IS 14882: Damping Materials - Graphical Presentation of the Complex Modulus

15 Pages·2000·1.2 MB·English

by  Bureau of Indian Standards

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IS 14882 (2000): Damping Materials - Graphical Presentation
of the Complex Modulus [MED 28: Mechanical Vibration and
Shock]
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Satyanarayan Gangaram Pitroda
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IS 14882:2000
1s0 10112:1991

IndianStandard
-.....—
DAMPING MATERIALS — GRAPHICAL
PRESENTATION OF THE COMPLEX MODULUS
ICS 17.160

0 BIS 2000
BUREAU OF INDIAN STANDARDS
MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHI 110002
October 2000
Price Group 5
Mechanical Vibration and Shock Sectional Committee, ME 28
NATIONAL FOREWORD
TiIIs Indian Standard which isidentical with ISO 10112:1991 ‘Damping materials –Graphical presentation
otthe complex modulus’ issued bythe International Organization for Standardization (ISO) was adopted
by the Bureau of Indian Standards on the recommendations of the Mechanical Vibration and Shock
Sechonal Committee and approval of the Mechanical Engineering Division Council.
The text of ISO standard has been approved as suitable for publication as Indian Standard without —..—
deviations. In the adopted standard, certain conventions are, however, not identical to those used in
Ind!an Standards. Attention is especially drawn to the following: r
a) Wherever the words ‘International Standard’ appear referring to this standard, they should be
read as ‘Indian Standard’.
b) Comma (,) has been used as adecimal marker while in Indian Standards, the current practice
is to use a full point (.) as the decimal marker.
For the purpose of deciding whether a particular requirement ofthis standard iscomplied with, the final
value, observed or calculated, expressing the result of a test or analysis, shall be rounded off in
accordance with IS2:1960 ‘Rules for rounding off numerical values (revisec/)’. The number ofsignificant
places retained in the rounded off value should be the same as that of the specified value in this
standard.
IS 14882:2000
ISO 10112:1991
Indian Standard
DAMPING MATERIALS — GRAPHICAL
PRESENTATION OF THE COMPLEX MODULUS
1 Scope T(t) is the shear stress;
y(l) is the shear strain;
This International Standard establishes the graph-
ical presentation of the complex modulus of P@) and Q@R)are polynomials in ~.
viscoelastic vibration damping materials which are
microscopically homogeneous, linear and The operator~ is defined as
thermorheologically simple. The complex modulus
pR= dfd tR (2)
may be the shear modulus, Young’s modulus, bulk
modulus, longitudinal wave propagation modulus,
The reduced time differential dtR is defined as
or Lame modulus, This graphical presentation is
convenient and sufficiently accurate for many vi- dtR= dt/(z7(T) .. (3)
bration damping materials.
where
The preferred nomenclature (parameters, symbols
and definitions) is also given. t is time, in seconds;
The primary purpose of this International Standard ~T(7) is the dimensionless temperature shift
is to improve communication among the diverse function [z] dependent on temperature,
technological fields concerned with vibration. damp- T, in kelvin.
ing materials.
The Fouriet’ transform (ft.) of equation (1) leads to
the definition of G, the complex shear modulus valid
for steady-state sinusoidal stress and strain, as
2 Nomenclature
G(ju.)R)= 7+(j@R)/y*@R) = Q~mR)/~(&) (4)
2.1 Complex modulus where T*@R) denotes the ft. of ?(t)
The operator form of the constitutive equation for the The reduced circular frequency, a~R,is given as
linear, isothermal, isotropic, microscopically homo-
OR= UXZfi7] = 2nfR= 2nfa7(7] .,. (5)
geneous, thermorheologically simple [see
equation (7)] viscoelastic material being deformed
which is a product of co, the circular frequency, in
in shear is defined 111as
radians per second, and the dimensionless tem-
~~)T(f) = ~(@f(f) ,., (1) perature shift function, while~R and f denote the re-
duced cyclic frequency and the cyclic frequency, in
where hertz.

1
IS 14882:2000
1s0 10112:1991
The complex shear modulus is dependent on both modulus, 1, and to the longitudinal wave propa-
frequency and temperature gation modulus W= A+ 2G,
G = G(c~,7) ...(6) A thermorheologically simple material is a material
for which the complex modulus may be expressed
If (and only io the dependency is expressed as as a complex valued function of one independent
G = G(ja}R)= G~coaf17)] ...(7) variable, namely reduced frequency, to represent its
variation with both frequency and temperature.
then the material is called thermorheologically sim-
NOTE1 Sometimes, the real modulus and the material
ple (TRS), Furthermore, equations (1) to (7) apply
loss factor are treated as independent functions of re- -----—
only to linear conditions.
duced frequency; while this can facilitate satisfactory
applications, it is aconceptual error.
Alternatively, consider a viscoelastic material el-
ement which undergoes a sinusoidal shear strain
[3] The complex modulus evaluated at a given tem-
perature and a given frequency represents both the
y = yAsin wt (8) magnitude and the phase relationships between
sinusoidal stress and strain.
which lags the sinusoidal shear stress by the phase
angle &.: 2.2 Datacheck
7 = 7A sin(~~ + d~) .,. (9)
H is presumed in this International Standard that a
The sinusoidal strain and stress may be represented set of valid complex modulus data (e.g., tables 1and
in complex notation as 2) has been obtained in accordance with good
practice (see, for example, ref. 141),It is recom-
y“ = YAejcot . ..(lo) mended that each set of data be routinely and
carefully scrutinized. As a minimum, the Ig VGversus
T+ = TAe j(cof + c$~) (11) Ig GM should be plotted (e.g., figure 1). If the set of
data represents a thermorheologicaliy simple ma-
The complex shear modulus, G, may be equivalently
terial, if an adjustment of modulus for temperature
defined as
and density is not appropriate and if the set of data
has no scatter, the set of data will plot as a curve
of vanishing width.
= GMcos &(l +,) tan &) = G~+jGl
Each point along the arc of the curve corresponds
= G’ +jG” = GR(I +jqG) ..(12) to a unique value of reduced frequency [see
equation (6)3. However, this is not considered in this
where plot. The material loss factor and the modulus mag-

nitude are cross-plotted, and the reduced frequency,
GM is the magnitude of the shear temperature, and frequency parameters do not oc-
modulus; cur explicitly, No part of any scatter in this plot can
be attributed to an imperfect temperature shift func-
GR= G’ is the real (storage) modulus;
tion.
G,= G“ = GRqG is the imaginary (loss) modu-
The loss factor versus modullJs magnitude logarith-
lus;
mic plot can reveal valuable information regarding
q~ = tan & is the material loss factor in scatter of the experimental data. The width of the
shear. band of data, as well as the departure of individual
points from the centre of the band, are indicative of
The concept holds for one-, two- and three- scatter. Acceptable scatter depends on the appli-
dimensional states of stress and strain [z]. Develop- cation. Nothing is revealed about the accuracy of the
ments similar to the above apply to Young’s temperature and frequency measurements or about
modulus, E, to the bulk modulus, K, to the Lam6 any systematic error.

2
IS 14882:2000
ISO 10112:1991
Table 1 – Complex modulus data
a~model
NALF NA A(1) A(2) A(3) A(4) A(5) A(6)
o 0
Complex modulus model
NVEM NB B(I) B(2) B(3) II(4) B(5) 8(6)
11 9 5,70 212 176 0,662 4,51OX 10-2 3,000X 10-2
B(7) B(8) B(9) B(1o) B(11) B(l2)
0,410 0,257 3,65 ------
Table 2 – Complex modulus data as a function of temperature and frequency
Temperature Frequency CR G, a7m
‘~
(K) (Hz) (MPa) (MPa)
254,2 7,800 244,0 0,1300 31,72 2,7956 X 104 7“
254,2 15,60 252,0 0,1140 28,73 2,7956 X 104 T
254,2 31,20 260,0 9,9700 x 10 2 25,92 2,7956 X 104 T
254,2 62,50 266,0 9,4100 x 102 25,03 2,7956 X 1047
254,2 125,0 275,0 9,4700 x 102 26,04 2,7956 X 104 T
254,2 250,0 281,0 7,2100 X 10-2 20,26 2,7956 X 1047’
254,2 500,0 292,0 8,1600 x 10 2 23,83 2,7956 X 104 7
254,2 1000 337,0 7,0300 x 10 2 23,69 2,7956 X 104 T
273,2 7,800 77,30 0,6230 48,16 33,947’
273,2 15,60 96,50 0,5410 52,21 33,947
273,2 31,20 119,0 0,4560 54,26 33,947
273,2 62,50 140,0 0,3850 53,90 33,94 1’
273,2 125,0 162,0 0,3330 53,95 33,94 7
273,2 250,0 185,0 0,2590 47,92 33,94 T
273,2 500,0 206,0 0,2320 47,79 33,94 T
273,2 1000 242,0 0,2020 48,88 33,94 7
283,2 7,800 22,90 0,8920 20,43 2,825 T
283,2 15,60 30,70 0,8690 26,68 2,8257’
283,2 31,20 42,10 0,8130 34,23 2,825 T
283,2 62,50 57,90 0,7310 42,32 2,825 T
283,2 125,0 77,30 0,6450 49,86 2,825 T
283,2 250,0 101,0 0,5320 53,73 2,8257’

283,2 500,0 126,0 0,4610 58,09 2,625 T
283,2 1000 1 61,0 0,3880 62,47 2,825 T
292,2 7,800 11,10 0,7450 8,270 0,64467’
292,2 15,60 14,00 0,8180 11,45 0,64467
292,2 31,20 18,30 0,8690 15,90 0,6446 T
292,2 62,50 24,80 0,8890 22,05 0,6446 T
292,2 125,0 34,60 0,8750 30,27 0,64467’
292,2 250,0 48,90 0,7860 38,44 0,64461’
292,2 500,0 68,00 0,7030 47,80 0,64467’
292,2 1000 94,80 0,6110 57,92 0,6446 7“
303,2 7,800 7,800 0,5520 4,306 0,1941 T
303,2 15,60 9,560 0,6610 6,319 0,1941 T
303,2 31,20 12,10 0,7620 9,220 0,1941 T
303,2 62,50 16,10 0,8560 J3,78 0,1941 7’
303,2 125,0 22,30 0,9120 20,34 0,1941 7’
303,2 250,0 30,70 0,8740 26,83 0,1941 T
303,2 500,0 45,60 0,8240 37,57 0,1941 T
303,2 1000 65,40 0,7470 48,85 0,1941 7’
313,2 7,800 6,000 0,3510 2,106 4,3088 X 10-27’
313,2 15,60 6,800 0,4480 3,046 4,3088 X 10 2T
313,2 31,20 7,940 0,5530 4,391 4,3088 X 10 2T
313,2 62,50 9,520 0,6610 6,293 4,3088 X 10-2 7’
313,2 125,0 11,80 0,7750 9,145 4,3088 X 10-2 7’
313,2 250,0 15,30 0,8450 12,93 4,3068 X 10-2 7’
313,2 500,0 20,80 0,8970 18,66 4,3088 X 10-27’
313,2 1000 30,20 0,8940 27,00 4,3088 X 102 7’
....
IS 14882:2000
ISO 10112:1991
Temperature Frequency GR qG G, ciflT)
(K) (Hz) (MPa) (MPa)
333,2 7,800 5,000 0,1100 0,5500 5,0831 X 10-3 T
333,2 15,60 5,200 0,1520 0,7904 5,0831 X 10-3 T
333,2 31,20 5,480 0,2140 1,173 5,0831 X 10-3 T
333,2 62,50 5,890 0,2890 1,702 5,0831 X 10-3 T
333,2 125,0 6,450 0,3940 2,541 5,0831 X 10--3 T
333,2 250,0 7,280 0,5060 3,684 5,0831 X 10-3 T
333,2 500,0 8,690 0,6010 5,223 5,083J X AO-3T .....
333,2 1000 11,00 0,8570 7,227 5,0831 X 10--3 T
353,2 7,800 4,950 3,2200 X 10-2 0,1594 7,6500x 10-4 T
3S3,2 15,60 5,010 4,5100 x 10-3 0,2260 7,6500x 10-4 T
353,2 31,20 5,0$0 7,0000x 10-3 0,3563 7,6500 X 10-4 T
353,2 62,50 5,210 0,1010 0,5262 7,6500 X 10-4 T
3S3,2 125,0 5,340 0,1580 0,8437 7,6500x 10-4 T
353,2 250,0 5,620 0,2360 1,326 7,6500x 10-4T
353,2 500,0 6,070 0,3170 1,924 7,6500 X 10--4 T
353,2 1O(X3 7,240 0,2680 2,085 7,6500 X 10-4 T
1
*
S’
*
*
j 10-1
%
!J *
* **

*
*
,*-2
1 10 102 ,03
Magnitude ofthe complex modulus, GM[MPa)
Figure f – Data quality check
IS 14882:2000
ISO 10112:1991
2.3 Temperature shift function a) the temperature shift function, a~7), has histori-
cally had a central role;
b) its slope, d(lg al-)/d T, is the crucial feature that
Thk? set of complex modulus data itself implicitly causes data to be correctly shifted; and
defines the temperature shift functio\n aT(7), pro-
vided the experimental ranges of tem-\perature an\d\c) the apparent activation energy [z], AIi~, is of in-
frequency are adequate. It is assumed that a single terest and is given by
\\
temperature shift function is applicable.
\ AHA= 2,303R7’2d(lg a7)/d7’ ...(13)
------
It is recommended that the following three functions
where R is the gas constant
be plotted for the experimental range of temperature
(e.g., figure 2) because R = 0,00828 NkmlgmolK (14)
0.22
108 Ii
0,2
107
0,18
Iof’ ‘\
0,16 \\
10s \
\ \
\
O,lG ,OL “\ \
\
h:0.12 Uh103 \ \ \ \ \
B \ \
\
: 0,1 10z \ \ ..
“.\ “.
t
10 ‘.1 ‘.
0,08
1
0,06
If)-l

0,04 1()-2
0.02 1()-3
220 2140 260 280 300 320 340 360 380
Temperature (K)
Key
aT
d(lgcz~/dT
.—— —— apparentactivatimeneqy
Figure 2 – Temperature shift function and its properties

5