Static and dynamic analysis of micro beams based on strain gradient elasticity theory

International Journal of Engineering Science

Volumn 47, Issue 4, 2009, Pages 487-498

  Kong, Shengli ^a   Zhou, Shenjie ^a   Nie, Zhifeng ^a   Wang, Kai ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Bernoulli Euler beam; Natural frequency; Non classical boundary conditions; Size effect; Strain gradient

Indexed keywords

ATOMIC FORCE MICROSCOPY; BOUNDARY CONDITIONS; BOUNDARY LAYER FLOW; CANTILEVER BEAMS; CONTACTS (FLUID MECHANICS); DIFFERENTIAL EQUATIONS; ELASTICITY; ELASTOHYDRODYNAMICS; ELECTRIC LOAD SHEDDING; FREQUENCY RESPONSE; NANOCANTILEVERS; NATURAL FREQUENCIES; PROGRAMMING THEORY; SIZE DETERMINATION; STRAIN MEASUREMENT;

BERNOULLI-EULER BEAM; NATURAL FREQUENCY; NON-CLASSICAL BOUNDARY CONDITIONS; SIZE EFFECT; STRAIN GRADIENT;

DYNAMIC ANALYSIS;

EID: 60449092814     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2008.08.008     Document Type: Article

References (37)

1. Hall N.A., Okandan M., and Degertekin F.L. Surface and bulk-silicon-micromachined optical displacement sensor fabricated with the SwIFT-Lite process. Journal of Microelectromechanical Systems 15 4 (2006) 770-776
2. Moser Y., and Gijs M.A.M. Miniaturized flexible temperature sensor. Journal of Microelectromechanical Systems 16 6 (2007) 1349-1354
3. Hung E.S., and Senturia S.D. Extending the travel range of analog-tuned electrostatic actuators. Journal of Microelectromechanical Systems 8 4 (1999) 497-505
4. De Boer M.P., Luck D.L., Ashurst W.R., et al. High-performance surface-micromachined inchworm actuator. Journal of Microelectromechanical Systems 13 1 (2004) 63-74
5. Qu H., and Xie H. Process development for CMOS-MEMS sensors with robust electrically isolated bulk silicon microstructures. Journal of Microelectromechanical Systems 16 5 (2007) 1152-1161
6. Mouaziz S., Boero G., Popovic R.S., et al. Polymer-based cantilevers with integrated electrodes. Journal of Microelectromechanical Systems 15 4 (2006) 890-895
7. Borca-Tasciuc T., Borca-Tasciuc D.-A., Graham S., et al. Annealing effects on mechanical and transport properties of Ni and Ni-Alloy electrodeposits. Journal of Microelectromechanical Systems 15 5 (2006) 1051-1059
8. Stelmashenko N.A., Walls M.G., Brown L.M., et al. Microindentations on W and Mo oriented single crystals: an STM study. Acta Metallurgica et Materialia 41 10 (1993) 2855-2865
9. Poole W.J., Ashby M.F., and Fleck N.A. Micro-hardness of annealed and work-hardened copper polycrystals. Scripta Materialia 34 4 (1996) 559-564
10. Guo X.H., Fang D.N., and Li X.D. Measurement of deformation of pure Ni foils by speckle pattern interferometry. Mechanical in Engineering 27 2 (2005) 21-25
11. Fleck N.A., Muller G.M., Ashby M.F., et al. Strain gradient plasticity: theory and experiment. Acta Metallurgica et Materialia 42 2 (1994) 475-487
12. Ma Q., and Clarke D.R. Size dependent hardness of silver single crystals. Journal of Materials Research 10 4 (1995) 853-863
13. Chong A.C.M., and Lam D.C.C. Strain gradient plasticity effect in indentation hardness of polymers. Journal of Materials Research 14 10 (1999) 4103-4110
14. Stolken J.S., and Evans A.G. Microbend test method for measuring the plasticity length scale. Acta Materialia 46 14 (1998) 5109-5115
15. Lam D.C.C., Yang F., Chong A.C.M., et al. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids 51 8 (2003) 1477-1508
16. A.W. McFarland, 2004, Production and analysis of polymer microcantilever parts, Ph.D, Georgia Institute of Technology, Atlanta.
17. 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 5 (2005) 1060-1067
18. Beskou S.P., Tsepoura K.G., Polyzos D., et al. Bending and stability analysis of gradient elastic beams. International Journal of Solids and Structures 40 2 (2003) 385-400
19. Papargyri-Beskou S., Polyzos D., and Beskos D.E. Dynamic analysis of gradient elastic flexural beams. Structural Engineering and Mechanics 15 6 (2003) 705-716
20. Giannakopoulos A.E., and Stamoulis K. Structural analysis of gradient elastic components. International Journal of Solids and Structures 44 10 (2007) 3440-3451
21. Mindlin R.D., and Tiersten H.F. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis 11 1 (1962) 415-448
22. Mindlin R.D. Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis 16 1 (1964) 51-78
23. Mindlin R.D. second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures 1 1 (1965) 417-438
24. Toupin R.A. Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis 11 1 (1962) 385-414
25. Zhou S.J., and Li Z.Q. Length scales in the static and dynamic torsion of a circular cylindrical micro-bar. Journal of Shandong University of Technology 31 5 (2001) 401-407
26. Kang X., and Xi Z.W. size effect on the dynamic characteristic of a micro beam based on cosserat theory. Journal of Engineering Strength 29 1 (2007) 1-4
27. Fleck N.A., and Hutchinson J.W. Phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids 41 12 (1993) 1825-1857
28. Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. Advances in Applied Mechanics 33 (1997) 296-358
29. Fleck N.A., and Hutchinson J.W. A reformulation of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 49 10 (2001) 2245-2271
30. Smyshlyaev V.P., and Fleck N.A. Role of strain gradients in the grain size effect for polycrystals. Journal of the Mechanics and Physics of Solids 44 4 (1996) 465-495
31. Yang F., Chong A.C.M., Lam D.C.C., et al. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures 39 10 (2002) 2731-2743
32. Park S.K., and Gao X.L. Bernoulli-Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering 16 11 (2006) 2355-2359
33. Kong S.L., ZHOU S.J., Nie Z.F., et al. The size-dependent natural frequency of Bernoulli-Euler micro-beams. International Journal of Engineering Science 46 5 (2008) 427-437
34. C.M. Chong, 2002, Experimental investigation and modeling of size effect in elasticity, Ph.D., Hong Kong University of Science and Technology (People's Republic of China), Hong Kong.
35. DYM C.L., and Shames I.H. Solid Mechanics: A Variational Approach (1984), China Railway Publishing House, Beijing
36. Ginsberg J.H. Mechanical and Structural Vibrations: Theory and Applications (2001), Wiley
37. Kitahara M. Boundary Integral Equation Methods in Eigenvalue Problems of Elastodynamics and Thin Plates (1985), Elsevier, Amsterdam