Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-28T17:15:16.669Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Bilayer Continuum Model Based on Gurtin-Murdoch and Consistent Couple-Stress Theories for Stability Analysis of Beam-Type Nanotweezers

Published online by Cambridge University Press:  01 July 2016

M. Keivani ,
A. Koochi  and
M. Abadyan
M. Keivani
Affiliation:
Sharekord University of Medical SciencesSharekord, Iran
A. Koochi
Affiliation:
Mechanical Engineering GroupShahrekord BranchIslamic Azad UniversityShahrekord, Iran
M. Abadyan*
Affiliation:
Mechanical Engineering GroupShahrekord BranchIslamic Azad UniversityShahrekord, Iran
*
*Corresponding author (abadyan@yahoo.com)
Get access

Abstract

Nano-scale beams might not be considered uniform isotropic since the energy of the surface layer and microstructure of the bulk part highly affect the mechanical characteristics of the beams. Herein, the impact of the energy of the surface layer and the microstructure of the bulk on the mechanical stability of beam-type nanotweezers are investigated. A new bilayer continuum model has been developed which incorporates the strain energy of the surface atoms as well as the microstructure-dependent strain energy of the bulk material. The recently-developed consistent couple stress elasticity (CCSE) in combination with the Gurtin-Murdoch surface theory is applied to derive the governing equation. The nonlinear governing equation was solved using numerical generalized differential quadrature (GDQ). Effects of various parameters including characteristics of the surface layer, microstructure of the bulk and external forces on the static and dynamic stability threshold of the nanostructure are demonstrated.

Keywords

NanotweezersGurtin-Murdoch surface theoryConsistent Couple Stress Elasticity (CCSE)Generalized Differential Quadrature (GDQ)
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 137 - 146
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Kim, P. and Lieber, C. M., “Nanotube Nanotweezers,” Science, 286, pp. 2148–2150 (1999).CrossRefGoogle ScholarPubMed
2. Akita, S. and Nakayama, Y., “Manipulation of Nanomaterial by Carbon Nanotube Nanotweezers in Scanning Probe Microscope,” Japanese Journal of Applied Physics, 41, pp. 4242–4245 (2002).CrossRefGoogle Scholar
3. Farrokhabadi, A., Mokhtari, J., Rach, R. and Abadyan, M., “Modeling the Influence of the Casimir Force on the Pull-In Instability of Nanowire-Fabricated Nanotweezers,” International Journal of Modern Physics B, 29 (2014).Google Scholar
4. Ramezani, A., “Stability Analysis of Electrostatic Nanotweezers,” Physica E, 43, pp. 1783–1791 (2011).CrossRefGoogle Scholar
5. Lakrad, F. and Belhaq, M., “Suppression of Pull-In Instability in MEMS Using a High-Frequency Actuation,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 3640–3646 (2010).CrossRefGoogle Scholar
6. Lin, W. H. and Zhao, Y. P., “Pull-In Instability of Micro-Switch Actuators: Model Review,” International Journal of Nonlinear Science and Numerical Simulation, 9, pp. 175–184 (2008).CrossRefGoogle Scholar
7. Zand, M. M. and Ahmadian, M. T., “Vibrational Analysis of Electrostatically Actuated Microstructures Considering Nonlinear Effects,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 1664–1678 (2009).CrossRefGoogle Scholar
8. Tajaddodianfar, F., Pishkenari, H. N., Yazdi, M. R. H. and Miandoab, E. M., “On the Dynamics of Bistable Micro/Nano Resonators: Analytical Solution and Nonlinear Behavior,” Communications in Nonlinear Science and Numerical Simulation, 20, pp. 1078–89 (2015).CrossRefGoogle Scholar
9. Baghani, M., “Analytical Study on Size-Dependent Static Pull-In Voltage of Microcantilevers Using the Modified Couple Stress Theory,” International Journal of Engineering Science, 54, pp. 99–105 (2012).CrossRefGoogle Scholar
10. Fakhrabadi, M. M. S. and Yang, J., “Comprehensive Nonlinear Electromechanical Analysis of Nanobeams Under DC/AC Voltages Based on Consistent Couple-Stress Theory,” Composite Structures, 132, pp. 1206–1218 (2015).CrossRefGoogle Scholar
11. Soroush, R., et al., “Investigating the Effect of Casimir and Van Der Waals Attractions on the Electrostatic Pull-In Instability of Nano-Actuators,” Physica Scripta, 82 (2010).CrossRefGoogle Scholar
12. Batra, R. C., Porfiri, M. and Spinello, D., “Effects of Casimir Force on Pull-In Instability in Micromembranes,” EPL (Europhysics Letters), 77 (2007).CrossRefGoogle Scholar
13. Abdi, J., Koochi, A., Kazemi, A. S. and Abadyan, M., “Modeling the Effects of Size Dependence and Dispersion Forces on the Pull-In Instability of Electrostatic Cantilever NEMS Using Modified Couple Stress Theory,” Smart Materials and Structures, 20 (2011).CrossRefGoogle Scholar
14. Gusso, A. and Delben, G. J., “Dispersion Force for Materials Relevant for Micro-and Nanodevices Fabrication,” Journal of Physics D: Applied Physics, 41 (2008).CrossRefGoogle Scholar
15. Batra, R. C., Porfiri, M. and Spinello, D., “Reduced-Order Models for Microelectromechanical Rectangular and Circular Plates Incorporating the Casimir Force,” International Journal of Solids and Structures, 45, pp. 3558–3583 (2008).CrossRefGoogle Scholar
16. Gusso, A. and Delben, G. J., “Influence of the Casimir Force on the Pull-In Parameters of Silicon Based Electrostatic Torsional Actuators,” Sensors and Actuators A, 135, pp. 792–800 (2007).CrossRefGoogle Scholar
17. Lin, W. H. and Zhao, Y. P., “Casimir Effect on the Pull-In Parameters of Nanometer Switches,” Microsystems Technologies, 11, pp. 80–85 (2005).CrossRefGoogle Scholar
18. Lin, W. and Zhao, Y., “Nonlinear Behavior for Nanoscale Electrostatic Actuators with Casimir Force. Chaos,” Solitons Fractals, 23, pp. 1777–1785 (2005).CrossRefGoogle Scholar
19. Koochi, A., Kazemi, A. S., Beni, Y. T., Yekrangi, A. and Abadyan, M., “Theoretical Study of the Effect of Casimir Attraction on the Pull-In Behavior of Beam-Type NEMS Using Modified Adomian Method,” Physica E, 43, pp. 625–632 (2010).CrossRefGoogle Scholar
20. Chan, H. B., Aksyuk, V. A., Kleiman, R. N., Bishop, D. J. and Capasso, F., “Nonlinear Micromechanical Casimir Oscillator,” Physical Review Letters, 87 (2001).CrossRefGoogle ScholarPubMed
21. Batra, R. C., Porfiri, M. and Spinello, D., “Review of Modeling Electrostatically Actuated Microelectromechanical Systems,” Smart Materials and Structures, 16 (2007).CrossRefGoogle Scholar
22. Wang, G. W., Zhang, Y., Zhao, Y. P. and Yang, G. T., “Pull-In Instability Study of Carbon Nanotube Tweezers Under the Influence of Van Der Waals Forces,” Journal of Micromechanics and Microengineering, 14 (2004).CrossRefGoogle Scholar
23. Dequesnes, M., Rotkin, S. V. and Aluru, N. R., “Calculation of Pull-In Voltages for Carbon-Nanotube-Based Nanoelectromechanical Switches,” Nanotechnology, 13 (2002).CrossRefGoogle Scholar
24. Rotkin, S. V., “Analytical Calculations for Nanoscale Electromechanical Systems,” Electrochemanical Society Proceeding, 6, pp. 90–97 (2002).Google Scholar
25. Spengen, W. M., Puers, R. and DeWolf, I., “A Physical Model to Predict Stiction in MEMS,” Journal of Micromechanics and Microengineering, 12, pp. 702–713 (2002).CrossRefGoogle Scholar
26. Gurtin, M. E. and Murdoch, A., “A Continuum Theory of Elastic Material Surfaces,” Archive for Rational Mechanics and Analysis, 57, pp. 291–323 (1975).CrossRefGoogle Scholar
27. Gurtin, M. E. and Murdoch, A., “Surface Stress in Solids,” International Journal of Solids and Structures, 14, pp. 431–440 (1978).CrossRefGoogle Scholar
28. He, J. and Lilley, C. M., “Surface Effect on the Elastic Behaviour of Static Bending Nanowires,” Nano Letters, 8, pp. 1798–180 (2008).CrossRefGoogle ScholarPubMed
29. Wang, G. F. and Feng, X. Q., “Surface Effects on Buckling of Nanowires Under Uniaxial Compression,” Applied Physics Letters, 94 (2009).Google Scholar
30. Yan, Z. and Jiang, L. Y., “The Vibrational and Buckling Behaviors of Piezoelectric Nanobeams with Surface Effects,” Nanotechnology, 22 (2011).CrossRefGoogle ScholarPubMed
31. Fu, Y. and Zhang, J., “Size-Dependent Pull-In Phenomena in Electrically Actuated Nanobeams Incorporating Surface Energies,” Applied Mathematical Modelling, 35, pp. 941–951 (2011).CrossRefGoogle Scholar
32. Ma, J. B., Jiang, L. and Asokanthan, S. F., “Influence of Surface Effects on the Pull-In Instability of NEMS Electrostatic Switches,” Nanotechnology, 21 (2010).CrossRefGoogle ScholarPubMed
33. Koochi, A., Hosseini-Toudeshky, H., Ovesy, H. R. and Abadyan, M., “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 (2013).CrossRefGoogle Scholar
34. Koochi, A., Kazemi, A. S. and Abadyan, M., “Influence of Surface Effect on Size-Dependent Instability of Nano-Actuator in Presence of Casimir Force,” Physica Scipta., 85 (2012).Google Scholar
35. Rokni, H. and Lu, W., “A Continuum Model for the Static Pull-In Behavior of Graphene Nanoribbon Electrostatic Actuators with Interlayer Shear and Surface Energy Effects,” Journal of Applied Physics, 113 (2013).CrossRefGoogle Scholar
36. Ansari, R. and Sahmani, S., “Surface Stress Effects on the Free Vibration Behavior of Nanoplates,” International Journal of Engineering Science, 49, pp. 1204–1215 (2011).CrossRefGoogle Scholar
37. Fleck, N. A., Muller, G. M., Ashby, M. F. and Hutchinson, J. W., “Strain Gradient Plasticity: Theory and Experiment,” Acta Metallurgica Et Materialia, 42, pp. 475–487 (1994).CrossRefGoogle Scholar
38. Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. and Tong, P., “Experiments and Theory in Strain Gradient Elasticity,” Journal of the Mechanics and Physics of Solids, 51, pp. 1477–1508 (2003).CrossRefGoogle Scholar
39. McFarland, A. W. and Colton, J. S., “Role of Material Microstructure in Plate Stiffness with Relevance to Microcantilever Sensors,” Journal of Micromechanics and Microengineering, 15 (2005).CrossRefGoogle Scholar
40. Eringen, A. C. and Edelen, D. G. B., “On Nonlocal Elasticity,” International Journal of Engineering Science, 10, pp. 233–248 (1972).CrossRefGoogle Scholar
41. Yang, F. A. C. M., Chong, A. C. M., Lam, D. C. C. and Tong, P., “Couple Stress Based Strain Gradient Theory for Elasticity,” International Journal of Solids and Structures, 39, pp. 2731–2743 (2002).CrossRefGoogle Scholar
42. Hadjesfandiari, A. R. and Dargush, G. F., “Couple Stress Theory for Solids,” International Journal of Solids and Structures, 48, pp. 2496–2510 (2011).CrossRefGoogle Scholar
43. Maranganti, R. and Sharma, P., “A Novel Atomistic Approach to Determine Strain-Gradient Elasticity Constants: Tabulation and Comparison for Various Metals, Semiconductors, Silica, Polymers and the (Ir) Relevance for Nanotechnologies,” Journal of the Mechanics and Physics of Solids, 55, pp. 1823–1952 (2007).CrossRefGoogle Scholar
44. Cao, Y., Nankivil, D. D., Allameh, S. and Soboyejo, W. O., “Mechanical Properties of Au Films on Silicon Substrates,” Materials and Manufacturing Processes, 22, pp. 187–194 (2007).CrossRefGoogle Scholar
45. Nix, W. D. and Gao, H., “Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity,” Journal of the Mechanics and Physics of Solids, 46, pp. 411–425 (1998).CrossRefGoogle Scholar
46. Wang, K. F. and Wang, B. L., “Influence of Surface Energy on the Non-Linear Pull-In Instability of Nano-Switches,” International Journal of Non-Linear Mechanics, 59, pp. 69–75 (2014).CrossRefGoogle Scholar
47. Dym, C. L. and Shames, I. H., Solid Mechanics: A Variational Approach, Railway Publishing House, Beijing (1984).Google Scholar
48. Klimchitskaya, G. L., Mohideen, U. and Mostepanenko, V. M., “Casimir and Van Der Waals Forces Between Two Plates or a Sphere (Lens) Above a Plate Made of Real Metals,” Physical Review A, 61 (2000).CrossRefGoogle Scholar
49. Boström, M. and Sernelius, B. E., “Fractional Van Der Waals Interaction Between Thin Metallic Films,” Physical Review B, 61 (2000).CrossRefGoogle Scholar
50. Shu, C. H., Differential Quadrature and Its Application in Engineering, First Edition, Springer, London (1999).Google Scholar
51. Miller, R. E. and Shenoy, Vijay. B., “Size-Dependent Elastic Properties of Nanosized Structural Elements,” Nanotechnology, 11, pp. 139–147 (2000).CrossRefGoogle Scholar