Higher Eigenmodes Vibration Cantilever's Resonance Frequency and Cantilever Spring Constant

Abstract:

Based on dynamics theory, we have built several structures models close to the real cantilever of atomic force microscope. This paper deduces the higher eigenmodes vibration of single-layer camped-free cantilever in the resonant frequency calculation formula, extend to derive the equation of the resonant frequency for the cantilever with a mass M* on the moving end, introduce and extend the design theory of thin-walled "equivalent" concept, establish the bi-layer or multi-layer film structure of the equivalent model, use the single-layer camped-free cantilever method discussed in the resonant frequency of the multi-layer cantilever beam. Make full use of the higher eigenmodes vibration model, to discuss the ideal condition of cantilever spring constant.

• Periodical: Applied Mechanics and Materials (Volumes 44-47)
• Pages: 489-493
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.44-47.489
• Online since: December 2010
• Authors: Qiang Xian Huang, Qi Hou
• Keywords: AFM, Cantilever, Cantilever Spring Constant, Resonance Frequency, Vibration

References

[1] U. Rabe and W. Arnold, Appl. Phys. Lett. 64(1994), 1493.

[2] O. V. Kolosov, M. R. Castell, C. D. Marsh, and A. Brix, Phys. Rev. Lett. 81(1998), 1046.

[3] R. W. Stark and W. M. Heckl, Rev. Sci. Instrum. 74(2003), 5111.

[4] T. R. Rodríguez and R. García, Appl. Phys. Lett. 84(2004), 449.

[5] Y.M. Tseytlin, Rev. Sci. Instrum. 79(2008).

[6] Y. Chen, Vibrations: Theoretical Methods, Addison-Wesley, (1966), p.225.

[7] E. B. Magrab: Vibration of Elastic structural members (1979).

[8] A. N. Krylov: Ship vibrations, in Collected Works, Vol. 10(1948) , Academy of Sciences of the USSR.

[9] J.P. Cleveland, S. Manne and D. Bocek, Rev. Sci. Instrum. 64 (1993, p.403—405.

[10] Sader.J. E, Larson. I, Mulvaney. P, Rev. Sci. Instrum, Vol 66(1995), pp.3789-3798.

[11] Sader.J. E, Chon J.W. M and Mulvaney. P, Sci. Instrum, Vol 70(1999) , p.3967—3969.

[12] C.P. Green, J.P. Cleveland and Sader.J. E Sci. Instrum, Vol 75(2004).