
11. Schmid S, Senn P, Hierold C. Electrostatically actuated nonconductive polymer microresonators in gaseous and aqueous environment. Sensors and Actuators A Physical. 2008;145-146:442-448. [Link] [DOI:10.1016/j.sna.2008.01.010]
12. Yan X, Brown WL, Li Y, Papapolymerou J, Palego C, Hwang JCM, et al. Anelastic stress relaxation in gold films and its impact on restoring forces in MEMS devices. Journal of Microelectromechanical Systems. 2009;18(3):570-576. [Link] [DOI:10.1109/JMEMS.2009.2016280]
13. Tuck K, Jungen A, Geisberger A, Ellis M, Skidmore G. A study of creep in polysilicon MEMS devices. Journal of Engineering Materials and Technology. 2005;127(1):90-96. [Link] [DOI:10.1115/1.1839214]
14. Larsen KP, Rasmussen AA, Ravnkilde JT, Ginnerup M, Hansen O. MEMS device for bending test: Measurements of fatigue and creep of electroplated nickel. Sensors and Actuators A Physical. 2003;103(1-2):156-164. [Link] [DOI:10.1016/S0924-4247(02)00306-0]
15. Lee HJ, Zhang P, Bravman JC. Stress relaxation in free-standing aluminum beams. Thin Solid Films. 2005;476(1):118-124. [Link] [DOI:10.1016/j.tsf.2004.10.001]
16. Fu YM, Zhang J. Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam. Acta Mechanica Sinica. 2009;25(2):211-218. [Link] [DOI:10.1007/s10409-008-0216-4]
17. Ghayesh MH, Farokhi H, Hussain Sh. Viscoelastically coupled size-dependent dynamics of microbeams. International Journal of Engineering Science. 2016;109:243-255. [Link] [DOI:10.1016/j.ijengsci.2016.09.004]
18. Attia MA, Mohamed SA. Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory. Applied Mathematical Modelling. 2017;41:195-222. [Link] [DOI:10.1016/j.apm.2016.08.036]
19. Li L, Zhang Q, Wang W, Han J. Dynamic analysis and design of electrically actuated viscoelastic microbeams considering the scale effect. International Journal of Non Linear Mechanics. 2017;90:21-31. [Link] [DOI:10.1016/j.ijnonlinmec.2017.01.002]
20. Veysi Gorgabad A, Rezazadeh Gh, Shabani R. A study on the nonlinear vibrations of electrostatically actuated micro beams with anelastic stress-strain behavior. Modares Mechanical Engineering. 2017;17(7):197-206. [Persian] [Link]
21. Ramini AH, Hennawi QM, Younis MI. Theoretical and experimental investigation of the nonlinear behavior of an electrostatically actuated in-plane MEMS arch. Journal of Microelectromechanical Systems. 2016;25(3):570-578. [Link] [DOI:10.1109/JMEMS.2016.2554659]
22. Qian YH, Ren DX, Lai SK, Chen SM. Analytical approximations to nonlinear vibration of an electrostatically actuated microbeam. Communications in Nonlinear Science and Numerical Simulation. 2012;17(4):1947-1955. [Link] [DOI:10.1016/j.cnsns.2011.09.018]
23. Fu Y, Zhang J, Wan L. Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS). Current Applied Physics. 2011;11(3):482-485. [Link] [DOI:10.1016/j.cap.2010.08.037]
24. Batra RC, Porfiri M, Spinello D. Vibrations of narrow microbeams predeformed by an electric field. Journal of Sound and Vibration. 2008;309(3-5):600-612. [Link] [DOI:10.1016/j.jsv.2007.07.030]

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