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Research Papers

Sound-Induced Motion of a Nanoscale Fiber

[+] Author and Article Information
R. N. Miles, J. Zhou

Department of Mechanical Engineering,
Binghamton University,
State University of New York,
Binghamton, NY 13902-6000

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 16, 2016; final manuscript received July 10, 2017; published online September 22, 2017. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 140(1), 011009 (Sep 22, 2017) (6 pages) Paper No: VIB-16-1354; doi: 10.1115/1.4037511 History: Received July 16, 2016; Revised July 10, 2017

An analysis is presented of the motion of a thin fiber, supported on each end, due to a sound wave that propagates in the direction perpendicular to its long axis. Predicted and measured results indicate that when fibers or hairs having a diameter measurably less than 1 μm are subjected to air-borne acoustic excitation, their motion can be a very reasonable approximation to that of the acoustic particle motion at frequencies spanning the audible range. For much of the audible range of frequencies resonant behavior due to reflections from the supports tends to be heavily damped so that the details of the boundary conditions do not play a significant role in determining the overall system response. Thin fibers are thus constrained to simply move with the surrounding medium. These results suggest that if the diameter or radius is chosen to be sufficiently small, incorporating a suitable transduction scheme to convert its mechanical motion into an electronic signal could lead to a sound sensor that very closely depicts the acoustic particle motion over a wide range of frequencies.

FIGURES IN THIS ARTICLE
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Topics: Fibers , Fluids , Acoustics
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References

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Figures

Grahic Jump Location
Fig. 1

The viscous force is not a strong function of the fiber radius r. The result of evaluating Eq. (2) is shown for a wide range of values of the radius r, assuming that the frequency is 1 kHz. The fiber is assumed to undergo a velocity of 1 m/s at each frequency. The fluid is assumed to be stationary at large distances from the fiber. The force varies by roughly a factor of 10 as the radius varies by a factor of 100 from 0.1 μm to 10 μm. As a result, as the fiber radius becomes small, fluid forces dominate over the forces on the left side of Eqs. (5) and (6).

Grahic Jump Location
Fig. 2

Photo of a 6 μm diameter, stainless steel wire, 3 cm long. This wire was driven by a plane sound wave in the Binghamton University anechoic chamber. The velocity of the midpoint of the wire was measured using a laser vibrometer, which produced the dot shown in the middle of the wire. The wire was soldered to two larger diameter wires which supported it at its ends.

Grahic Jump Location
Fig. 3

Predicted and measured velocity of a 6 μm diameter wire driven by sound. The amplitude of the complex transfer function of the wire velocity relative to the acoustic particle velocity is shown. The predicted results were obtained using Eq. (15). The wire is shown in Fig. 2. The velocity was measured using a Polytec OFV 534 laser vibrometer sensor with an OFV-5000 controller. Measurements were performed in the anechoic chamber at Binghamton University. The sound field was measured using a B&K 4138 1/8th inch reference microphone. The acoustic particle velocity was estimated from the measured pressure using Eq. (1).

Grahic Jump Location
Fig. 4

Predicted amplitude of the sound-induced velocity of a thin fiber relative to the acoustic particle velocity for various values of the fiber diameter. The response was predicted at its midpoint (x = L/2) using Eq. (15). The wire is assumed to have a length L = 3 cm. The material properties are chosen to represent stainless steel.

Grahic Jump Location
Fig. 5

When the diameter of the fiber is reduced sufficiently, the response becomes nearly independent of frequency. Measured and predicted results are shown for a PMMA fiber having a diameter of approximately 800 nm and length 3 mm. The measured data were obtained using the same procedure as those of Fig. 3. The data are normalized relative to the acoustic particle velocity in a plane wave field which is related to the measured pressure through Eq. (1). This estimated acoustic particle velocity used to normalize the data is essentially the fluid velocity one would see if the fiber and measurement apparatus were not present. When the curve shows a straight line with a value of unity, it means that the fiber is moving exactly as the air would in a sound field that was not disturbed by the presence of a sensor.

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