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Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope
J. Appl. Phys. 92, 6262 (2002); doi:10.1063/1.1512318
Issue Date: 15 November 2002
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The frequency response of a cantilever beam is strongly dependent on the fluid in which it is immersed. In a companion study, Sader [J. Appl. Phys. 84, 64, (1998)] presented a theoretical model for the flexural vibrational response of a cantilever beam, that is immersed in a viscous fluid, and excited by an arbitrary driving force. Due to its relevance to applications of the atomic force microscope (AFM), we extend the analysis of Sader to the related problem of torsional vibrations, and also consider the special case where the cantilever is excited by a thermal driving force. Since longitudinal deformations of AFM cantilevers are not measured normally, combination of the present theoretical model and that of the companion study enables the complete vibrational response of an AFM cantilever beam, that is immersed in a viscous fluid, to be calculated. ©2002 American Institute of Physics.
| History: | Received 11 March 2002; accepted 12 August 2002 |
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REFERENCES (33)
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- W.-H. Chu, Technical Report No. 2, DTMB, Contract NObs-86396(X), Southwest Research Institute, San Antonio, Texas, 1963.
- U.S. Lindholm, D. D. Kana, W.-H. Chu, and H. N. Abramson, J. Ship Res. 9, 11 (1965).
- J. E. Sader, J. Appl. Phys. 84, 64 (1998).
- L. Landweber, J. Ship Res. 11, 143 (1967).
- G. Y. Chen, R. J. Warmack, T. Thundat, D. P. Allison, and A. Huang, Rev. Sci. Instrum. 65, 2532 (1994).
- T. E. Schäffer, J. P. Cleveland, F. Ohnesorge, D. A. Walters, and P. K. Hansma, J. Appl. Phys. 80, 3622 (1996).
- F.-J. Elmer and M. Dreier, J. Appl. Phys. 81, 7709 (1997).
- D. A. Walters, J. P. Cleveland, N. H. Thomson, P. K. Hansma, M. A. Wendman, G. Gurley, and V. Elings, Rev. Sci. Instrum. 67, 3583 (1996).
- H.-J. Butt, P. Siedle, K. Seifert, K. Fendler, T. Seeger, E. Bamberg, A. Weisenhorn, K. Goldie, and A. Engel,
J. Microsc. 169, 75 (1993) . - M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, and E. McFarland, J. Appl. Phys. 81, 2480 (1997).
- J. W. M. Chon, P. Mulvaney, and J. E. Sader, J. Appl. Phys. 87, 3978 (2000).
- L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, London, 1959).
- J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999).
- G. Behme and T. Hesjedal, J. Appl. Phys. 89, 4850 (2001).
- G. Bogdanovic, A. Meurk, and M. W. Rutland,
Colloids Surf., B 19, 397 (2000) . - G. Behme, T. Hesjedal, E. Chilla, and H.-J. Frölich, Appl. Phys. Lett. 73, 882 (1998).
- S. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering (Wiley, New York, 1974). We only consider the case where coupling between flexural and torsional vibrations is negligible.
- H.-J. Butt and M. Jaschke,
Nanotechnology 6, 1 (1995) . - This condition also holds for cantilevers composed of crystalline materials, provided the crystal orientation is fixed along the entire length of the cantilever.
- This can also be satisfied for cantilevers with sharp edges, since the radius of curvature of such edges is always greater than zero in practice.
- The convention adopted for the Reynolds number conforms with Ref. 30. We note that the Reynolds number is often associated with the nonlinear convective inertial term of the Navier–Stokes equation. This latter convention has not been adopted here.
- R. J. Roark, Formulas for Stress and Strain (McGraw-Hill, New York, 1943).
- The product GK is commonly referred to as the torsional rigidity of the beam.
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
- G. G. Stokes Math. Phys. Pap. 5, 207 (1886).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
- E. O. Tuck,
J. Eng. Math. 3, 29 (1969) . - Note that the undamped modes for flexural vibration presented in Ref. 3 form an orthonormal, rather than orthogonal basis set.
- A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Pergamon, London, 1959).
- G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University, Cambridge, England, 1974).
- This is typically satisfied if the laser spot is positioned at the center of the quadrant in the split photodiode.
- A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations (CRC, Boca Raton, 1998).
- H. Hochstadt, Integral Equations (Wiley, New York, 1973).
