Journal of Applied and Computational Mechanics

Investigation of the vdW Force-Induced Instability in Nano-scale Actuators Fabricated form Cylindrical Nanowires

Document Type : Research Paper

Authors

1 Department of Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of Engineering, Ramsar Branch, Islamic Azad University, Ramsar, Iran

Abstract

The presence of van der Waals (vdW) force can lead to mechanical instability in freestanding nano-scale actuators. Most of the previous researches in this area have exclusively focused on modeling the instability in actuators with one actuating components. While, less attention has been paid to actuators consist of two actuating components. Herein, the effect of the vdW force on the instability of freestanding actuators with two parallel actuating components is investigated. Conventional configurations including cantilever and double-clamped geometries are investigated. A continuum mechanics theory in conjunction with Euler-beam model is applied to obtain governing equations of the systems. The nonlinear governing equations of the actuators are solved using two different approaches, i.e. the modified Adomian decomposition and the finite difference method. The maximum length of the nanowire and minimum initial gap which prevents the instability is computed.

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References
[1]. C. H. Ke and H. D. Espinosa. Nanoelectromechanical Systems and Modeling, In  Handbook of Theoretical and Computational Nanotechnology, M. Rieth, W. Schommers and P. D. Gennes Ed., Chapter 121, American Scientific Publishers, Valencia, CA, USA, 2006.
[2]. A. Koochi, A. Noghrehabadi and M. Abadyan. Approximating the effect of van der Waals force on the instability of electrostatic nano-cantilevers. Int. J. Mod. Phys. B., 25(29), 3965-3976, 2011.
[3]. P. M. Osterberg. Electrostatically actuated micromechanical test structures for material property measurement, PhD Dissertation, Massachusetts Institute of Technology (MIT), Cambridge, MA, 1995.
[4]. P. M. Osterberg, R. K. Gupta, J. R. Gilbert, and S. D. Senturia. Quantitative Models for the Measurement of Residual Stress, Poisson Ratio and Young's Modulus using Electrostatic Pull-in of Beams and Diaphragms.  Proc. Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 184, 1994.
[5]. R. C. Batra, M. Porfiri and D. Spinello. Review of modeling electrostatically actuated microelectromechanical systems. Smart Mater. Struct., 16, pp R23-R31, 2004.
[6] Abadian, N., Gheisari, R., Keivani, M., Kanani, A., Mokhtari, J., Rach, R., & Abadyan, M. Effect of the centrifugal force on the electromechanical instability of U-shaped and double-sided sensors made of cylindrical nanowires. Journal of the Brazilian Society of Mechanical Sciences and Engineering, pp. 1-20, 2016.
[7] Keivani, M., Kanani, A., Mardaneh, M. R., Mokhtari, J., Abadyan, N., & Abadyan, M. Influence of Accelerating Force on the Electromechanical Instability of Paddle-Type and Double-Sided Sensors Made of Nanowires. International Journal of Applied Mechanics, 8(01), 1650011, 2016.
[8] Keivani, M., Khorsandi, J., Mokhtari, J., Kanani, A., Abadian, N., & Abadyan, M. Pull-in instability of paddle-type and double-sided NEMS sensors under the accelerating force. Acta Astronautica, 119, pp. 196-206, 2016.
[9] Keivani, M., Mokhtari, J., Kanani, A., Abadian, N., Rach, R., & Abadyan, M. A size-dependent model for instability analysis of paddle-type and double-sided NEMS measurement sensors in the presence of centrifugal force. Mechanics of Advanced Materials and Structures, (just-accepted), 1-40, 2016.
[10]. A. Noghrehabadi, Y. T. Beni, A. Koochi, A. S. Kazemi, A. Yekrangi, M. Abadyan and et al. Closed-form Approximations of the Pull-in Parameters and Stress Field of Electrostatic Cantilever Nano-actuators Considering van der Waals Attraction. Procedia Engineering, 10, 3750-3756, 2011.
[11]. A. Koochi, N. fazli, R. Rach and M. Abadyan. Modeling the pull-in instability of the CNT-based probe/actuator under the Coulomb force and the van der Waals attraction. Latin American Journal of solids and structures. 11, 1315-1328, 2014.
[12]. A. Koochi, H. Hosseini-Toudeshky, H. R. Ovesy and M. Abadyan. Modeling the Influence Of Surface Effect On Instability Of Nano-Cantilever In Presence Of Van Der Waals Force. International Journal of Structural Stability and Dynamics, 13(04), 1250072, 2013.
[13] Farrokhabadi, A., Mokhtari, J., Koochi, A., & Abadyan, M. A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers. Indian Journal of Physics,89(6), 599-609, 2015.
[14]. A. Farrokhabadi, R. Rach and M. Abadyan. Modeling the static response and pull-in instability of CNT nanotweezers under the Coulomb and van der Waals attractions. Physica E: Low-dimensional Systems and Nanostructures, 53, 137-145, 2013.
[15]. Mokhtari, J., Farrokhabadi, A., Rach, R., & Abadyan, M. Theoretical modeling of the effect of Casimir attraction on the electrostatic instability of nanowire-fabricated actuators. Physica E: Low-dimensional Systems and Nanostructures, 68, 149-158, 2015.
[16]. J. Duan, R. Rach and A. Wazwaz. Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems. International Journal of Non-Linear Mechanics, 49, 159-169, 2013.
[17]. L. Zhang, S. V. Golod, E. Deckardt, V. Prinz and D. Grützmacher. Free-standing Si/SiGe micro- and nano-objects. Physica E, 23(3-4), 280-284, 2004.
[18]. A. Koochi, A. Kazemi and M. Abadyan. Simulating Deflection and Determining Stable Length of Freestanding Carbon Nanotube Probe/Sensor In The Vicinity Of Graphene Layers Using A Nanoscale Continuum Model. Nano Vol. 6, No. 5, 419–429, 2011.
[19]. A. Koochi, A. Kazemi, A. Noghrehabadi, A. Yekrangi and M. Abadyan. New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets. Materials & Design, 32(5), 2949-2955, 2012.
[20]. W. M. van Spengen, R. Puers and I. DeWolf. A physical model to predict Stiction in MEMS. J. Micromech. Microeng., 12, 702-713, 2002.
[21]. J. M. Dequesnes, S. V. Rotkin and N. R. Aluru. Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches. Nanotechnology, 13, 120-131, 2002.
[22]. S. V. Rotkin, Microfabricated Systems and MEMS VI: Proceedings of the International Symposium, Hesketh P. J., Ang S. S., Davidson J. L., Hughes H. G. and Misra D. Ed, Electrochemical Society Inc., Penningtone, New Jersey, USA, 90, 2002.
[23]. W. H. Lin and Y. P. Zhao. Dynamics behavior of nanoscale electrostatic actuators. Chin. Phys. Lett., 20, 2070-2073, 2003.
[24]. H. M. Sedighi and K.H. Shirazi. Dynamic pull-in instability of double-sided actuated nano-torsional switches. Acta Mechanica Solida Sinica, 2013.
[25]. Y. Fu, J. Zhang and L. Wan. Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS). Current Applied Physics, 11, 482-485, 2011.
[26]. C. Ke. Resonant pull-in of a double-sided driven nanotube-based electromechanical resonator. Journal of Applied Physics, 105, 024301, 2009.
[27]. A. Farrokhabadi, A. Koochi and M. Abadyan. Modeling the instability of CNT tweezers using a continuum model. Microsyst Technol 20, 291–302, 2014.
[28]. J.N. Israelachvili, Intermolecular and Surface Forces, 3rd ed.; Elsevier: Amsterdam, The Netherlands, Chapter 13, 2011.
[29]. H. M. Sedighi Size-dependent dynamic pull-in instability of vibrating electrically actuated micro-beams based on the strain gradient elasticity theory, Acta Astronautica, 2014.
[30]. R. Soroush, A. Koochi, A. S. Kazemi, A. Noghrehabadi, H. Haddadpour and M. Abadyan. Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nanoactuators. Phys. Scripta. 82, 045801, 2010.
[31]. R. Rach. A convenient computational form for the Adomian polynomials. Journal of Mathematical Analysis and Applications, 102, 415-419, 1984.
[32]. R. Rach, A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011. Kybernetes, 41(7,8), 1087-1148, 2012.
[33]. J. Abdi, A. Koochi, A. S. Kazemi and M. Abadyan. Modeling the Effects of Size Dependency and Dispersion Forces on the Pull-In Instability of Electrostatic Cantilever NEMS Using Modified Couple Stress Theory. Smart Materials and Structures, 20, 055011, 2011.
Journal of Applied and Computational Mechanics
Volume 2, Issue 1
March 2016
Pages 8-20