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Research Papers

Viscosity Measurement by the Free Vibrations of Homogeneous Viscoelastic Sphere

[+] Author and Article Information
Hidemi Akimoto

Collaborative Research Center,  Hiroshima University, 2-313 Kagamiyama Higashi-Hiroshima, Hiroshima 739-8527, Japanakimoto@hiroshima-u.ac.jp

Katsuhiko Nagai

Faculty of Integrated Arts and Sciences,  Hiroshima University, 1-7-1 Kagamiyama Higashi-Hiroshima, Hiroshima 739-8521, Japannagai@minerva.ias.hiroshima-u.ac.jp

Naoki Sakurai1

Faculty of Integrated Arts and Sciences,  Hiroshima University, 1-7-1 Kagamiyama Higashi-Hiroshima, Hiroshima 739-8521, Japannsakura@hiroshima-u.ac.jp

1

Corresponding author.

J. Appl. Mech 79(4), 041002 (May 08, 2012) (8 pages) doi:10.1115/1.4005551 History: Received October 13, 2010; Accepted July 05, 2011; Posted January 31, 2012; Published May 08, 2012; Online May 08, 2012

In this paper, a nondestructive method to measure bulk and shear viscosities of a homogeneous viscoelastic sphere using free vibration is investigated by taking into account a single Voigt model for viscous and elastic stress tensors. For the viscosity measurement, Q value characterizing the damping due to the viscous effect is used. The formulation of the Q value for spheroidal and torsional modes is theoretically made based on the redefinition of the coefficients of bulk and shear viscosities as positive values. Newly introduced coefficients A and B constituting Q value formula, which correspond to bulk and shear deformations in the free vibration, are numerically calculated for spheroidal and torsional modes, respectively. The method to measure the viscosity by using the observed values of vibration and coefficients A and B is presented, and the example to apply the method is also shown. This study may find applications in rheology of soft material where viscous effects of spherical structures matter.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

xT (=ωR/cT ) is plotted as a function of Poisson’s ratio σ for mode l = 0, 1, 2, 3, 4, 5 of spheroidal mode

Grahic Jump Location
Figure 2

xT (=ωR/cT ) is plotted as a function of Poisson’s ratio σ for mode l = 0, 1, 2, 3, 4, 5 of torsional mode

Grahic Jump Location
Figure 3

The coefficients A and B versus Poisson’s ratio σ for spheroidal modes nSl with l = 0, 1, 2, 3, 4, 5 and n = 0, 1, 2

Grahic Jump Location
Figure 4

The coefficient B versus Poisson’s ratio σ for torsional modes nTl with l = 0, 1, 2, 3, 4, 5 and n = 0, 1, 2

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