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Dynamic interactions between oscillating cantilevers: Nanomechanical modulation using surface forces
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Image of FIG. 1.
FIG. 1.

(a) Schematic of the experimental setup. The optical transducer (PD: photodetector), amplifiers (A), phase shifter ( ), and amplitude controller are the components of a positive feedback circuit (dashed box), which drives the high-frequency cantilever at resonance at a prescribed amplitude via a PZS. The demodulator and PID controller form a detection circuit, which keeps the frequency shift (and hence the average gap between cantilevers) at a desired value. The inset shows the lumped mass models for the two cantilevers. (b) Spectral density of the high-frequency cantilever oscillations. Two arrows at the upper and lower sidebands of the carrier at 153.8 kHz correspond to the thermal oscillations of the low-frequency cantilever. The inset shows the upper sideband in displacement units.

Image of FIG. 2.
FIG. 2.

(a) Normalized sideband signals. The signals are normalized using the highest measured signal values. The data traces are taken at the positions shown with the arrows in (b). Because the resonance frequency shifts significantly, the frequency axis is displayed as measured from the resonance frequency . (b)The observed shift in the resonance frequencies of both cantilevers. (c) The change in the dimensionless dissipation of both cantilevers. The dissipation increases dramatically in the shaded region, suggesting that soft contact interactions start to become dominant. Error bars in all the data are smaller than the symbol sizes unless shown explicitly. The snap to contact with accompanying instabilities in the high-frequency signal determines the position of zero in the -axes of the plots in (b) and (c).


Generic image for table
Table I.

Unperturbed parameters for the two Silicon microcantilevers used in our experiments. The stiffness values are provided by the manufacturer. The effective mass is calculated using and . Both and are approximate.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamic interactions between oscillating cantilevers: Nanomechanical modulation using surface forces