Size Effect on Natural Frequency of Cantilever Micro-Beams Based on a Modified Couple Stress Theory

Abstract:

The natural frequency of cantilever micro-beams is solved analytically on the basis of modified couple stress theory. The governing equations are obtained by a combination of the basic equations of modified couple stress theory and Hamiltons principle. The size effect on natural frequencies of the cantilever micro-beams is analyzed. It is found that the natural frequencies of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

• Periodical: Advanced Materials Research (Volumes 694-697)
• Pages: 221-224
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.694-697.221
• Online since: May 2013
• Authors: Sheng Li Kong
• Keywords: Couple Stress Theory, Natural Frequency, Size Effect

References

[1] D.C.C. Lam, F. Yang and A.C.M. Chong: J. Mech. Phys. Solids. Vol. 51 (2003), p.1477

[2] A.W. McFarland, J.S. Colton: J. Micromech. Microeng. Vol. 15 (2005), p.1060

[3] N.A. Fleck, G.M. Muller and M.F. Ashby: Acta Metall. Mater. Vol. 42 (1994), p.475

[4] R.A. Toupin: Arch. Ration. Mech. An. Vol. 11 (1962), p.385

[5] R.D. Mindlin: Arch. Ration. Mech. An. Vol. 16 (1964), p.51

[6] F. Yang, A.C.M. Chong and D.C.C. Lam: Int. J. Solid Struct. Vol. 39 (2002), p.2731

[7] C.L. Dym, I.H. Shames: Solid Mechanics: a Variational Approach (China Railway Publishing House, China 1984), (in Chinese)

[8] H.Y. Hu: Mechanical Vibration (Beijing University of Aeronautics and Astronautics Press, China 2005), (in Chinese)