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Hydrodynamic coupling between micromechanical beams oscillating in viscous fluids
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10.1063/1.2423254
/content/aip/journal/pof2/19/1/10.1063/1.2423254
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/1/10.1063/1.2423254

Figures

Image of FIG. 1.
FIG. 1.

(a) Array of microbeams of arbitrary cross sections in fluid. (b) Sketch of the boundary value problem for oscillating cylinders of arbitrary cross sections. Axes of the cylinders lie along the axis. Each cross-hashed region is a microbeam cross section and is the contour of integration. (c) Sketch of the boundary value problem for two oscillating rectangular cross-sectional microbeams. is the vector basis corresponding to the , , and coordinate system.

Image of FIG. 2.
FIG. 2.

Variation of (a) the real part and (b) the imaginary part of nondimensional pressure jump across the microbeam 1 with gap ratio . The axis in this plot was chosen to be from to 0 as the microbeam’s absolute position varied as the gap was changed. Plots for (dotted line), (dashed line), (dash-dotted line), (line joining circles), (line joining squares), and (solid line) are shown. (c) Variation of the nondimensional transverse hydrodynamic force and (d) the nondimensional hydrodynamic torque on microbeam 1 with varying . Parameters used are , , and . The transverse force and torque per unit length are nondimensionalized by .

Image of FIG. 3.
FIG. 3.

(a) Real part of the component of fluid velocity for an infinite wall vibrating along the direction at . (b) Real part of the component of fluid velocity for a microbeam . (c) Variation of phase of the fluid velocity along . The length scales for both plots are nondimensionalized by . is used for the microbeam velocity profile.

Image of FIG. 4.
FIG. 4.

The real (a) and imaginary (b) parts of the component of fluid velocity due to a microbeam vibrating in unbounded fluid. Plots for are shown.

Image of FIG. 5.
FIG. 5.

Variation of the nondimensional transverse hydrodynamic force per unit length on microbeam 1 with the relative phase between the two microbeams. Parameters used are , , and . The transverse force per unit length is nondimensionalized by .

Image of FIG. 6.
FIG. 6.

Variation of the nondimensional transverse hydrodynamic force per unit length with amplitude ratio on microbeam 1 for in-phase and out-of-phase oscillation of the two microbeams. Other parameters used are and . The transverse force per unit length is nondimensionalized by .

Image of FIG. 7.
FIG. 7.

Variation of (a) the real part and (b) the imaginary part of nondimensional transverse hydrodynamic force across microbeam 1 with gap ratio for in-phase oscillations of the two microbeams. These forces are normalized by their corresponding values at the same in unbounded fluid.

Image of FIG. 8.
FIG. 8.

Plot of the nondimensional gap required for the transverse hydrodynamic force [(Eq. (16)] to reach 99% of the unbounded fluid values versus the nondimensional frequency. Parameters used are and .

Image of FIG. 9.
FIG. 9.

Imaginary and real part of the hydrodynamic function as a function of of microbeam 1 for different nondimensional gaps (a), different amplitude ratios (b), and different relative phases (c) between the two microbeams. Parameters used in (a) are and ; parameters used in (b) are and ; parameters used in (c) are and .

Image of FIG. 10.
FIG. 10.

An array of equally sized and equally spaced thin microbeams.

Image of FIG. 11.
FIG. 11.

Variation of (a) the imaginary part and (b) the real part of hydrodynamic function for the first three microbeams in the five-microbeam array of Fig. 10 for in-phase oscillations of the microbeams with .

Tables

Generic image for table
Table I.

Convergence study for the nondimensional hydrodynamic transverse force and torque per unit length acting on microbeam 1 with , , , and . These calculations are performed for two infinitesimally thin, oscillating microbeams coupled hydrodynamically to each other. The transverse force and torque per unit length are nondimensionalized by .

Generic image for table
Table II.

Range of parameter values used in this paper.

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/content/aip/journal/pof2/19/1/10.1063/1.2423254
2007-01-11
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hydrodynamic coupling between micromechanical beams oscillating in viscous fluids
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/1/10.1063/1.2423254
10.1063/1.2423254
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