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Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope
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10.1063/1.2136418
/content/aip/journal/jap/98/11/10.1063/1.2136418
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/11/10.1063/1.2136418

Figures

Image of FIG. 1.
FIG. 1.

Rectangular cantilever beam a distance above a surface. The origin of the coordinate system is at the center of mass at the clamped end. Thickness of the beam is .

Image of FIG. 2.
FIG. 2.

Normalized thermal spectra of flexural vibration for . (a) Fundamental mode in gas with , . Quality factors, obtained using Eq. (9), are for , respectively; (b) Fundamental mode in liquid with , . for all resonance peaks.

Image of FIG. 3.
FIG. 3.

Peak and resonant frequencies of fundamental flexural resonance for immersion in gas. ; . (a) Peak frequency relative to frequency in vacuum . (b) Resonant frequency in the absence of dissipative effects in the fluid relative to frequency in vacuum . The gray area represents the region enclosed by the and the curves in (a).

Image of FIG. 4.
FIG. 4.

Peak and resonant frequencies of fundamental flexural resonance for immersion in liquid ; . (a) Peak frequency relative to frequency in vacuum . (b) Resonant frequency in the absence of dissipative effects in the fluid relative to frequency in vacuum . The gray area represents the region enclosed by the and the curves in (a).

Image of FIG. 5.
FIG. 5.

Quality factor of the fundamental mode of flexural vibration for . (a) Gas, and (b) liquid, .

Image of FIG. 6.
FIG. 6.

Normalized thermal spectra of torsional vibration for . (a) Fundamental mode in gas with , . Quality factors , obtained using Eq. (17), are for , respectively; (b) Fundamental mode in liquid with , . Note that in both instances, the thermal spectra lies atop the spectra.

Image of FIG. 7.
FIG. 7.

Peak and resonant frequencies of fundamental torsional resonance for immersion in gas. ; . (a) Peak frequency relative to frequency in vacuum . (b) Resonant frequency in the absence of dissipative effects in the fluid relative to frequency in vacuum . The gray area represents the region enclosed by the and the curves in (a).

Image of FIG. 8.
FIG. 8.

Peak and resonant frequencies of fundamental torsional resonance for immersion in liquid. ; . (a) Peak frequency relative to frequency in vacuum . (b) Resonant frequency in the absence of dissipative effects in the fluid relative to frequency in vacuum . The gray area represents the region enclosed by the and the curves in (a).

Image of FIG. 9.
FIG. 9.

Quality factor of the fundamental mode of torsional vibration for . (a) Gas, and (b) liquid, .

Image of FIG. 10.
FIG. 10.

Ratio of peak noise levels of flexural and torsional vibration, for (solid line); (long dash, long space); (long dash, short space); (long dash, short dash); (short dash). (a) Gas: , and (b) liquid: , .

Tables

Generic image for table
Table I.

Coefficients of , Eq. (A2a), for various values of .

Generic image for table
Table II.

Coefficients of , Eq. (A2b), for various values of .

Generic image for table
Table III.

Coefficients of , Eq. (A4a), for various values of .

Generic image for table
Table IV.

Coefficients of , Eq. (A4b), for various values of .

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/content/aip/journal/jap/98/11/10.1063/1.2136418
2005-12-15
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/11/10.1063/1.2136418
10.1063/1.2136418
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