Volume 19, Issue 2 (February 2019)
Modares Mechanical Engineering 2019, 19(2): 247-258 |
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1- Applied Designing Department, Mechanical Engineering Faculty, Tarbiat Modares University, Tehran, Iran
2- Applied Designing Department, Mechanical Engineering Faculty, Tarbiat Modares University, Tehran, Iran , ghazavim@modares.ac.ir
2- Applied Designing Department, Mechanical Engineering Faculty, Tarbiat Modares University, Tehran, Iran , ghazavim@modares.ac.ir
Abstract: (8058 Views)
Nonlinear behavior of an initially curved fully clamped microbeam is investigated in this paper. The microbeam is laminated between two thin piezoelectric layers along its length. Applying voltage to the piezoelectric layers induces a lengthwise force in the microbeam which, in turn, changes the initial rise and the bending stiffness of the microbeam. This feature is used to tune the frequency and the bistability band of the initially curved microbeam for the first time in this paper. The microbeam is electrostatically actuated as well. The governing equation of motion is obtained, using the Hamilton’s principle and the size effect is considered in the formulation of the problem utilizing the strain gradient theory. Static response of the system is obtained, using the Newton-Raphson numerical approach. The natural frequency of the system is obtained for various electrostatic voltages. The influence of piezoelectric actuation and size effect is studied on the static behavior and the frequency of the microbeam. Dynamic response of the microbeam in the vicinity of the primary resonance is obtained, using shooting technique and in some cases by the method of multiple scales. The effect of size and piezoelectric excitation on the primary resonance is investigated. The secondary resonance of the microbeam subjected to subharmonic resonance of order 1/2 and the influence of size on it is also studied.
Keywords: Initially curved microbeam, Piezoelectric layers, Strain gradient theory, Primary resonance, Secondary resonance
Article Type: Original Research |
Subject:
Dynamics
Received: 2018/04/2 | Accepted: 2018/10/10 | Published: 2019/02/2
Received: 2018/04/2 | Accepted: 2018/10/10 | Published: 2019/02/2
References
1. Younis MI. MEMS linear and nonlinear statics and dynamics. New York: Springer Science & Business Media; 2011. [Link] [DOI:10.1007/978-1-4419-6020-7]
2. Younis MI, Ouakad HM, Alsaleem FM, Miles R, Cui W. Nonlinear dynamics of MEMS arches under harmonic electrostatic actuation. Journal of Microelectromechanical Systems. 2010;19(3):647-656. [Link] [DOI:10.1109/JMEMS.2010.2046624]
3. Charlot B, Sun W, Yamashita K, Fujita H, Toshiyoshi H. Bistable nanowire for micromechanical memory. Journal of Micromechanics and Microengineering. 2008;18(4):045005. [Link] [DOI:10.1088/0960-1317/18/4/045005]
4. Al Hafiz MA, Kosuru L, Ramini A, Chappanda KN, Younis MI. In-plane MEMS shallow arch beam for mechanical memory. Micromachines. 2016;7(10):191. [Link] [DOI:10.3390/mi7100191]
5. Intaraprasonk V, Fan S. Nonvolatile bistable all-optical switch from mechanical buckling. Applied Physics Letters. 2011;98(24):241104. [Link] [DOI:10.1063/1.3600335]
6. Joe DJ, Linzon Y, Adiga VP, Barton RA, Kim M, Ilic B, et al. Stress-based resonant volatile gas microsensor operated near the critically buckled state. Journal of Applied Physics. 2012;111(10):104517. [Link] [DOI:10.1063/1.4720473]
7. Ouakad HM. An electrostatically actuated MEMS arch band-pass filter. Shock and Vibration. 2013;20(4):809-819. [Link] [DOI:10.1155/2013/819398]
8. 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]
9. Krylov S, Ilic BR, Schreiber D, Seretensky S, Craighead H. The pull-in behavior of electrostatically actuated bistable microstructures. Journal of Micromechanics and Microengineering. 2008;18(5):055026. [Link] [DOI:10.1088/0960-1317/18/5/055026]
10. Das K, Batra RC. Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems. Journal of Micromechanics and Microengineering. 2009;19(3):035008. [Link] [DOI:10.1088/0960-1317/19/3/035008]
11. Krylov S, Dick N. Dynamic stability of electrostatically actuated initially curved shallow micro beams. Continuum Mechanics and Thermodynamics. 2010;22(6-8):445-468. [Link] [DOI:10.1007/s00161-010-0149-6]
12. 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]
13. Bataineh AM, Younis MI. Dynamics of a clamped-clamped microbeam resonator considering fabrication imperfections. Microsystem Technologies. 2015;21(11):2425-2434. [Link] [DOI:10.1007/s00542-014-2349-7]
14. Chen X, Meguid SA. On the parameters which govern the symmetric snap-through buckling behavior of an initially curved microbeam. International Journal of Solids and Structures. 2015;66:77-87. [Link] [DOI:10.1016/j.ijsolstr.2015.04.011]
15. Mc Farland AW, Colton JS. Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering. 2005;15(5):1060. [Link] [DOI:10.1088/0960-1317/15/5/024]
16. Chen X, Meguid SA. Snap-through buckling of initially curved microbeam subject to an electrostatic force. Proceedings of the Royal Society A. 2015;471:20150072. [Link] [DOI:10.1098/rspa.2015.0072]
17. Ghayesh MH, Farokhi H, Alici G. Size-dependent electro-elasto-mechanics of MEMS with initially curved deformable electrodes. International Journal of Mechanical Sciences. 2015;103:247-264. [Link] [DOI:10.1016/j.ijmecsci.2015.09.011]
18. Tajaddodianfar F, Nejat Pishkenari H, Hairi Yazdi MR, Maani Miandoab E. Size-dependent bistability of an electrostatically actuated arch NEMS based on strain gradient theory. Journal of Physics D Applied Physics. 2015;48(24):245503. [Link] [DOI:10.1088/0022-3727/48/24/245503]
19. Tajaddodianfar F, Nejat Pishkenari H, Hairi Yazdi MR, Maani Miandoab E. On the dynamics of bistable micro/nano resonators: Analytical solution and nonlinear behavior. Communications in Nonlinear Science and Numerical Simulation. 2015;20(3):1078-1089. [Link] [DOI:10.1016/j.cnsns.2014.06.048]
20. Ghayesh MH, Farokhi H. Bistable nonlinear response of MEMS resonators. Nonlinear Dynamics. 2017;90(3):1627-1645. [Link] [DOI:10.1007/s11071-017-3753-1]
21. Lam DCC, Yang F, Chong ACM, Wang J, Tong P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-1508. [Link] [DOI:10.1016/S0022-5096(03)00053-X]
22. Nikpourian AR, Ghazavi MR, Azizi S. On the nonlinear dynamics of a piezoelectrically tuned micro-resonator based on non-classical elasticity theories. International Journal of Mechanics and Materials in Design. 2018;14(1):1-19. [Link] [DOI:10.1007/s10999-016-9357-y]
23. Preumont A. Mechatronics: Dynamics of electromechanical and piezoelectric systems. Dordrecht: Springer Science & Business Media; 2006. [Link]
24. Ballas RG. Piezoelectric multilayer beam bending actuators: Static and dynamic behavior and aspects of sensor integration. Heidelberg: Springer Science & Business Media; 2007. [Link]
25. Azizi S, Ghazavi MR, Rezazadeh Gh, Ahmadian I, Cetinkaya C. Tuning the primary resonances of a micro resonator, using piezoelectric actuation. Nonlinear Dynamics. 2014;76(1):839-852. [Link] [DOI:10.1007/s11071-013-1173-4]
26. Farokhi H, Ghayesh MH, Amabili M. Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. International Journal of Engineering Science. 2013;68:11-23. [Link] [DOI:10.1016/j.ijengsci.2013.03.001]
27. Meirovitch L. Fundamentals of vibrations. Long Grove: Waveland Press; 2010. [Link]
28. Maani Miandoab E, Nejat Pishkenari H, Yousefi Koma A. Dynamic analysis of electrostatically actuated nanobeam based on strain gradient theory. International Journal of Structural Stability and Dynamics. 2015;15(04):1450059. [Link] [DOI:10.1142/S021945541450059X]
29. Nayfeh AH, Balachandran B. Applied nonlinear dynamics: Analytical, computational and experimental methods. Hoboken: John Wiley & Sons; 2008. [Link]
30. Azizi S, Chorsi MT, Bakhtiari Nejad F. On the secondary resonance of a MEMS resonator: A conceptual study based on shooting and perturbation methods. International Journal of Non-Linear Mechanics. 2016;82:59-68. [Link] [DOI:10.1016/j.ijnonlinmec.2016.02.003]
31. Osterberg PM, Senturia SD. M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures. Journal of Microelectromechanical Systems. 1997;6(2):107-118. [Link] [DOI:10.1109/84.585788]
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