Continuum models incorporating surface energy for static and dynamic response of nanoscale beams

IEEE Transactions on Nanotechnology

Volumn 9, Issue 4, 2010, Pages 422-431

  Liu, Chang ^a   Rajapakse, R K N D ^a,b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Mechanistic model; nanobeam; surface energy effect

Indexed keywords

ANALYTICAL TOOL; ARBITRARY CROSS SECTION; CLAMPED ENDS; CLASSICAL BEAM THEORY; CLOSED-FORM ANALYTICAL SOLUTIONS; CONTINUUM MODEL; CONTINUUM THEORY; CROSS-SECTIONAL SHAPE; FREE VIBRATION CHARACTERISTIC; LENGTH SCALE; MECHANISTIC MODELS; NANO ELECTROMECHANICAL SYSTEMS; NANO SCALE; NANOSCALE STRUCTURE; NUMERICAL RESULTS; SILICON BEAMS; STATIC AND DYNAMIC BEHAVIORS; STATIC AND DYNAMIC RESPONSE; STATIC RESPONSE; SURFACE ELASTIC CONSTANTS; SURFACE ENERGIES; SURFACE RESIDUAL STRESS; THICK BEAM;

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; DYNAMIC RESPONSE; ELECTRIC LOAD SHEDDING; NANOSTRUCTURED MATERIALS; NANOWIRES; NUMERICAL ANALYSIS; SURFACE CHEMISTRY; SURFACE PROPERTIES; SURFACE TENSION; VIBRATION ANALYSIS;

INTERFACIAL ENERGY;

EID: 77954581621     PISSN: 1536125X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNANO.2009.2034142     Document Type: Article

References (25)

1. H. G. Craighead, "Nanoelectromechanical systems," Science, vol.290, pp. 1532-1535, 2000.
2. K. L. Ekinci and M. L. Roukes, "Nanoelectromechanical systems," Rev. Sci. Instrum., vol.76, pp. 061101-1-061101-12, 2005.
3. G. M. Rebeiz, RF MEMS Theory, Design, and Technology. Hoboken, NJ: Wiley, 2003.
4. E. W. Wong, P. E. Sheehan, and C. M. Lieber, "Nanobeam mechanics: Elasticity, strength and toughness of nanorods and nanotubes," Science, vol.277, pp. 1971-1975, 1997.
5. R. E. Miller and V. B. Shenoy, "Size dependent elastic properties of structural elements," Nanotechnology, vol.11, pp. 139-147, 2000.
6. B. Lee and R. E. Rudd, "First-principles study of the Young's modulus of Si <001> nanowires," Phys. Rev. B, vol.75, p. 041305(R), 2007.
7. L. G. Zhou and H. Huang, "Are surface elastically softer or stiffer?" Appl. Phys. Lett., vol.84, pp. 1940-1942, 2004.
8. P. Villain, P. Beauchamp, K. F. Badawi, P. Goudeau, and P. O. Renault, "Atomistic calculation of size effects on elastic coefficients in nanometersized tungsten layers and wires," Scripta Mater., vol.50, pp. 1247-1251, 2004.
9. B. I. Yakobson, "Nanomechanics," in Handbook of Nanoscience, Engineering and Technology. Boca Raton, FL: CRC Press, 2003, Ch. 17, pp. 848-878.
10. M. E. Gurtin and A. I. Murdoch, "A continuum theory of elastic material surfaces," Arch. Ration. Mech. Anal., vol.57, pp. 291-323, 1975.
11. M. E. Gurtin and A. I. Murdoch, "Addenda to our paper: A continuum theory of elastic material surfaces," Arch. Ration. Mech. Anal., vol.59, pp. 389-390, 1975.
12. V. B. Shenoy, "Atomistic calculations of elastic properties of metallic fcc crystal surfaces," Phys. Rev., vol.71, pp. 094104-1-094104-11, 2005.
13. M. E. Gurtin, X. Markenscoff, and R. N. Thurston, "Effect of surface stress on the natural frequency of thin crystals," Appl. Phys. Lett., vol.29, pp. 529-530, 1976.
14. G. Y. Chen, T. Thundat, E. A. Wachter, and R. J. Warmack, "Adsorptioninduced surface stress and its effects on resonance frequency of microcantilevers," J. Appl. Phys., vol.77, pp. 3618-3622, 1995.
15. C.W. Lim and L. H. He, "Size-dependent nonlinear response of thin elastic films with nano-scale thickness," Int. J. Mech. Sci., vol.46, pp. 1715- 1726, 2004.
16. P. Lu, L. H. He, H. P. Lee, and C. Lu, "Thin plate theory including surface effects," Int. J. Solids Struct., vol.43, pp. 4631-4647, 2006.
17. Y. T. Yang, K. L. Ekinci, X. M. H. Huang, L. M. Schiavone, and M. L. Roukes, "Monocrystalline silicon carbide nanoelectromechanical systems," Appl. Phys. Lett., vol.78, pp. 162-164, 2001.
18. X. M. H. Huang, C. Zorman, M. Mehregany, andM. L. Roukes, "Nanodevice motion at microwave frequencies," Nature, vol.421, pp. 496-496, 2003.
19. J. H. Lee, K. H. Yoon, and T. S. Kim, "Characterization of resonant behavior and sensitivity using micromachined PZT cantilever," Integr. Ferroelectr., vol.50, pp. 43-52, 2002.
20. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, 3rd ed. London, England: Chapman & Hall.
21. S. P. Timoshenko, Schwingungsprobleme der Technik. Berlin,Germany: Verlag von Julius Springer, 1932.
22. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity. NewYork: McGraw-Hill, 1970.
23. D. J. Inman, Engineering Vibration. Englewood Cliffs, NJ: Prentice- Hall, 1996.
24. M. E. Gurtin and A. I. Murdoch, "Surface stress in solids," Int. J. Solids Struct., vol.14, pp. 431-440, 1978.
25. M. S. Daw and M. I. Baskes, "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals," Phys. Rev. B, vol.29, pp. 6443-6453, 1984.