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Research Papers

Vibration Response of Elastic Disks in Surrounding Fluid: Viscous Versus Acoustic Effects

[+] Author and Article Information
Anirban Jana1

School of Mechanical Engineering, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907-2088anirban@psc.edu

Arvind Raman2

School of Mechanical Engineering, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907-2088raman@purdue.edu

1

Present address: Pittsburgh Supercomputing Center, Carnegie Mellon University, 300 South Craig Street, Pittsburgh, PA 15213.

2

Corresponding author.

J. Vib. Acoust 132(6), 061001 (Sep 14, 2010) (8 pages) doi:10.1115/1.4001497 History: Received September 03, 2008; Revised March 18, 2010; Published September 14, 2010; Online September 14, 2010

The vibrations of thin, elastic, circular disks such as musical cymbals, hard disk drives, and microscale resonators are significantly influenced by the presence of a surrounding fluid. The energy of disk vibrations is known to dissipate into viscous losses and to radiate away as sound. However, the relative importance of these mechanisms is not well understood. In this paper, we present three-dimensional computations of the fluidic impedance of thin, elastic disks vibrating with small amplitudes under ambient conditions. These computations encompass both macroscale and microscale disks, a wide range of operating frequencies, and different fluidic environments. Viscous fluidic impedances are computed using a finite element model, whereas acoustic fluidic impedances are computed using a boundary element method. For a disk with a given clamping ratio vibrating in a specific mode, the nondimensional viscous impedance depends on the unsteady Reynolds number, while the nondimensional acoustic impedance depends on the ratio of structural to acoustic wavelengths. It is shown that viscous losses dominate the fluid damping of disks in data storage and circular saw applications and of conventional disk microresonators. However, for ultrahigh frequency resonators, acoustic radiation must be taken into account to correctly estimate the overall fluid damping. The computed fluidic impedances are expected to be an important aid in the design of a wide range of disk resonators up to the megahertz regime.

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Figures

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Figure 5

[(a) and (b)] Percentage change in the viscous impedance of the (0,3) mode of the κd=0.147 disk, with decrease in the radius of the cylindrical enclosure, at two different nondimensional drive frequencies. The enclosure height is kept fixed at H∗=150h∗. [(c) and (d)] Percentage change in the viscous impedance of the (0,3) mode of the κd=0.147 disk, with decrease in the height of the cylindrical enclosure, at two different nondimensional drive frequencies. The enclosure radius is kept fixed at R∗=1.75b∗.

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Figure 6

Variation of the acoustic impedance with the nondimensional wave number k of several modes of a disk having clamping ratio κd=0.147: (a) the real part (acoustic radiation damping) and (b) the imaginary part (acoustic added mass).

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Figure 1

(a) Four different mode shapes of the disk. The mode shapes are labeled as (m,n), where m is the number of nodal circles and n is the number of nodal diameters. (b) The unmeshed ADINA model of the disk in the fluid filled enclosure. Also shown along the disk periphery is the imposed disk velocity for the (0,3) mode. (c) A section of the ADINA model showing the 3D mesh of the fluid domain.

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Figure 2

The three-dimensional fluid velocity field around the κd=0.147 disk oscillating in its (0,3) mode with β=3.6×105 in a large enclosure (R∗=1.75b∗, H∗=150h∗) at an instant of time when the disk displacement is near its maximum

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Figure 3

The instantaneous fluid pressure field around the κd=0.147 disk oscillating in its (0,3) mode with β=3.6×105 in a large enclosure (R∗=1.75b∗, H∗=150h∗) projected onto two different planes in the fluid domain: (a) on the y=0 plane, which is perpendicular to the disk surfaces and contains an antinode, and (b) on the z=10−5 m plane, which is parallel to the disk surfaces and lying just above the top surface. These pressure field plots correspond to an instant of time when the fluid pressures are near their maximum.

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Figure 4

Variation in the viscous impedance with the nondimensional frequency of several modes of disks having different clamping ratios in a large enclosure (R∗=1.75b∗, H∗=150h∗): (a) the real part (viscous damping) and (b) the imaginary part (viscous added mass). Different markers (and colors in online version) indicate different disk modes as described by the legends. Different linestyles indicate different clamping ratios: The solid line is κd=0.147, and the broken line is κd=0.293.

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