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.

References

References
1.
Jaerisch
,
P.
, 1880, “
On the Vibrations of an Isotropic Elastic Sphere
,”
J. Pure Appl. Math.
,
88
, p.
131
.
2.
Lamb
,
H.
, 1882, “
On the Vibrations of an Elastic Sphere
,”
Proc. London Math. Soc.
,
13
, pp.
189
212
.
3.
Chree
,
C.
, 1889, “
The Equations of an Isotropic Elastic Solid in Polar and Cylindrical Coordinates, Their Solutions and Applications
,”
Trans. Cambridge Philos. Soc.
,
14
, pp.
250
369
.
4.
Ferry
,
J. D.
, 1980,
Viscoelastic Properties of Polymers
,
3d ed.
John Wiley & Sons
,
New York
.
5.
Nielsen
,
L. E.
, 1974,
Mechanical Properties of Polymers and Composites
,
Marcel Dekker
,
New York.
6.
Terasaki
,
S.
,
Sakurai
,
N.
,
Yamamoto
,
R.
,
Wada
,
N.
, and
Nevins
,
D. J.
, 2001, “
Changes in Cell Wall Polysaccharides of Kiwifruit and the Visco-Elastic Properties Detected by a Laser Doppler Method
,”
J. Jpn. Soc. Hortic. Sci.
,
70
(
5
), pp.
572
580
.
7.
Soong
,
T. T.
, and
Dargush
,
G. F.
, 1997,
Passive Energy Dissipation Systems in Structural Engineering
,
John Wiley & Sons
,
New York.
8.
Landau
,
L. D.
,
Lifshitz
,
E. M.
,
Kosevich
,
A. M.
, and
Pitaevskii
,
L. P.
, 1986,
Theory of Elasticity
,
3rd ed.
(English),
Pergamon Press
,
New York.
9.
Love
,
A. E. H.
, 1944,
A Treatise on the Mathematical Theory of Elasticity
,
4th ed.
,
Dover
,
New York.
10.
Ashby
,
N.
, and
Dreitlein
,
J.
, 1975, “
Gravitational Wave Reception by a Sphere
,”
Phys. Rev. D
,
12
(
2
), pp.
336
349
.
11.
Lobo
,
J. A.
, 1995, “
What Can We Learn About Gravitational Wave Physics With an Elastic Spherical Antenna?
,”
Phys. Rev. D
,
52
(
2
), pp.
591
604
.
12.
Macdonald
,
G. J. F.
, and
Ness
,
N. F.
, 1961, “
A Study of the Free Oscillations of the Earth
,”
J. Geophys. Res.
,
66
(
6
), pp.
1865
1911
.
13.
Sato
,
Y.
, and
Usami
,
T.
, 1962, “
Basic Study on the Oscillation of a Homogeneous Elastic Sphere: I. Frequency of the Free Oscillations
,”
Geophys. Mag.
,
31
, pp.
15
24
.
You do not currently have access to this content.