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Unified theory of gas damping of flexible microcantilevers at low ambient pressures
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Image of FIG. 1.
FIG. 1.

(a) A schematic of the microcantilever with length , width and thickness , and (b) a schematic representation of the boundary conditions for the ES-BGK calculations imposed in the computational model (cantilever cross-sectional plane).

Image of FIG. 2.
FIG. 2.

Comparison of the predictions of the free-molecular model (Ref. 8), the no-slip unsteady Stokes flow model (Ref. 4) and the ES-BGK-model-based fit with the experimental gas damping values for microcantilever (a) A in its first mode, (b) A in its second mode, (c) C in its first mode, (d) F in its first mode, (e) F in its second mode, and (f) F in its third mode. The horizontal bars on the experimental values are due to the uncertainty in pressure values and the vertical bars represent the uncertainty caused due to the uncertainty in estimating structural damping. The insets are the experimentally measured vibration modes.

Image of FIG. 3.
FIG. 3.

The normalized pressure and the stream-traces plotted for (a) and (b) . Note that only half width of the microcantilever is shown for each of the two cases.


Generic image for table
Table I.

Geometric properties and frequencies of phosphorus-doped silicon microcantilevers (Ref. 12) with and Young’s modulus (Ref. 12). The length and the width are obtained from scanning electron microscope images of the microcantilevers. The thickness is estimated by choosing such that it minimizes the rms error between the predicted and measured in vacuo frequencies for the first three modes of each microcantilever.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Unified theory of gas damping of flexible microcantilevers at low ambient pressures