Vibration Damping Characterization of Linseed oil based Elastomers for its Effectiveness to Attenuate Structural Vibration

ArticleinJournal of Applied Polymer Science · December 2013with72 Reads
Impact Factor: 1.77 · DOI: 10.1002/app.39607
Abstract

Vibration damping properties of elastomers prepared from linseed oil were characterized by Dynamic mechanical analyzer (DMA) in a temperature range of -50 to 100 oC and frequency range of 5Hz to 1 kHz. The maximum damping loss factor, varies from 0.78 to 1.32, the room temperature (25 oC) loss factor, in the range of 0.56 to 1.08 and the temperature range ( ) for effective damping ( 0.3) varies from 63 oC to 74.4 oC in different elastomers. The elastomers behave as a good vibration damper both in lower and higher frequency range. Thus these elastomers exhibit good damping behaviour in a wide range of temperature and frequency, a primary requirement for practical damping applications. A modal constrained layer damping system (CLD) constructed utilizing these elastomers exhibits its potentiality to attenuate structural vibrations with respect to mild steel bare plate resonator under laboratory fabricated testing methodology.

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Available from: Rakesh Das, Apr 29, 2015
Vibration Damping Characterization of Linseed Oil-Based Elastomers
for Its Effectiveness to Attenuate Structural Vibration
Rakesh Das,
1
Rajesh Kumar,
2
Patit P. Kundu
1
1
Department of Polymer Science and Technology, University of Calcutta, Kolkata 700009, India
2
Precision Metrology Laboratory, Department of Mechanical Engineering, Sant Longowal Institute of Engineering & Technology,
Sangrur, Punjab 148106, India
Correspondence to: P. P. Kundu (ppk923@yahoo.com).
ABSTRACT: Vibration damping properties of elastomers prepared from linseed oil were characterized by dynamic mechanical analyzer
in a temperature range of 250 to 100
C and frequency range of 5 Hz to 1 kHz. The maximum damping loss factor, tan dðÞ
max
varies from 0.78 to 1.32, the room temperature (25
C) loss factor, tan dðÞ
rt
in the range of 0.56–1.08 and the temperature range
(DT) for effective damping tan d 0:3ðÞvaries from 63
C to 74.4
C in different elastomers. The elastomers behave as a good vibra-
tion damper both in lower and higher frequency range. Thus these elastomers exhibit good damping behavior in a wide range of
temperature and frequency, a primar y requirement for practical damping applications. A modal constrained layer damping system
constructed utilizing these elastomers exhibits its potentiality to attenuate structural vibrations with respect to mild steel bare plate
resonator under laboratory fabricated testing methodolog y.
V
C
2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3611–3623, 2013
KEYWORDS: elastomers; glass transition; properties and characterization
Received 28 January 2013; accepted 1 June 2013; Published online 26 June 2013
DOI: 10.1002/app.39607
INTRODUCTION
Uncontrolled vibrations in structures, dynamic systems, and
machines cause fatigue, damage, and structural failure under
resonance condition. Therefore, vibration control is a serious
engineering challenge. The v ibrations and noise control can be
reduced by a number of ways. These are generally classified into
active and passive methods.
1–3
The active damping is attained
through sensing and activation to suppress the vibration in real
time using sensor and actuator which are usually piezoelectric
devices.
4–6
In passive damping, several methods are available.
Sometimes, it involves the modification of the system stiffness/
mass to alter the resonance frequencies which can reduce the
unwanted vibration as long as excitation frequencies remain
unchanged. But in most cases, the vibrations need to be isolated
or dissipated by using isolator or damping materials.
In passive damping treatments, polymeric materials are exten-
sively used in sound and vibration damping applications
because of their inherent damping characteristics.
7–9
Researchers
developed polymeric materials like polymer blend and inter-
penetrating polymeric network (IPN) as high performance
damping materials.
10,11
The basic principle of the passive damp-
ing is the dissipation of vibration energy by transforming it into
heat energy. The ability of a material to dissipate vibration
energy is defined by loss factor. Loss factor is defined by the
ratio of energy dissipated to energy stored in a cycle of vibra-
tion. Dynamic mechanical analysis (DMA) is a ver y powerful
tool for the measurement of damping loss factor of a polymer
in a wide temperature and frequency range.
12
An extensive research work has been already performed on
natural oil to obtain functional polymeric materials
13–18
because of its low production cost, universal availabilit y, and
biodegradabili t y.
19,20
Among the different natural oils, linseed
oil is the most abundant, cheap and easily available non-
edible o il.
21
Li and Larock
22
synthesized cationic po ly meric
materials having good damping behavior from soybean oil.
Even though, they synthesized cationic poly meric materials
from corn and fish oil and characterized by DMA,
23,24
there
are no repor ted work of DMA characterization in a wide
range of frequency and analysis of any damping treatment to
attenuate structural vibration using a polymeric material pre-
pared from linseed oil.
In the present study, the damping properties of linseed oil based
elastomers have been analyzed through a dynamic mechanical
analyzer in a wide range of temperature and frequency. The
elastomers are copolymer of linseed oil, styrene (ST ) and
divinylbenzene (DVB), prepared by cationic polymerization
technique. The variation of damping properties of different elas-
tomers has been optimized.
V
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Page 1
The major part of this ar ticle is the employment of elastomers
for the treatment in constrained layer damping (CLD) to
attenuate structural vibration and to study the material per-
formance. The constrained layer or active CLD system uses
three layered sandwich system which is formed by laminating
base plate to a viscoelastic layer and then adding a constraining
layer. In case of CLD, metal or fiber reinforced plastic and for
active constraining layer damping, piezoelectric actuator is used
as a constraining layer.
25–27
The constraining layer causes the
viscoelastic damping layer to deform in shear, dissipating
mechanical energy. A typical constrained layer structure is
shown in Figure 1. The CLD configurations provide a highly
effective noise and vibration control mechanism in numerous
applications like machiner y, structural engineering, automobiles,
and aircraft applications over a wide range of frequency.
1,28–30
In our present work, linseed oil based elastomers are used as a
viscoelastic damping layer in a modal CLD configuration. A
testing system has been fabricated for determining damping loss
factor of the test pieces for CLD system. The objective of this
fabrication is to provide simpler and cheaper method for inves-
tigation of damping behavior of CLD system around room tem-
perature. The frequency response of the CLD system is
evaluated in a medium range of frequency (5 Hz to 1.5 kHz)
under the cantilevered boundary condition.
EXPERIMENTAL
Materials
Linseed oil used in our study was obtained from the local mar-
ket of Kolkata. ST, DVB (55 mol % DVB and 45 mol % ethylvi-
nylbenzene) and boron trifluoride diethyl etherate complex were
purchased from Sigma-Aldrich, USA. Methanol, dichlorome-
thane, concentrated sulfuric acid were purchased from Merck,
India. Potassium hydroxide was purchased from SRL Chemical
Co, India.
Preparation of Elastomers from Linseed Oil
The elastomers were synthesized by cationic polymerization
technique. Boron trifluoride diethyl etherate was used as initia-
tor and it was modified before its use in polymerization to
reduce its reactivity for homogeneous polymerization. The ini-
tiator was modified by its mixing with methyl ester of linseed
oil in the weight of 3 : 5 with constant stirring at 0
C. Methyl
ester of linseed oil was used for better miscibility with initiator,
leading to uniform distribution of initiator in reaction mixtures.
Methyl ester was prepared in two consecutive steps in a transes-
terification process using the methodology of the transesterifica-
tion double step process.
31
Polymeric materials were prepared by heating the mixture of
concentration of regular linseed oil, ST, and DVB in a glass
mold. The desired amount of ST and DVB were added to the
linseed oil and the mixture was vigorously stirred. Then, the
mixture was cooled and initiator was added slowly with con-
stant stirring at low temperature. After the homogeneous mix-
ing, the resulting mixture was transferred to a glass mold (150
mm 3 150 mm 3 3 mm) and the mold was then sealed with
silicon adhesive. After that, the mold was kept at room temper-
ature for 12 h and then, it was heated sequentially at different
temperatures and different time interval such as, at 60
C for 12
h, at 110
C for 24 h, and finally post-cured at 120
C for 3 h. In
our experiment, the linseed oil content in the original composi-
tion of samples was varied from 45% to 65% and in the
remaining aromatic content the ST and DVB are taken in fixed
internal ratio of 3 : 2 in SET I and 1 : 1 in SET II. The initiator
was maintained at 8% level in all the samples. The detailed feed
compositions of different samples are provided in Table I.
Fourier Transform Infrared Spectrometry of Elastomers
The synthesized elastomers are analyzed by attenuated total
reflectance (ATR) method of Fourier transform infrared (FTIR)
spectrometry. The samples were analyzed by Bruker, Germany
FTIR spectrometer (Model: Alpha-E) and the peak was recorded
in absorbance. A total of 42 scans at 4 cm
21
resolution were
collected to get an average spectrum.
Characterization of Vibration Damping Properties
of Elastomers
Vibration damping properties of the elastomers of SET I and
SET II on basis of viscoelasticity were determined throug h
dynamic mechanical analyzer. A rectangular specimen of dimen-
sion 35 mm 3 6mm3 2 mm was tested in strain controlled
tension mode by Metravib Dynamic Mechanical Analyzer
(Model: VA 4000) at a fixed frequency of 5 Hz and dynamic
strain of 0.0025%. Each specimen was cooled under liquid
nitrogen to 250
C and then heated up to 100
C under helium
at a heating rate 3
C/min. The viscoelastic materials usually
possess both elastic and viscous properties and the moduli are
Figure 1. Sketch of a ty pical CLD system.
Table I. Detailed Feed Compositions of Different Elastomers
SET
Sample
ID
Linseed
oil (%)
Styrene
(%)
Divinylbenzene
(%)
Initiator
(%)
I S1Lin45 45 28 19 8
S2Lin50 50 25 17 8
S3Lin55 55 22 15 8
S4Lin60 60 19 13 8
II S5Lin50 50 21 21 8
S6Lin55 55 18.5 18.5 8
S7Lin60 60 16 16 8
S8Lin65 65 13.5 13.5 8
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generally modelled in complex domain. The complex moduli of
a typical viscoelastic material are defined by the equation set
2
;
E 5E
0
1iE
00
5E
0
ð11igÞ
G 5G01iG005G 0 11igðÞ
(1)
where, E is the elastic modulus in tension/compression and G is
the elastic modulus in shear, respectively. The real part of the
moduli is associated with its elastic behavior and is defined as
storage modulus. The imaginary part of the moduli is associated
with its viscous behavior and is defined by loss modulus. The
loss factor is defined by g or tan d which is the ratio of loss
modulus and storage modulus and measures the material damp-
ing capacity. The storage modulus (E
0
), loss modulus (E
00
), and
damping loss factor (tan d ) were recorded as a function of tem-
perature. The main relaxation temperature (T
a
) of the polymer
was obtained from the peak of the loss tangent plot. The cross-
link densities (v
e
) were determined from the rubbery modulus
plateau based on the theory of rubber elasticity
8,32
;
E
0
53v
e
RT (2)
where, E
0
is the storage modulus (Young’s) of the crosslinked
polymer in the plateau region, R is the universal gas-constant
(8.314 J mol
21
K
21
),v
e
is the crosslinking density and T is the
absolute temperature (K). The variation of loss factor and cross-
linking densities was optimized with the varying content of lin-
seed oil of different samples.
As the shear in the viscoelastic core of the CLD system causes
the dissipation of excitation energy of different frequencies, the
frequency scan of elastomers of SET II were carried out in shear
mode on a dynamic mechanical analyzer. The disc samples of
1 10 mm 3 2.5 mm height were analyzed at 25
C in a fixed
dynamic strain 0.001% and in frequency range of 5 Hz to 1
kHz by Metravib Dynamic Mechanical Analyzer (Model: VA
4000). The shear viscoelastic parameters, i.e. the storage modu-
lus (G0), loss modulus (G00), and damping loss factor (tan d)
were obtained as a function of frequency.
Construction of Specimens for Constrained Layer
Damping Treatment
The linseed oil based elastomers were employed to study its per-
formance in constrained layered damping system. A
constrained-layer damping system was constructed using a base
plate of mild steel as vibrating layer, and an identical plate of
mild steel as a constraining layer. The elastomers were sand-
wiched between vibrating layer and constraining layer. The size
of mild steel plate was of 100 mm 3 100 mm 3 2 mm whereas
the size of elastomer was of 100 mm 3 100 mm 3 3 mm. The
three pieces were fixed together as shown in Figure 1, using a
very thin layer of epoxy adhesive. In the experiment, the elasto-
mers having different compositions were used keeping vibrating
layer and constraining layer fixed for all systems.
Fabrication of Experimental Set-up and Technique
The bare plate and the sandwiched test piece were tested under
cantilevered condition, i.e. the plate is fixed at one edge and other
edgeswerefree.Thebareplatewastestedtovalidatethemeasure-
ment system. The base plate was excited by the sinusoidal excita-
tion which was generated by an electrodynamic shaker of MB
Dynamics, USA (Modal 2 Exciter). The shaker was controlled by
function generator of Aplab Limited, India (Model FG 2MD) and
amplifier of MB dynamics, USA (US-20 W). A sinusoidal wav e-
form of varying frequency and c onstant amplitude of 500 mV
(RMS) was applied with the help of function generator. The
response of the bare plate and sandwiched test piece was picked
up by piezoelectric accelerometer of Metra Mass-und Frequenz-
technik, Germany (Model KS94B.100*/01). The accelerometer was
connected with digital storage oscilloscope of Aplab Limited, India
(Model D36100C) interfaced with PC, where the resulting wave
form is displayed. The schematic of the experimental set up and
fixture for holding exciter and test piece are shown in Figure 2. In
case of testing of bare plate, the resonance frequencies (f
n
)ofdif-
ferent mode (n) were noted to determine the magnitude of corre-
sponding mode shape (-) using the plate equation
33
;
E5
12 12t
2
ðÞqa
4
h
2
3
2pf
n
-

2
(3)
where, E is the Young’s modulus of the base material, q is the den-
sity of the material, t is the Poissons ratio of the material, a is the
side of the plate, h is the thickness of the plate, f
n
is the natural fre-
quency of the nth mode of the plate, and - is the corresponding
mode shape function of vibration. A sinusoidal waveform of ampli-
tude 500 mV (RMS) and a varying frequency from 30 Hz to 1.5
kHz was applied to the bare plate in cantilevered condition. The res-
onance frequencies of different modes were recorded and the corre-
sponding mode shape functions were calculated. The experimental
results of mode shape function were compared with theoretical val-
ues from the literature.
34
The displacement and acceleration wave-
form of the base plate as a function of frequency are plotted.
The resonance frequencies and half power bandwidth of sand-
wiched specimens for each mode of vibration from 30 Hz to
1.5 kHz were recorded to calculate loss factor. The loss factor of
the bare plate and CLD system was calculated by bandwidth
method using the equation
35
;
g52f5
Df
f
r
(4)
where, g is the loss factor, fis the damping ratio, Df is the half
power bandwidth, and f
r
is the resonance frequency.
Also, the loss factor is calculated using logarithmic decrement
method using the equation
35
;
g52f52
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
11
2p
d

2
q
(5)
where, dis the logarithmic decrement, defined by
d5
1
r
ln
A
i
A
i1r

(6)
where, r is the number of cycles, f is the damping ratio, A
i
is the first
significant amplitude, and A
i1r
is the amplitude after r cycles. This
method gives the response of the CLD system under periodic excita-
tion in a lower range of fre quency. For experiment using logarithmic
decrement method, a sinusoidal waveform of 6 Hz, 10 Hz, and 15
Hz frequency and amplitude of 1 .5 V ( RMS) was supplied to the
shaker. The time decay waveform of the system was recorded by
oscilloscope and the loss factor is calculated using this waveform.
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RESULTS AND DISCUSSIONS
FTIR Spectroscopy Analysis of the Elastomers
The FTIR spectrum of elastomer (S2Lin50) is shown in Figure
3. The spectrum of sample S2Lin50 is the representative spec-
trum of all elastomers. The transmittance peak at 1741 cm
21
is
for the carbonyl group (AC@O) in ester linkage of the oil and
it is the characteristic peak of the oil content in the elastomer.
The transmittance peak at 690 cm
21
is due to ACAH out of
plane bending of aromatic ring of ST and DVB and it is the
characteristic peak of aromatic content in elastomer.
36
In cati-
onic polymerization reaction, DVB acts as a crosslinker and ST
as a comonomer. The main polymer chain is composed of
crosslinked polymer of ST and DVB in which the linseed oil
molecule is grafted. The schematic of polymerization reaction is
shown in Scheme 1. The oil and aromatic part present in elasto-
mers have two part one free part and another crosslinked part.
Figure 3. FTIR spectrum of elastomer. [Color figure can be viewed in the online issue, which is available at wi leyonlinelibrary.com.]
Figure 2. A: Schematic of experimental set up for damping measurement and (B) schematic of fixture for holding exciter and test piece.
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This free part is viscous and crosslinked part is elastic in nature.
Thus, the elastomer is viscoelastic in nature. The free oil as well
as other free portion present in elastomers helps in plasticiza-
tion of the crosslinked insoluble polymers. The crosslinked elas-
tic part has a major effect on the properties of the elastomers.
Damping Properties of the Elastomers
The variations of storage modulus, loss modulus and loss factor
with temperature for different elastomers having varying linseed
oil concentration are shown in Figure 4. The variation of
parameters of SET I in Figure 4 are representatives of DMA of
all samples. The main relaxation temperature (T
a
), crosslinking
densities (v
e
), maximum damping loss factor, tan dÞ
max
damp-
ing loss factor at room temperature, i.e. at 25
C tan dÞ
rt
, stor-
age modulus at 0
C E
0
ðÞand storage modulus at room
temperature E
0
ðÞ
rt
are listed in Table II. In Figure 4, the
temperature dependence of loss factor, storage modulus, and
loss modulus are shown in the temperature range of 250
Cto
100
C. From Table II, it is clear that damping loss factor
improves with an increase in linseed oil concentration in the
original compositions of the samples. The T
a
shifts to lower
temperature w ith an increase in linseed oil concentration in the
original composition of the samples. In tan d vs. temperature
curve of Figure 4, a very low intense peak of tan d arises in the
temperature range of 250
Cto0
C. The synthesized elastomers
have two parts, one crossliked polymer chain of ST-DVB in
which the linseed oil is grafted and second unreacted part com-
prising free linseed oil and homopolymers of ST and DVB and
a small proportion of copolymer of ST-DVB. The grafted lin-
seed oil content and free linseed oil content are determined
through spectroscopic characterization technique
37
and listed in
Table III. The crosslinked part is elastic and unreacted part is
Scheme 1. Schematic of cationic polymerization reaction.
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viscous in nature. The T
a
is the relaxation temperature of the
crosslinked elastic part. The low intense peak of tan d arises due
to presence of free linseed oil which is not thermodynamically
miscible with the crosslinked polymer network. Also, there are
two segments in the crosslinked polymer chain with different
mobility. The linseed oil segment is flexible whereas aromatic
ST-DVB segment is rigid. Also, the unreacted linseed oil allows
the material to plasticize and soften. The damping, which is
energy dissipation, occurs in polymers because of intermolecular
friction and molecular relaxation.
38
Crosslinking plays an
important role in determining the damping behavior of the
thermosetting materials.
12
As the degree of crosslinking
decreases, the damping property of the polymers improves. The
DVB plays as a crosslinker in cationic polymerization as it has
two reactive C@C bonds per molecule. Thus, the higher concen-
tration of DVB increases the degree of crosslinking and restricts
the motion of the polymer chain which reduces the damping
properties. The damping property of elastomers increases with an
increase in linseed oil content in the original compositions. Also,
the ester group of linseed oil directly attached to the polymer
backbone greatly contributes to improve the damping property.
39
The increase in linseed oil content means a decrease in DVB
content as a result of which the degree of crosslinking of resulting
elastomer decreases. At the same time, the increase in linseed oil
content leads to an increase in free oil content in elastomers as
described in Table III which has a direct effect to soften cross-
linked part of the elastomer. Thus, the increase in linseed oil con-
tent in the original compositions of elastomers improves the
damping property. The variation of loss factor with linseed oil
content in the samples is shown in Figure 4. The loss factor
increases linearly with an increase in linseed oil content. The
higher DVB content in sample S5Lin50 reduces its damping loss
factor with respect to sample S2Lin50 though both have 50% oil
in their compositions. The presence of linseed oil in resulting
elastomers has a potential effect in resulting elastomers to
improve the damping behavior. The samples containing more
than 60% oil are not suitable because of low strength. It is
required to control the ratio of crosslinked part to viscous part
content in resulting elastomers to get optimum damping and
proper strength. The loss factor (tan d) becomes maximum at
primary relaxation temperature (T
a
). At primary relaxation tem-
perature or near about it, the chains begin reptate back and forth
along their length. The excitation energy dissipates in the cross-
linked polymer chain due to this molecular motion which
Figure 4. DMA results. A: Variation of tan d with temperature, (B) variation of storage modulus with temperature, (C) variation of loss modulus with
temperature, and (D) Variation of loss factor and storage modulus with linseed oil content. [Color figure can be viewed in the online issue, which is
available at w ileyonlinelibrary.com.]
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transforms excitation energy into heat energy.
40,41
The glass tran-
sition temperature increases with increasing crosslinking density.
8
As increase in linseed oil content reduces the degree of crosslink-
ing, the T
a
shifts to a lower temperature with an increase in lin-
seed oil content in the elastomers.
The hig h tan d value (tan d0.3) of the materials in a range of
broad te mperature is very crucial for effective damping .
42
The
temperature ranges (DT) for effective damping of elastomers
evaluated from plot of tan d versus temper ature curve are
listed in Table II. The tan dÞ
max
value of elastomers ranges
from 0.78 to 1.32 and DT varies from 63 to 74.4
C. In case of
sample 8, DT is 50
C. In case of samples containing hig her
concentration of linseed oil (55– 65%) in original composi-
tions, the loss factors at lower temperatures (0
Cornear0
C)
are alway s greater than 0.48. The room temperature (25
C)
loss factors of the elastomers are in the range of 0.56–1.08
which are much higher than minimum required loss factor for
effective damping,
42
this value is e ven higher than different
polyurethane-based IPN,
11,39
polymer blend,
10
and comparable
to c rosslinked com posites, hybrids.
43,44
It is well known that
the g lass transition region of the polymer exhibits maximum
potential for sound and v ibration damping.
7
As the primar y
relaxation temperature of these elastomers are in the range of
15.2–46.3
C, i.e. around room temperature, they are very
appropriate damping materials f or practical applications.
These elastomers can be e mployed in different damping con-
figurations which provide highly effective noise and vibration
control mechanism in numerous applications.
1,29
From the storage modulus plot of Figure 4, it is observed that
storage moduli of all samples are high at 0
Candareinthe
range of 0.608 3 10
7
to 36.7 3 10
7
as recorded in Table II. As
the temperature increases, the storage moduli exhibit a sharp
decrease in the temperature region 10–40
C, which corresponds
to a primary relaxation process followed by a rubbery plateau at
temperature above 40
C. The sharp drop in storage moduli cor-
respond to the temperature at which tan d is maximum, indicat-
ing a maximum dissipation of vibration energy. The storage
modulus at 0
C and at room temperature (25
C) increases with
an increase in DVB content and decrease in linseed oil content in
the original composition of the samples. Storage modulus meas-
ures the amount of energy stored in crosslinked structures per
Table II. Dyanamic Mechanical Analysis Result of Elastomers
S Sample Compositions
Dynamic mechanical analysis results
E ID T
a
Crosslinking (tand)
max
(tand)
x
DT(
C) (E’) (E’)
rt
(E”) (E”)
rt
(
C) 310
7
310
7
310
7
T density310
2
tand (Pa) (Pa) (Pa) (Pa)
(mol/m
3
) 0.3
I S1Lin45 Oil451ST28 46.3 4.34 1.07 0.56 72 36.7 16.2 9.38 6.22
119DVB1In8
S2Lin50 Oil501ST25 37.3 3.50 1.15 0.87 70.7 32 9.35 9.03 2.7
117DVB1In8
S3Lin55 Oil551ST22 33 2.53 1.23 1.08 74.4 20.8 0.59 8.3 1.3
115DVB1In8
S4Lin60 Oil601ST19 23.3 1.15 1.32 1.3 69.7 0.76 0.14 0.48 0.12
113DVB1In8
II S5Lin50 Oil501ST21 43.4 4.30 0.79 0.57 63.6 36.5 6.9 9.89 3.87
121DVB1In8
S6Lin55 Oil551ST18.5 32.6 2.81 0.78 0.72 69 24.2 2.68 7.45 1.86
118.5DVB1In8
S7Lin60 Oil601ST16 22.8 2.01 0.87 0.86 67.7 1.00 0.46 0.60 0.34
116DVB1In8
S8Lin65 Oil651ST13.5 15.2 1.04 0.95 0.81 50 0.61 0.12 0.33 0.07
113.5DVB1In8
Table III. Grafted and Free Oil Content in Elastomers
SET Sample ID
Bound oil
content(%)
Free oil
content (%)
I S1Lin45 38.4 12.9
S2Lin50 46.7 13.2
S3Lin55 43.6 20.5
S4Lin60 40.1 27.6
II S5Lin50 45.5 12.5
S6Lin55 44 19
S7Lin60 39.5 28.5
S8Lin65 35 38
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cycle of external excitation and it is recoverable strain energy of
any specimen under deformation. The highly crosslinked struc-
tures absorb more excitation energy than to dissipate as a result
of which storage modulus increases. The degree of crosslinking
decreases with an increase in linseed oil content and decrease in
DVB content. This results in decrease in storage modulus.
In Figure 4, the variation of loss modulus (E
00
)withtempera-
ture is also shown. Like storage moduli, loss moduli of all
samples are also high at 0
C and have the range of 9.89 3 10
7
to 0.33 3 10
7
Pa as recorded in Table II. It e xhibits a sharp
decrease in the temperature range of 10
Cto40
C, which
corresponds to tan dÞ
max
of tan d vs. T curve. The room tem-
perature loss mod uli E00Þ
rt
are in the range of 6.22 3 10
7
Pa
to 0.07 3 10
7
Pa. Like storage modulus, the loss modulus also
decreases with an increase in linseed oil content. In eq. (1),
the imaginary part is the loss modulus and it measures the
amount of energy dissipated as heat due to deformation of
materials. The applied stress which is proportional to applied
energy to def orm the elastomeric material is higher for highly
crosslinked structure. Thus, t he loss modul us for highly cross-
linked structure is higher as it generates more heat energ y due
to deformation.
Figure 5. The variation of shear storage modulus, shear loss modulus, and loss factor with frequency. [Color figure can be viewed in the online issue,
which is available at wileyonlinelibrary.com.]
ARTICLE
3618 J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.39607 WILEYONLINELIBRARY.COM/APP
Page 8
The crosslinking densities as listed in Table II follow the same
trend as storage modulus. The elastomer with the highest DVB
content (sample S1Lin45) shows highest modulus. There is a
decrease in crosslinking density with an increase in linseed oil
concentration and decrease in DVB content in the original com-
positions of the samples. The crosslinking density of the elasto-
mers is proportional to plateau modulus. The plateau modulus
increases with an increase of DVB content and decrease in lin-
seed oil content as a result of higher crosslinking density.
The frequency scan of samples of SET II in shear mode was per-
formed in dynamic mechanical analyzer to study viscoelastic
properties of the elastomers. The shear storage modulus (G0),
shear loss modulus (G00), and shear damping loss factor (tan d)
are plotted as a function of frequency in Figure 5. The shear
storage modulus and loss modulus increase and the damping
loss factor decreases with an increase of frequency. The storage
modulus (G0) represents the elastic behavior and loss modulus
(G00) represents the dissipated energy. Here, the loss factor
which is the ratio of G00 to G0 predicts about the frequency
response of the damping behavior. The frequency response of
G0 and G00 measures the relative motion of all molecules in the
bulk. The increase in elastic modulus G0 may result from the
change in molecular chain rigidity and the interaction between
polymer chains. The increase in G00 arises due to increase in rel-
ative motion between polymer chains. The G0 increases more
Figure 6. Frequency response of (A) bare plate displacement, (B) bare plate acceleration, (C) CLD system displacement, and (D) CLD system
acceleration.
Table IV. Bare Plate Vibration Test Results
Physical parameters
of mild steel bare plate
Mode of
vibration
Resonance
frequency
(f
r
)(Hz)
Band
Width
(Df)(Hz)
Mode shape function (-)value
Loss
factor (g)Experimental Theoretical [37]
E 5 2.1310
11
kg/m
2
1
st
bending mode 190.4 8 3.82 3.49 0.042
q 5 7850kg/m
3
t 5 0.3 1
st
torsional mode 453.8 2.4 9.09 8.54 0.0053
a 5 0.1m 2
nd
bending mode 908 23 18.21 21.44 0.0253
h 5 0.002m 1
st
plate mode 1216 16 24.4 27.46 0.0132
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WWW.MATERIALSVIEWS.COM WILEYONLINELIBRARY.COM/APP J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.39607 3619
Page 9
steeply than G00 with an increase in frequency, as a result the
loss factor slightly decreases with an increase in frequency in
case of linseed oil based elastomers. At a fixed temperature, the
loss factor of conventional elastomers increases with frequency
and exhibits a transition in the higher range of frequency.
2
But
in case of linseed oil based elastomers, there is no transition
observed up to 1 kHz applied frequency. The moduli
(G0andG00) decrease and loss factor increases with an increase
in linseed oil content of elastomers in consistence with previous
results. Thus, in Figure 5, the moduli (G0&G00) are lower but
tan d is higher in S7 Lin60 than S5Lin50.
Structural Vibration Attenuation Through Constrained Layer
Damping Treatment
The bare plate in cantilevered condition was tested to validate
the fabricated experimental set up and technique used to evalu-
ate system damping loss factor of CLD system. The bare plate
behaves as a resonator under applied vibration and this vibra-
tion is controlled through CLD systems. The displacement and
acceleration of bare plate in response to frequency is shown in
Figure 6. The natural frequencies of different mode of vibra-
tions, corresponding experimental and theoretical mode shape
function values, and loss factors are listed in Table IV. The
experimental mode shape function values slightly deviate from
theoretical mode shape function values because the boundary
condition on plate is not applied in ideal way. The clamping
force of the fixed end of the plate and the boundary condition
are kept constant throughout the experiment. The frequency
response of CLD systems using different elastomers is recorded.
The displacement and acceleration of CLD system using sample
S1Lin45 as a function of frequency are plotted in Figure 6. It is
a representative plot of all systems. The displacement and accel-
eration amplitude of the CLD system reduces measurably with
respect to bare plate. The resonance frequencies of different
mode of vibration and corresponding system loss factors for all
systems calculated by bandwidth method are listed in Table V.
The standard deviation (r) of each loss factor is also calculated
and included in Table V. The variation in system loss factors in
Table V. Loss Factor for CLD Samples Using Bandwidh Method
SET
CLD System
using samples Mode of vibiration
Resonance
frequency
(f
r
)(Hz)
Band width
(Df)(Hz)
loss
factor (g)
Standard deviation
of loss factor (r)
I S1Lin45 1
st
bending mode 330 54.2 0.164 14310
24
1
st
torsional mode 602 34.8 0.058 4310
24
2
nd
bending mode 1260 49 0.039 10310
24
1
st
plate mode 1355 135 0.1 8.3310
24
S2Lin50 1
st
bending mode 308 56.7 0.184 15310
24
1
st
torsional mode 600 37.3 0.062 5310
24
2
nd
bending mode 1230 94 0.076 3.6310
24
1
st
plate mode 1353 1.97 0.146 10310
24
S3Lin55 1
st
bending mode 255.3 54 0.212 13310
24
1
st
torsional mode 589.8 39 0.066 5.4310
24
2
nd
bending mode 1152 113 0.098 8.7310
24
1
st
plate mode 1300 210 0.162 21310
24
S4Lin60 1
st
bending mode 246 55 0.223 15310
24
II 1
st
torsional mode 585 39.8 0.068 6.8310
24
2
nd
bending mode 1145 123 0.108 10310
24
1
st
plate mode 1287 220 0.171 14310
24
S5Lin50 1
st
bending mode 360.7 50 0.139 12310
24
1
st
torsional mode ]602 34.7 0.058 7.7310
24
2
nd
bending mode 1234 38 0.031 3310
24
1
st
plate mode 1340 104 0.078 4310
24
S6Lin55 1
st
bending mode 281.7 40.2 0.142 13310
24
1
st
torsional mode 585 34.3 0.059 5.4310
24
2
nd
bending mode 1143 51.9 0.045 3.5310
24
1
st
plate mode 1291 112 0.087 2.8310
24
S7Lin60 1
st
bending mode 265 44.5 0.168 13310
24
1
st
torsional mode 582.8 34.45 0.059 3310
24
2
nd
bending mode 1138 90.6 0.08 1.2310
24
1
st
plate mode 1261 141 0.112 6.5310
24
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3620 J. APPL. POLYM. SCI. 2013, DOI: 10.1002/APP.39607 WILEYONLINELIBRARY.COM/APP
Page 10
various mode are in the range of 0.139–0.223 for 1st bending
mode, in the range of 0.078–0.171 for 1st plate mode, in the
range of 0.058–0.068 for 1st torsional mode and it varies from
0.031–0.108 for 2nd bending mode. In comparison to base plate
loss factor, the loss factor of CLD systems improve 3.3 times to
5.3 times in 1st bending mode, 6 times to 13 times in 1st plate
mode, 10 times to 13 times in 1st torsional mode, and 1.2 times
to 4.2 times in 2nd bending mode. Thus, the CLD systems
exhibit an efficient vibration damping ability. In these CLD sys-
tems, the applied external vibration dissipates mainly due to
shear in the elastomeric core sandwiched between vibrating base
layer and constraining layer. When the base layer undergoes
bending vibration, the elastomeric core material is forced to
deform in shear, because of the upper stiff base layer. Thus the
vibration damping properties of the core materials are very sig-
nificant. The system loss factor of CLD system increases with an
increase in loss factor value of core elastomeric materials. The
effect of elastomers comprising varying amount of linseed oil
on system damping of CLD systems are optimized. According
to DMA, the loss factor of elastomers increases with an increase
in linseed oil content. Thus, the loss factor of CLD system
increases with an increase in linseed oil content in elastomeric
core. The system loss factor increases from CLD system contain-
ing sample S1Lin45 to CLD system containing S4Lin60 for SET
I and increases from CLD system containing S5Lin50 to
S7Lin60 for SET II. In this modal CLD system, the system
damping is only observed by varying the core elastomeric mate-
rials of finite thickness. The thickness of core materials can also
be controlled to get optimum damping. The type of constrained
layer materials also affects the damping of CLD system.
The loss factor of bare plate and the loss factor of CLD systems
at a lower range of frequency were evaluated by logarithmic
decrement method. The harmfulness caused by low frequency
vibration below 10 Hz is very serious such as earth quake, wind
induced vibration and track vibration and so on. The elasto-
mers exhibited a good damping behavior in DMA in low fre-
quency range. The time decay curve of bare plate and CLD
system comprising sample S1Lin45 is shown in Figure 7. The
bare plate waveform exhibits very negligible decay but the CLD
system exhibits very sharp decay within 10–15 cycles. The loss
factor of bare plate and the system loss factor of CLD systems
in 6 Hz, 10 Hz, and 15 Hz applied frequency are listed in Table
VI. The standard deviation of loss factor (r) is also calculated
and furnished in Table VI. The loss factor slightly increases with
an increase in frequency. The system loss factor increases with
Table VI. Loss Factor of CLD Samples by Logarithmic Decrement Method
Sample
6Hz 10Hz 15Hz
loss
factor (g)
Standard
deviation
of loss factor (r)
loss
factor (g)
Standard deviation
of loss factor (r)
loss
factor (g)
Standard
deviation
of loss factor (r)
Bare 0.0056 4.3310
25
0.0057 3310
25
0.0058 4.7310
25
CLD system using 0.065 4.3310
24
0.066 5.4310
24
0.067 5.3310
24
S1Lin45
CLD system using 0.077 4.2310
24
0.078 2.6310
24
0.078 3310
24
S2Lin50
CLD system using 0.084 5310
24
0.085 2.7310
24
0.087 3.3310
24
S3Lin55
CLD system using 0.093 4310
24
0.094 3.5310
24
0.094 3.7310
24
S4Lin60
CLD system using 0.069 2.6310
24
0.069 3310
24
0.069 2310
24
S5Lin50
CLD system using 0.073 2.6310
24
0.075 3310
24
0.074 2310
24
S6Lin55
CLD system using 0.078 4.5310
24
0.078 2.5310
24
0.078 1.3310
24
S7Lin60
Figure 7. Time decay waveform of bare plate and sandwiched plate using
sample S1Lin45 for CLD system. [Color figure can be viewed in the
online issue, which is available at wileyonlinelibrary.com.]
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Page 11
variation of elastomers from S1Lin45 to S4Lin60 and S5Lin50
to S7Lin60 for CLD systems in consistent with previous results.
In comparison with bare plate loss factor, the system loss factors
of different systems increase from 11 times to 16 times at 6 Hz
applied frequency. Thus, these CLD systems are also effective to
fulfill the requirements of practical damping application.
CONCLUSIONS
A variety of elastomers have been developed from linseed oil
having potential applications in vibration damping systems to
control unwanted vibrations. The DMA results of the elastomers
reveal that the maximum damping loss factor, tan dÞ
max
varies
from 0.78 to 1.32 and temperature range (DT) for effective
damping (tan d0.3) varies from 63
C to 74.4
C. The room
temperature (25
C) loss factor tan dÞ
rt
is in the range of 0.56–
1.08. The loss factor increases with an increase in linseed oil
content in the elastomer samples. Thus the elastomers exhibit
good damping behavior in a wide range of temperature. The
damping behavior of elastomers in shear was optimized as a
function of frequency at room temperature (25
C) in a fre-
quency range 5 Hz to 1 kHz. The shear storage modulus (G0),
shear loss modulus (G00) increases with frequency and the shear
loss factor slightly decreases with frequency. The elastomers
behave as a good vibration damper both in lower frequency
range (around 10 Hz) and higher frequency range (around 1
kHz).
A modal CLD system is constructed employing these elastomers
as a core material of sandwiched system. The system loss factors
were evaluated in different mode of plate vibration by band
width method in the range of 5 Hz to 1.5 kHz. In each mode
of vibration the loss factor of the CLD system increases signifi-
cantly in comparison with the loss factor of the mild steel plate
resonator. The loss factor in low frequency range (5–15 Hz) was
evaluated by logarithmic decrement method. In comparison
with bare plate, the loss factor of different CLD systems is
increased from 11 times to 16 times at 6 Hz applied frequency.
Thus, this modal CLD systems exhibit an extensive effectiveness
to attenuate structural vibration of any frequency from 5 Hz to
1.5 kHz.
ACKNOWLEDGMENT
The financial support under major research project scheme
(F.No.36-251(2008) (SR)) from University Grant Commission
(UGC), New Delhi, India is highly acknowledged.
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Supplementary resources

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