Acoustical and dynamic mechanical measurements were carried out on a commercial polyurethane rubber, DeSoto PR1547. The sound speed and attenuation were measured over the range from 12.5 to 75 kHz and 3.9 to 33.6 °C. Shear modulus was measured from 10−4 to 2 Hz and −36 to 34 °C. The peak heights of the shear loss tangent varied with temperature, demonstrating thermorheological complexity. At higher temperatures, time–temperature superpositioning could be applied, with the shift factors following the Williams–Landel–Ferry equation. From the combined acoustical and mechanical measurements, values for the dynamic bulk modulus were determined. Moreover, superposition of the bulk modulus data was achieved using the shift factors determined from the dynamic mechanical shear measurements. Finally, this work illustrates the capability and the working rules of acoustical measurements in a small tank.

1.
J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1980), Chap. 11.
2.
W.
Philippoff
and
J.
Brodnyan
, “
Preliminary results in measuring dynamic compressibilities
,”
J. Appl. Phys.
26
,
846
849
(
1955
).
3.
J. E.
McKinney
,
S.
Edelman
, and
R. S.
Marvin
, “
Apparatus for the direct determination of the dynamic bulk modulus
,”
J. Appl. Phys.
27
,
425
430
(
1956
).
4.
J. E.
McKinney
,
H. V.
Belcher
, and
R. S.
Marvin
, “
The dynamic compressibility of a rubber-sulfur vulcanizate and its relation to free volume
,”
Trans. Soc. Rheol.
4
,
347
362
(
1960
).
5.
J.
Burns
,
P. S.
Dubbelday
, and
R. Y.
Ting
, “
Dynamic bulk modulus of various elastomers
,”
J. Polym. Sci., Part B: Polym. Phys.
28
,
1187
1205
(
1990
).
6.
P. S.
Dubbelday
and
J.
Burns
, “
Dynamic bulk modulus of soft elastomers
,”
J. Wave-Material Interaction
5
and 6,
181
210
(
1991
).
7.
B. P.
Holownia
and
E. H.
James
, “
Determination of dynamic bulk modulus of elastomers using pressure measurement
,”
Rubber Chem. Technol.
66
,
749
753
(
1993
).
8.
R. L.
Willis
,
T. S.
Stone
,
Y. H.
Bertholot
, and
W. M.
Madigosky
, “
An experimental-numerical technique for evaluating the bulk and shear dynamic moduli of viscoelastic materials
,”
J. Acoust. Soc. Am.
102
,
3549
3555
(
1997
).
9.
R. L.
Willis
,
L.
Wu
, and
Y. H.
Bertholot
, “
Determination of the complex Young and shear dynamic moduli of viscoelastic materials
,”
J. Acoust. Soc. Am.
109
,
611
621
(
2001
).
10.
R.
Meister
,
C. J.
Marhoeffer
,
R.
Sciamanda
,
L.
Cotter
, and
T.
Litovitz
, “
Ultrasonic viscoelastic properties of associated liquids
,”
J. Appl. Phys.
31
,
854
870
(
1960
).
11.
A.
DiMeglio
and
L. S.
Wang
, “
A variational method for the identification of viscoelastic parameters from experimental data
,”
J. Acoust. Soc. Am.
108
,
2746
2753
(
2000
).
12.
J. C.
Piquette
, “
Determination of the complex dynamic bulk modulus of elastomers by inverse scattering
,”
J. Acoust. Soc. Am.
77
,
1665
1673
(
1985
).
13.
M. P.
Hagelberg
and
R. D.
Corsaro
, “
A small pressurized vessel for measuring the acoustic properties of materials
,”
J. Acoust. Soc. Am.
77
,
1222
1228
(
1985
).
14.
I. D. Groves, “Twenty years of underwater electroacoustic standards,” Naval Research Laboratory Formal Report, No. FR-07735 (1975).
15.
K. W. Ng, “Transducer structure,” US Patent 5,367,500, issued 22 November 1994.
16.
H.
Wang
,
Q. M.
Zhang
,
L. E.
Cross
, and
A. O.
Sykes
, “
Clamping effect on the piezoelectric properties of poly(vinylidene fluoride-trifluoroethylene) copolymer
,”
Ferroelectrics
150
,
255
266
(
1993
).
17.
S. F.
Morse
,
P. L.
Marston
, and
G.
Kaduchak
, “
High-frequency backscattering enhancements by thick finite cylindrical shells in water at oblique incidence
,”
J. Acoust. Soc. Am.
103
,
785
794
(
1998
).
18.
A. J.
Rudgers
and
C. A.
Solvoid
, “
Apparatus-independent acoustical-material characteristics obtained from panel-test measurements
,”
J. Acoust. Soc. Am.
76
,
926
934
(
1984
).
19.
J. C.
Piquette
, “
Direct measurements of edge diffraction from soft underwater acoustic panels
,”
J. Acoust. Soc. Am.
95
,
3090
3099
(
1994
).
20.
J. C. Piquette, “Conventional oblique-incidence panel test procedures,” Naval Undersea Warfare Center-NPT Technical Memorandum 01-035 (2001).
21.
J. A.
Archer-Hall
and
D.
Gee
, “
A single integral computer method for axisymmetric transducers with various boundary conditions
,”
NDT Int.
13
,
95
101
(
1980
).
22.
N. Yen, private communication.
23.
L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics, 3rd ed. (Wiley, New York, 1982), p. 107, Eq. 5.22.
24.
R.
Kronig
, “
On the theory of dispersion of x-rays
,”
J. Opt. Soc. Am.
12
,
547
557
(
1926
).
25.
R.
Kronig
and
H. A.
Kramers
, “
Zur theorie der absorption und dispersion in den Röntgenspektren (Theory of absorption and dispersion in x-ray spectra)
,”
Z. Phys.
48
,
174
179
(
1928
).
26.
M.
O’Donnell
,
E. T.
Jaynes
, and
J. G.
Miller
, “
Kramers–Kronig relationship between ultrasonic attenuation and phase velocity
,”
J. Acoust. Soc. Am.
69
,
696
701
(
1981
).
27.
P. G.
Santangelo
and
C. M.
Roland
, “
Temperature dependence of mechanical and dielectric relaxation in cis-1,4-polyisoprene
,”
Macromolecules
31
,
3715
3719
(
1998
).
28.
D. J.
Plazek
, “
Temperature dependence of viscoelastic behavior of polystyrene
,”
J. Phys. Chem.
69
,
3480
3487
(
1965
).
29.
D. J.
Plazek
, “
Temperature-dependence of the viscoelastic behavior of poly(vinyl acetate)
,”
Polymer J.
12
,
43
53
(
1980
).
30.
K. L.
Ngai
,
A.
Schonhals
, and
E.
Schlosser
, “
An explanation of anomalous dielectric-relaxation properties of poly(propylene glycol)
,”
Macromolecules
25
,
4915
4919
(
1992
).
31.
D. J.
Plazek
,
C.
Bero
,
S.
Neumeister
,
G.
Floudas
,
G.
Fytas
, and
K. L.
Ngai
, “
Viscoelastic properties of amorphous polymers. 3. Low-molecular-weight poly(methylphenylsiloxane)
,”
Colloid Polym. Sci.
272
,
1430
1438
(
1994
).
32.
L. I.
Palade
,
V.
Verney
, and
P.
Attane
, “
Time-temperature superposition and linear viscoelasticity of polybutadienes
,”
Macromolecules
28
,
7051
7057
(
1995
).
33.
D. J.
Plazek
I.-C.
Chay
,
K. L.
Ngai
, and
C. M.
Roland
, “
Viscoelastic properties of polymers. 4. Thermorheological complexity of the softening dispersion in polyisobutylene
,”
Macromolecules
28
,
6432
6436
(
1995
).
34.
D. J.
Plazek
and
D. L.
Plazek
, “
Viscoelastic behavior of atactic polypropylene
,”
Macromolecules
16
,
1469
1475
(
1983
).
35.
P. G.
Santangelo
,
K. L.
Ngai
, and
C. M.
Roland
, “
Temperature dependence of relaxation in polypropylene and poly(ethylene-co-propylene)
,”
Macromolecules
29
,
3651
3653
(
1996
).
36.
M. L.
Williams
,
R. F.
Landel
, and
J. D.
Ferry
, “
Mechanical properties of substances of high molecular weight. 19. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids
,”
J. Am. Chem. Soc.
77
,
3701
3707
(
1955
).
37.
R. N.
Capps
, “
Dynamic Young’s moduli of some commercially available polyurethanes
,”
J. Acoust. Soc. Am.
73
,
2000
2005
(
1983
).
38.
J. Jarzynski, “Mechanisms of Sound Attenuation in Materials,” in Sound and Vibration Damping with Polymers, edited by R. D. Corsaro and L. H. Sperling, ACS Symposium Series 424 (American Chemical Society, Washington, DC, 1990).
39.
C. A.
Bero
and
D. J.
Plazek
, “
Volume-dependent rate-processes in an epoxy-resin
,”
J. Polym. Sci., Part B: Polym. Phys.
29
,
39
47
(
1991
).
40.
C. G.
Robertson
,
J. E.
Monat
, and
G. L.
Wilkes
, “
Physical aging of an amorphous polyimide: enthalpy relaxation and mechanical property changes
,”
J. Polym. Sci., Part B: Polym. Phys.
37
,
1931
1946
(
1999
).
41.
S. L.
Simon
,
J. W.
Sobieski
, and
D. J.
Plazek
, “
Volume and enthalpy recovery of polystyrene
,”
Polymer
42
,
2555
2567
(
2001
).
42.
G. B.
McKenna
,
Y.
Leterrier
, and
C. R.
Schultheisz
, “
The evolution of material properties during physical aging
,”
Polym. Eng. Sci.
35
,
403
410
(
1995
).
43.
M. M.
Santore
,
R. S.
Duran
, and
G. B.
McKenna
, “
Volume recovery in epoxy glasses subjected to torsional deformations—the question of rejuvenation
,”
Polymer
32
,
2377
2381
(
1991
).
This content is only available via PDF.
You do not currently have access to this content.