© 2016 The Korean Society of Rheology and Springer 301
Korea-Australia Rheology Journal, 28(4), 301-313 (November 2016)DOI: 10.1007/s13367-016-0031-6
www.springer.com/13367
pISSN 1226-119X eISSN 2093-7660
Dynamic blocked transfer stiffness method of characterizing the magnetic field
and frequency dependent dynamic viscoelastic properties of MRE
Umanath R Poojary1,*, Sriharsha Hegde
2 and K.V. Gangadharan
1
1Department of Mechanical Engineering, National Institute of Technology Karnataka, Mangalore 575025, India2Department of Aeronautical and Automobile Engineering, Manipal Institute of Technology, Manipal 576104, India
(Received February 6, 2016; final revision received September 19, 2016; accepted September 22, 2016)
Magneto rheological elastomer (MRE) is a potential resilient element for the semi active vibration isolator.MRE based isolators adapt to different frequency of vibrations arising from the source to isolate the struc-ture over wider frequency range. The performance of MRE isolator depends on the magnetic field and fre-quency dependent characteristics of MRE. Present study is focused on experimentally evaluating thedynamic stiffness and loss factor of MRE through dynamic blocked transfer stiffness method. The dynamicstiffness variations of MRE exhibit strong magnetic field and mild frequency dependency. Enhancementsin dynamic stiffness saturate with the increase in magnetic field and the frequency. The inconsistent vari-ations of loss factor with the magnetic field substantiate the inability of MRE to have independent controlover its damping characteristics.
Keywords: MRE, direct stiffness method, viscoelasticity, dynamic stiffness, loss factor
1. Introduction
Base isolation is an effective way of minimizing the
threat to the structure's durability by isolating it from dam-
aging vibrations. Passive isolation through a flexible ele-
ment between the source and the disturbance is a commonly
adapted base isolation technique. The flexible element iso-
lates the structure by decoupling the transmitted vibration
from the source to the receiver. The passive isolators are
effective only at a particular operating frequency and
exhibit poor adaptability to different frequency of distur-
bances arising from the source (Eem et al., 2011; Li et al.,
2013; Stelzer et al., 2003). Limitations of passive isolation
technique are overcome by real time tunable smart mate-
rial based semi active isolators. The attributes possessed
by MRE analogues to a conventional viscoelastic resilient
element make it a potential smart material for semi active
isolation application (Eem et al., 2011; Kim et al., 2010;
Li et al., 2012; Opie and Yim, 2011).
MRE is a smart polymer composite comprising of fer-
romagnetic powdered ingredients embedded in a polymer
matrix. The ferromagnetic ingredients impart smart nature
to MRE by aligning along the flux lines of externally
applied magnetic field. The field induced characteristics of
MRE are assessed in terms of MR effect (Lokander and
Stenberg, 2003). MR effect is influenced by many pro-
cessing parameters like the type of matrix (Zhu et al.,
2013), type of filler particles (Koo et al., 2012; Lokander
and Stenberg, 2003; Padalka et al., 2010; Stepanov et al.,
2012), shape of the magnetic filler (Song et al., 2009), size
of the filler particle (Bose and Roder, 2009; Fan et al.,
2011; Hegde et al., 2014), volume percentage of filler par-
ticle (Boczkowska and Awietjan, 2009; Hegde et al.,
2015; Lokander and Stenberg, 2003; Qiao et al., 2012;
Tian et al., 2013), additives or plasticizers (Chen et al.,
2008a; Ge et al., 2013; Li and Sun, 2011), pre-cure vis-
cosity of the matrix (Lokander and Stenberg, 2003), and
the magnetic field applied during curing process (Lu et al.,
2012). The major factors influencing the MR effect are
type of filler particle, percentage content, and the type of
matrix. The optimum MR effect exists for the MRE with
a carbonyl iron particle (CIP) content of 25-30% by vol-
ume (Demchuck and Kuz'min, 2002; Hegde et al., 2015;
Lokander and Stenberg, 2003).
MRE also constitutes the group of filled elastomers due
to the embedded ferromagnetic fillers (Li and Sun, 2011).
Filler addition enhances the properties of elastomer by
inducing the reinforcing effect (Funt, 1988). The reinforc-
ing fillers are either nano sized or micron sized. In nano
size filler reinforced elastomers, the reinforcing effect is
dominated by the formation of filler aggregates (Funt,
1988; Ramier et al., 2006; Chazeau et al., 2000). How-
ever, the micron sized fillers impart reinforcing effect by
the formation of the matrix-filler interface (Stacer et al.,
1990; Stelandre et al., 2003; Gauthier et al., 2004). Unlike
elastic materials, the property of filled elastomer is neither
fully elastic nor fully viscous. This behavior is referred to
as viscoelastic, where the response includes the contribu-
tion of viscous and elastic effects (Lakes, 2009). The vis-
coelastic property of filled elastomer is influenced by the
operating parameters like, frequency, input strain, and the
temperature, which it inherited from the matrix (De La
Fuente et al., 2003; Leopoldes et al., 2004; Stacer et al.,
1990). Similar to the filled elastomer, the properties of*Corresponding author; E-mail: [email protected]
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
302 Korea-Australia Rheology J., 28(4), 2016
MRE under non-magnetized state are influenced by the
aforementioned operating parameters (Agirre-Olabide et
al., 2014; Chen et al., 2007; Gong et al., 2012; Li et al.,
2010a; Lu et al., 2012; Sun et al., 2008; Wang et al.,
2006). In addition, under magnetized state, MRE also
exhibits field dependent viscoelastic properties.
The viscoelastic properties of a filled elastomer are mea-
sured by transient method or dynamic rheological tech-
nique (Kumar et al., 2012). Transient method includes the
measurement of decaying rate of stress for the applied
constant instantaneous strain (Basdogon and Dikmen,
2011; Li et al., 2010b) or by measuring the rate of increase
in strain for the application of constant and instantaneous
stress (Lakes, 2009). The dynamic tests are preferred for
viscoelastic property characterization due to the inability
of transient method to effectively characterize the fre-
quency and the strain dependent response (Gunasekaran
and Ak, 2000). The dynamic test includes the measure-
ment of stress (strain) response of viscoelastic material for
input harmonic strain (stress) (Brown, 1996; Lakes, 2009)
in resonance (Gade et al., 1994; Medalia, 1978) or in non-
resonance region (Ooi and Ripin, 2011; Thompson et al.,
1998). The viscoelastic properties in non-resonance regions
are measured by DMA (Ramorino et al., 2003), Rheom-
eter (Li et al., 2010a) or from forced vibration tests (Lin
et al., 2003; Nadeau and Champoux, 2000; Ooi and Ripin,
2011; Thompson et al., 1998) as described in ISO 10846-
1. The forced vibration test method (ISO 10846-1) includes
direct stiffness measurement (ISO 10846-2) or indirect
stiffness measurement (ISO 10846-3). Direct method includes
two different types of dynamic stiffness estimations; dynamic
drive point stiffness and dynamic blocked transfer stiff-
ness. Susceptibility of dynamic drive point stiffness to the
mass between the force transducer and the test element
limits its applicability over higher frequencies (Nadeau
and Champoux, 2000; Ooi and Ripin, 2011). On the con-
trary, the dynamic blocked transfer stiffness overcomes
this limitation by estimation of stiffness with respect to the
blocked force (Nadeau and Champoux, 2000; Ooi and
Ripin, 2011). The viscoelastic property estimation from
dynamic blocked stiffness measurement is through the
receptance plot (Lin et al., 2003; Ooi and Ripin, 2011),
transmissibility plot (Koblar and Boltežar, 2016; Mallik et
al., 1999; Ramorino et al., 2003) or hysteresis loop (Ju et
al., 2012; Zhu et al., 2012). The hysteresis loop provides
the real time indication of linear viscoelastic response, and
it offers a simple procedure to extract dynamic stiffness
and loss factor (Brown, 1996).
The present study aims at experimentally evaluating the
magnetic field and the frequency dependent viscoelastic
properties of MRE through dynamic blocked transfer stiff-
ness method. Experiments are performed to assess the
effective operating range of RTV silicone based isotropic
MRE by harmonically exciting at frequencies below 80
Hz (representing the low frequency region as per ISO
10846-1) and magnetic field up to 318 kA/m. The dynamic
stiffness and loss factor are evaluated from the force-dis-
placement system hysteresis loops.
2. Experimental
2.1. Theoretical background
2.1.1. Dynamic stiffness
Dynamic stiffness represents the response of the visco-
elastic material in the linear viscoelastic region. It is
defined as the ratio of force response of MRE for the input
harmonic displacement (ISO 10846-1).
The viscoelastic property measurement approach of MRE
through direct stiffness method is schematically illustrated
in Figs. 1a and 1b. Input harmonic excitation to MRE
induces a force, F1 at the input end and a blocked force,
Fig. 1. (Color online) (a) and (b) Schematic representation of direct stiffness measurement approach for the characterization of MRE.
(c)-(e) Graphical representation of force-displacement system hysteresis loop.
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 303
F2 at the blocked end. The ratio, F2/X1 represents the
dynamic blocked transfer stiffness, which comprises of
viscous and elastic response of MRE (Lakes, 2009).
The mathematical representation of dynamic blocked
transfer stiffness is given by (Nadeau and Champoux, 2000),
(1)
where, K* represents the dynamic blocked transfer stiff-
ness. The in-phase component (K'), represents the stiff-
ness of MRE (real part of the dynamic blocked transfer
stiffness) and the out-of-phase component (K″), signifies
the energy dissipation capacity (imaginary part of the
dynamic blocked transfer stiffness). The in-phase and out-
of-phase components of the dynamic stiffness are evalu-
ated from the dynamic response of the system under sinu-
soidal input. In the linear viscoelastic region, the response
blocked force for the sinusoidal input displacement (Eq.
(2) and Fig. 1c) is also sinusoidal (Eq. (3) and Fig. 1d) in
nature but lags the displacement by a phase angle δ.
, (2)
. (3)
The in-phase and out-of-phase components of dynamic
blocked transfer stiffness are expressed as,
. (4)
The modified complex force-displacement response is
expressed as,
(5)
where, η =tanδ is the loss factor of MRE.
The viscoelastic response of MRE is represented in the
form of the force-displacement hysteresis loop by elimi-
nating the parameter t in Eq. (5). The mathematical expres-
sion to evaluate the dynamic stiffness and loss factor from
the force-displacement hysteresis loop (Fig. 1e) is given
by (Brown, 1996),
, (6)
Loss factor, . (7)
2.1.2. Energy dissipation
Energy dissipation of MRE under dynamic loading is
measured from the area under the force displacement hys-
teresis loop. The mathematical representation of deforma-
tion induced energy absorbed per unit volume by MRE at
time t is given by (Lakes, 2009),
. (8)
The energy dissipation under harmonic loading is ex-
pressed as,
.
(9)
The Ws represents the energy stored and Wd represents
the dissipated energy. Negligible inertial effect in dynamic
blocked transfer stiffness approach completely restores the
energy stored during stretching of the molecular configu-
ration (Luo et al., 2010).
The amount of energy dissipation estimated from the
dynamic blocked transfer stiffness for one complete cycle
of deformation is expressed as,
. (10)
The energy dissipation associated with viscous damping
in the material is given by (McConnel, 1995),
(11)
where, K″ = Cω. C represents the equivalent damping
capacity of MRE.
2.2. MRE synthesisThe fabrication process of isotropic MRE involves two
steps: mixing and curing. The MRE samples are prepared
by compounding 27% by volume CIP (diameter 5 μm;
BASF; Type CN) and 73% by volume of RTV silicone
matrix. The RTV silicone matrix is a two-part elastomer
(the weight ratio of base to crosslinker is 100:5) from
Dow Corning. MRE samples are prepared by blending the
particles and the matrix to form a homogenous mixture.
The mixture is then poured to an aluminium mould and
degassed in a vacuum chamber. Samples are cured at
room temperature under constant pressure for 15 h.
2.3. Dynamic property measurementThe schematic of dynamic viscoelasticity property mea-
surement experimental setup in SDOF configuration is
shown in Fig. 2. Sinusoidal signals generated from NI
PXI-5412 function generator are fed to the electrodynamic
shaker though a power amplifier system. MRE sample to
be tested in a single shear mode configuration (Li and
Sun, 2011) is fixed to the electrodynamic shaker through
a stinger. The magnetic field is provided by an electro-
magnet and field intensity is measured by Tesla gauge
(Lake Shore, Model 410). Force at the blocked end is
measured by a force transducer (KISTLER, type 9712).
The input strain to MRE is monitored by the signals from
an accelerometer (KISTLER, K-shear) attached to the
input end (ISO:10846-2). The sensed signals from accel-
erometer and force transducer are acquired through NI
PXI-4496 data-acquisition system.
Viscoelastic property measurements of MRE are per-
K* = K′ iK″+( ) =
F2 t( )
X1 t( )-----------
X1 t( ) = X1,0 sinωt
F2 t( ) = F2,0 sin ωt δ+( )
K′ = F2,0
X1,0
--------cosδ and K″ = F2,0
X1,0
--------sinδ
F t( ) = K′ 1 iη+( )X t( )
K* =
F0
X0
-----
η = FB
FA
------
W = 0
2π
ω
------
∫ F t( )X·
t( )dt
W = ωF0X0 0
2π
ω
------
∫ cosωt sinωt cosδ + sin2ωt sinδ( )dt = Ws+Wd
Wd = πF2,0X1,0 sinδ = πK″X 1,0
2
Wd = πCωX 1,0
2
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
304 Korea-Australia Rheology J., 28(4), 2016
formed under steady state harmonic excitation to exclude
the errors associated with frequency sweep (Hegde et al.,
2015). The experiments are performed at frequencies: 6
Hz, 10 Hz, 20 Hz, 25 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz,
and 80 Hz. The influence of magnetic field is evaluated by
extending the viscoelastic property measurement studies
at different magnetic field strengths (0 kA/m, 159 kA/m,
239 kA/m, and 318 kA/m). Experiments are performed at
1.25% strain to ensure linear viscoelastic response. To
exclude the stress softening effect, MRE samples are sub-
jected to preconditioning cycles (Lion and Kardelky,
2004; Höfer and Lion, 2009).
Consistency and accuracy in the viscoelastic property
characterization are ensured by performing the experi-
ments on three identical MRE samples. Each set of exper-
iments is repeated 10 times, and the average value has
been considered for the analysis. The stable response of
the system is ensured by measuring the 10 cycles for each
loading case. The error bar representation is adapted to
indicating the uncertainty in dynamic stiffness and loss
factor estimation. MRE samples are allowed a recovery
period of 15 mins (Stacer et al., 1990) between successive
measurements to exclude the effect of deformation history
on the measured viscoelastic properties.
3. Results and Discussion
3.1. Steady state force-displacement relationshipThe steady state response of MRE is evaluated from the
force-displacement hysteresis loops. Figs. 3a and 3b rep-
resent the frequency dependent hysteresis loops recorded
for 0 kA/m and 318 kA/m. The variation in magnetic field
and frequency dependent hysteresis behavior of MRE is
assessed from the resistance force offered by the MRE at
the blocked end. The maximum resistance force offered
by MRE at 6 Hz and 0 kA/m magnetic field is 0.3416 N.
Fig. 2. (Color online) (a) Schematic representation of dynamic viscoelastic property measurement experimental setup and (b) an image
of the main apparatus.
Fig. 3. (Color online) (a) and (b) Steady state hysteresis loops of MRE at different frequencies corresponding to 0 kA/m and 318 kA/
m magnetic field.
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 305
Resistance force experienced by the MRE is increased to
0.429 N by increasing the frequency to 80 Hz. As evident
from the inset of Fig. 3, the effects of frequency on the
variation in hysteresis characteristics are not pronounced,
and it diminished above 50 Hz. The frequency dependent
saturation behavior of MRE can be correlated to the rigid
composite characteristics exhibited by the filled rubber
with the increase in frequencies (Chen et al., 2007).
The frequency dependency is a typical characteristic
observed in unfilled elastomer when it is subjected to har-
monic loading (Deshpande, 2010). This behavior is asso-
ciated with the relaxation of polymer chains under the
applied deformation. At low frequency, the chains have
sufficient time to rearrange themselves and therefore, the
viscous effect dominates the response of elastomer. With
the increase in frequency, the chains become rigid as the
time available for the molecular rearrangement is less,
which results in pseudo-solid behavior (Ahmed et al., 2006;
Chen and Xu, 2011; Ginic-Markovic et al., 2000). The
relaxation behavior of the unfilled elastomer is affected by
the addition of fillers, which influences its frequency
dependency characteristics. Embedded fillers occupy the
Fig. 4. (Color online) (a)-(f) Magnetic field dependent hysteresis characteristics of MRE at different frequencies.
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
306 Korea-Australia Rheology J., 28(4), 2016
space between the bulk polymer chains and offer restric-
tion to the mobility of the polymer chains under harmonic
loading (Jong, 2005; Osman and Atallah, 2006). This
reduced motion of polymer chains imparts pseudo-solid
behavior at lower frequencies compared to the unfilled
rubber (De La Fuente et al., 2003; Funt, 1988; Leopoldes
et al., 2004; Osman and Atallah, 2006). The above phe-
nomena can be evident from the saturation in hysteresis
characteristics of MRE with the increase in frequency
above 50 Hz.
Figures 4a-4f represent the variation in hysteresis behav-
ior of MRE with the increase in magnetic field at different
excitation frequencies. The hysteresis behavior of MRE
varies with the increase in magnetic field. The field induced
variation is pronounced up to a magnetic field of 239 kA/m
and the variation is not articulated for the increase in mag-
netic field from 239-318 kA/m. Field induced hysteresis
characteristics of MRE are associated with the interaction
between the ferromagnetic fillers, which functions as
magnetic dipoles under magnetic field (Dong et al., 2012).
These interactions vary the mechanical properties by alter-
ing the internal microstructure of MRE (Stepanov et al.,
2008).
Field dependent variation in hysteresis behavior of MRE
is unaffected by the increase in frequency. Corresponding
to 6 Hz, the maximum resisting force experienced by the
MRE is increased from 0.337 N at 0 kA/m to 0.571 N at
318 kA/m. The cumulative increase in resisting force is
53.33%. Under similar conditions, increasing the frequency
to 80 Hz, the resisting force is increased by 49.12%.
3.2. Dynamic stiffness of MREDynamic stiffness is referred to as the ratio of the resist-
ing force offered by the MRE for the given input displace-
ment. Fig. 5a represents the variation of dynamic stiffness
of MRE at different frequency and magnetic field. The
dynamic stiffness of MRE enhances with the increase in
magnetic field and the frequency.
Magnetic field induced enhancement in dynamic stiff-
ness of MRE is assessed in terms of MR effect (Jolly et
al., 1996; Lokander and Stenberg, 2003). The variation in
MR effect with the frequency and the magnetic field is
represented in Fig. 5b. MR effect is enhanced with the
increase in magnetic field which signifies the increased
interaction between the ferromagnetic fillers. Variation in
MR effect corresponding to 318 kA/m magnetic field is
listed in Table 1. The dynamic stiffness of MRE under non-
magnetized state and at 318 kA/m magnetic field is denoted
by Ko and ΔK0.318, respectively. The MR effect is denoted
by the ratio ΔK0.318/Ko. As evident from Table 1, frequency
dependent variation in MR effect with the increase in fre-
quency is not pronounced, which signifies the weak depen-
dency of frequency on the field induced property enhance-
ments of MRE.
Field induced stiffness enhancement of MRE is attributed
to the localized compression of the matrix caused by the
magnetic force in the vicinity of the filler. The mechanism
of the magnetic field induced localized compression of the
matrix is schematically represented in Fig. 6. The phe-
nomenon of localized compression can be analysed on a
unit cell of MRE (Jolly et al., 1996). Unit cell represen-
Fig. 5. (Color online) (a) Magnetic field induced dynamic stiffness measured at different frequencies and (b) absolute increase in
dynamic stiffness at different magnetic field and frequency.
Table 1. MR effect (dynamic stiffness enhancement) of MRE at
different frequencies.
Frequency K0 K0.318 ΔK0.318 ΔK0.318/K0
(Hz) (kN/m) (kN/m) (kN/m) (%)
6 4.478 6.952 2.474 55.24
15 4.781 7.414 2.633 55.07
25 4.91 7.617 2.707 55.11
50 5.2 7.99 2.79 53.65
60 5.365 8.04 2.675 49.86
80 5.51 8.1 2.59 47.00
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 307
tation is an enlarged view of a section of the microstruc-
ture image in Fig. 6a, comprising of a pair of ferromagnetic
fillers separated by elastomer matrix. Schematic represen-
tation of MRE unit cell under non-magnetized and mag-
netized state is represented in Figs. 6b and 6c, respectively.
The dipole interactions induce a magnetic force of attrac-
tion and compress the matrix locally (Leng et al., 2015) as
illustrated in Fig. 6c. Localized compression increases the
stiffness of the matrix in the vicinity of the fillers and con-
tributes to the overall stiffness enhancement when bulk
effect is considered.
As evident from Fig. 5b, the field induced dynamic stiff-
ness enhancement of MRE is pronounced up to a mag-
netic field of 239 kA/m but the enhancement is not
significant between 239 kA/m and 318 kA/m. The dispar-
ity in dynamic stiffness enhancement is associated with
the variation in the energy interaction between the dipoles.
The interaction energy E, between a pair of dipoles in a
MRE unit cell is expressed as (Liao et al., 2012),
(12)
where, µ0 is the permeability of vacuum, µm is the relative
permeability of the elastomer matrix, d0 is the separation
distance of two adjacent particles, ζ = , and
m is the magnetic dipole moment of each iron particle.
As illustrated in the Fig. 6c, the magnetic force of attrac-
tion between the fillers varies the separation distance
between the dipoles which is expressed as (Guo et al.,
2014),
(13)
where, εmatrix is the localized compressive strain experi-
enced by the matrix. The εmatrix is increased with the
increase in magnetic field. The increase in εmatrix enhances
the energy interaction between the dipoles by reducing the
separation distance.
The compressive force arising from the field induced
interaction between the fillers increases the εmatrix, which
in turn enhances the localized stiffness of the matrix
(Fukushi et al., 2013; Martinelli, 2005). At lower mag-
netic field, the variation in εmatrix, is dominated by the
magnetic force of attraction. But, under higher magnetic
field, the contribution of matrix resistance force arising
from the localized stiffness enhancement results in reduc-
tion of variations in εmatrix. This phenomenon influences
the field induced energy interaction between the fillers and
imparts saturation behavior to MRE above 239 kA/m as
reported in past studies. (Chen et al., 2008a; Chen et al.,
2008b; Li and Gong, 2008).
3.3. Energy dissipation and equivalent dampingVibration isolation characteristics of a material depend
upon the ability to dissipate energy. Variation in energy
dissipated under different magnetic fields, and frequencies
are depicted in Fig. 7. The energy dissipation monotoni-
cally increases with the increase in magnetic field as well
as the frequency. Energy dissipation recorded for 6 Hz and
0 kA/m magnetic fields is 0.052 mN-m. Increasing the
magnetic field to 318 kA/m, the energy dissipation is
increased to 0.084 mN-m with a total increase of 0.028
mN-m. The field induced enhancement in energy dissipa-
tion is consistent with the increase in frequency. At 80 Hz
excitation frequency, the energy dissipation of MRE is
enhanced by 0.0292 mN-m for the increase in magnetic
field from 0 kA/m to 318 kA/m.
The energy dissipation (D) of MRE under dynamic
loading is the cumulative contribution of energy dissipa-
tion of the matrix (Dm), energy dissipation of the particles
(Dp), energy dissipation due to friction at matrix-filler
interface (Dpm), and energy dissipation due to ferromag-
E = 1
4πμmμ0
------------------–4ζm
2
d 0
3------------
Σk 0=
k=∞1/k
31.202≈
d = d0 1 εmatrix–( )
Fig. 6. (Color online) (a) Microstructure image of MRE, (b) schematic representation of a MRE unit cell under non-magnetized state,
and (c) unit cell of MRE under magnetized state representing the localized compression of the matrix.
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
308 Korea-Australia Rheology J., 28(4), 2016
netic filler-filler interaction (Dpp). The energy dissipation
capacity, D is expressed mathematically as (Chen et al.,
2008b; Fan et al., 2011; Ju et al., 2012),
. (14)
Energy dissipation of the micron sized filler particles is
minimum compared to the other effects (Ju et al., 2012).
The modified equation of D by excluding the effect of Dp
is written as,
. (15)
The relative slippage between the particles constitutes
the energy dissipation from the ferromagnetic filler-filler
interaction (Dpp). Contribution of Dpp on energy dissipation
in filled elastomers is significant at higher filler reinforce-
ment (Yang et al., 2012). The scope for filler-filler inter-
actions exists with the increase in number of filler particles
resulting from the increased filler particle content. As evi-
dent from the microstructure images shown in Fig. 6a, the
major contribution to Dpp in MRE arises from the agglom-
eration of CIP. The CIP particles are clustered at the sites
of agglomeration and surrounded by polymer matrix. The
fillers at the agglomeration experience relative slippage
under non-magnetized state, which is inhibited by the
presence of filler interactions under magnetic field. Mag-
netic force binds the particles at the agglomeration sites by
reducing the scope for relative slippage, which in turn
diminishes the contribution of Dpp on energy dissipation of
MRE.
The energy dissipation of the matrix, Dm represents the
intrinsic damping of the polymer matrix of MRE (Yang et
al., 2012). The Dm in MRE results from the polymer chain
friction at the molecular level of the matrix (Fay et al.,
1991). The chain friction is caused by the interaction
between the adjacent polymer chains during the coordi-
nated chain movement under harmonic shear loading (Tsai
and Whang, 2001; Tsai et al., 2007). The mechanism of
chain friction differs under magnetized as well as non-
magnetized state of MRE, which is attributed to the field
induced interactions between the fillers. The localized
compression caused by the magnetic force of attraction
brings the adjacent molecules of polymer chains closer, by
reducing the separation distance. This state can be envi-
sioned as the increase in chain density with the decrease
in inter-lock chain separation distance (Tsai and Whang,
2001). Figs. 8a and 8c represents the variation in number
of polymer chains per unit area in the vicinity of fillers
under non-magnetized and magnetized states. The unit
area under magnetized state is characterized by increased
number of polymer chains, which increases the interaction
between the chains and hence the chain friction. This dif-
ference in chain friction results increased contribution of
Dm on D of MRE.
Matrix-filler interface friction energy dissipation (Dpm)
depends on the interaction between the particle and matrix
at the interface (Yang et al., 2012). The Dpm is pronounced
in weakly bonded interface (Chen et al., 2008a; Ge et al.,
2013; Li and Gong, 2008; Li and Sun, 2011) which is
characterized by unstable chemical crosslink between the
matrix and the filler. This results in frictional energy dis-
sipation under the imposed deformation. The microstruc-
ture image of MRE shown in Fig. 6a reveals the existence
of a weakly bonded interface between the matrix and the
fillers as reported in past studies (Chen et al., 2008a; Qiao
et al., 2012).
The frictional energy dissipation, Dpm in MRE with weakly
bonded interface is mathematically expressed as (Chen et
al., 2008b; Li and Gong, 2008),
D = Dm + Dp + Dpm + Dpp
D = Dpp + Dm + Dpm
Fig. 7. (Color online) Variation in magnetic field dependent
energy dissipation of MRE at different frequencies.Fig. 8. (Color online) (a-b) MRE unit cell under non-magnetized
and magnetized states, (c) number of polymer chains per unit
area in the vicinity of ferromagnetic filler under non-magnetized
state of MRE unit cell, and (d) number of polymer chains per
unit area in the vicinity of ferromagnetic filler under magnetized
state of MRE unit cell.
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 309
(16)
where, F is the sliding friction force between the particle
and the matrix, n is the number of interfaces, and s is the
relative displacement at the interface.
The frictional force at the interface is mathematically
expressed as a function of normal force N and the friction
factor µ as (Chen et al., 2008b),
. (17)
The expression for the frictional energy dissipation Dpm
in terms of normal force N is given by,
. (18)
The normal force at the interface is a function of mag-
netic field, which causes the disparity in interface friction
energy dissipation. Under non-magnetized state of MRE,
the normal force is constant and it increases with the
increase in magnetic field. Increased normal force increases
the interface friction force and promotes interface friction
energy dissipation.
The contributions of Dm, Dpm, and Dpp on D are different
under magnetized as well as non-magnetized state. The
modified expression for energy dissipation in MRE under
magnetized state is expressed as,
. (19)
The cumulative contribution of Dm and Dpm increases the
energy dissipation with the increase in magnetic field. The
energy dissipation is pronounced between 0 kA/m and 239
kA/m, but above 239 kA/m, the energy dissipation is not
pronounced. This disparity in field induced energy dissi-
pation is attributed to the saturation behavior of MRE as
discussed in section 3.2. The saturation behavior of MRE
is characterized by the reduction in field induced localized
compression. This diminishes the field induced enhance-
ments in Dm and Dpm and contributes to reduction in
enhancements of D above 239 kA/m.
3.4. Loss factorLoss factor is defined as the ratio of imaginary to the
real part of the complex stiffness function (Lakes, 2009)
and it is estimated from the hysteresis loop (Brown, 1996).
Fig. 9 represents the variation in loss factor of MRE with
the magnetic field and the frequency. The loss factor of
MRE decreases with the increasing frequency, which is
attributed to the dominance of real part of the complex
stiffness over the imaginary part (Osman and Atallah,
2006; Yurkeli et al., 2001).
As evident from Fig. 9, MRE exhibits a unique trend in
loss factor variation with the increase in magnetic field.
The loss factor is decreased with the increase in magnetic
field up to 239 kA/m and it demonstrated an increasing
trend for the increasing the magnetic field from 239 kA/
m to 318 kA/m. The unique nature of loss factor variation
is analysed from the field induced variation in equivalent
viscous damping and stiffness.
For a SDOF system, the loss factor η is given by (Ungar
and Kerwin Jr., 1962),
(20)
where, C and K′ are the equivalent viscous damping capac-
ity and stiffness of the MRE, respectively, and ω is the
angular frequency of excitation. Variation of C and K′ with
respect to the magnetic field is represented in Fig. 10. The
equivalent damping capacity C of MRE is estimated from
Eq. (11) and the stiffness component, K′ is evaluated from
the resultant dynamic stiffness.
As represented in Fig. 10, MRE exhibits both C and K′
variations with respect to frequency and magnetic field.
Frequency dependent variation of C is more pronounced
compared to the stiffness. The variation of C with fre-
quency is more articulated for the frequencies up to 50 Hz
which is attributed to the dominance of viscous effect
(Deshpande, 2010; Payne, 1966). The contribution of vis-
cous component is diminished with frequency above 50
Hz indicating the dominance of elastic component (Jong,
2005; Osman and Atallah, 2006).
Modified expression for loss factor by incorporating the
field induced changes in C and K′ is expressed as,
(21)
where, Cref and K′ref are the corresponding equivalent damp-
ing and stiffness measured at reference magnetic field
strength. The incremental change in C and K′ with the
increase in magnetic field is denoted as ΔCincr and ΔK′incr,
respectively. The incremental change represents the increase
corresponding to the value measured at the next higher
Dpm = nFs
F = nμN
Dpm = nμN
D = Dm + Dpm
η = Cω
K′--------
η = Cref ΔCincr+( )ω
Kref′ ΔKiner′+-----------------------------------
Fig. 9. (Color online) Variation of magnetic field dependent loss
factor observed at different frequencies.
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
310 Korea-Australia Rheology J., 28(4), 2016
incremental magnetic field relative to the value registered
for reference magnetic field. For example, the C value
measured at 239 kA/m is taken as reference to evaluate
the incremental change in C between 239 kA/m to 318
kA/m.
The magnetic field dependent variation in ΔCincr and
ΔK′incr are represented in Fig. 11. As evident from the
graph, the increase in ΔCincr and ΔKincr is pronounced for
the increase in magnetic field between 0 kA/m-239 kA/m.
The variation in ΔCincr and ΔKincr is minimum for the mag-
netic field range of 239 kA/m-318 kA/m. For the magnetic
field below 239 kA/m, the field induced variations in
ΔKincr is pronounced over ΔCincr. But, ΔCincr increase is
pronounced compared to ΔKincr increase for an increase in
magnetic field from 239 kA/m to 318 kA/m. The differ-
ence in ΔKincr and ΔCincr variations with respect to the
magnetic field contributes to the field induced increase
trend and decreasing trend in loss factor.
4. Conclusion
This study is focused on experimentally investigating
the influence of magnetic field and frequency on dynamic
viscoelastic properties of MRE through blocked transfer
stiffness method. The experimental results show that the
dynamic viscoelastic properties of MRE are frequency
and magnetic field dependent. The Influence of magnetic
field on the dynamic viscoelastic property is stronger com-
pared to the frequency. Viscoelastic properties of MRE
saturate with the magnetic field as well as with the fre-
quency. The saturation limit for viscoelastic properties of
tested MRE sample is around 50 Hz and 239 kA/m mag-
netic field. The field induced property enhancement in
MRE has least influence on the frequency. The loss factor
of MRE cannot be controlled independently as it is a func-
tion of field induced enhancement in stiffness and equiv-
alent damping.
Fig. 10. (Color online) (a) Magnetic field and frequency dependent stiffness variation of MRE and (b) magnetic field and frequency
dependent equivalent viscous damping variation of MRE.
Fig. 11. (Color online) (a) Magnetic field induced incremental change in stiffness and (b) magnetic field induced incremental change
in equivalent damping.
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 311
Acknowledgements
The authors acknowledge the funding support from
SOLVE: The Virtual Lab@NITK (Grant number: No.
F.16-35/2009-DL Ministry of Human Resources Develop-
ment) (www.solve.nitk.ac.in) and experimental facility
provided by Centre for System Design (CSD): A Centre
of excellence at NITK-Surathkal.
References
Agirre-Olabide, I., J. Berasategui, M.J. Elejabarrieta, and M.M.
Bou-Ali, 2014, Characterization of the linear viscoelastic
region of magnetorheological elastomers, J. Intell. Mater. Syst.
Struct. 25, 2074-2081.
Ahmed, J., H.S. Ramaswamy, and P.K. Pandey, 2006, Dynamic
rheological and thermal characteristics of caramels, LWT-Food
Sci. Technol. 39, 216-224.
Basdogon, I. and E. Dikmen, 2011, Modeling viscoelastic response
of vehicle door seal, Exp. Tech. 35, 29-35.
Boczkowska, A. and S.F. Awietjan, 2009, Smart composites of
urethane elastomers with carbonyl iron, J. Mater. Sci. 44, 4104-
4111.
Bose, H. and R. Roder, 2009. Magnetorheological elastomers
with high variability of their mechanical properties, J. Phys.-
Conf. Ser. 149, 012090.
Brown, R.P. 1996, Physical Testing of Rubber, 3rd ed., Chapman
& Hall, London.
Chazeau, L., J.D. Brown, L.C. Yanyo, and S.S. Stenstein, 2000,
Modulus recovery kinetics and other insights into the Payne
effect for filled elastomer, Polym. Compos. 21, 202-222.
Chen, L., X.L. Gong, and W.H. Li., 2008a, Effect of carbon black
on the mechanical performances of magnetorheological elas-
tomers, Polym. Test 27, 340-345.
Chen, L., X.L. Gong, and W.H. Li., 2008b, Damping of magne-
torheological elastomers, Chin. J. Chem. Phys. 15, 271-274.
Chen, L., X.L. Gong, W.Q. Jiang, J.J. Yao, H.X. Deng, and W.H.
Li, 2007, Investigation on magnetorheological elastomers
based on natural rubber, J. Mater. Sci. 42, 5483-5489.
Chen, Y. and C. Xu, 2011, Specific nonlinear viscoelasticity
behaviors of natural rubber and zinc dimethacrylate composites
due to multi-crosslinking bond interaction by using rubber pro-
cess analyzer 2000, Polym. Compos. 32, 1593-1600.
De La Fuente, J.L., M. Fernández-García, and M.L. Cerrada,
2003, Viscoelastic behavior in a hydroxyl-terminated polybu-
tadiene gum and its highly filled composites: Effect of the type
of filler on the relaxation processes, J. Appl. Polym. Sci.
88,1705-1712.
Demchuck, S.A. and V.A. Kuz'min, 2002, Viscoelastic properties
of magnetorheological elastomers in the regime of dynamic
deformation, J. Eng. Phy. Thermophys. 75, 396-400.
Deshpande, A.P., 2010, Oscillatory shear rheology for probing
nonlinear viscoelasticity of complex fluids: Large amplitude
oscillatory shear, In: Deshpande, A.P., J.M. Krishnan, and
P.B.S. Kumar, eds., Rheology of Complex Fluids, Springer,
New York, 87-110.
Dong, X., N. Ma, M. Qi, J. Li, R. Chen, and J. Ou, 2012, The
pressure-dependent MR effect of magnetorheological elasto-
mers, Smart Mater. Struct. 21, 075014.
Eem, S.H., H.J. Jung, and J.H. Koo, 2011, Application of MR
elastomers for improving seismic protection of base-isolated
structure, IEEE Trans. Magn. 47, 2901-2904.
Fan, Y.C., X. Gong, S. Xuan, W. Zhang, J. Zheng, and W. Jiang,
2011, Interfacial friction damping properties in magnetorheo-
logical elastomers, Smart Mater. Struct. 20, 035007.
Fay, J.J., C.J. Murphy, D.A. Thomas, and L.H. Sperling, 1991,
Effect of morphology, crosslink density, and miscibility on
interpenetrating polymer network damping effectiveness,
Polym. Eng. Sci. 31, 1731-1741.
Fukushi, T., S.H. Kim, S. Hashi, and K. Ishiyama, 2013, Mag-
netic silicone rubber: Fabrication and analysis with application,
J. Korean Phys. Soc. 63, 686-690.
Funt, J.M., 1988, Dynamic testing and reinforcement of rubber,
Rubber Chem. Technol. 61, 842-865.
Gade, S., K. Zaveri, H. Konstantin-Hansen, and H. Herlufsen,
1994, Complex modulus and damping measurements using
resonant and non-resonant methods, In: Zaveri, K., eds., Tech-
nical Review: Damping Measurements - From Impulse Response
Functions - From Resonance and Non-resonance Excitation
Techniques, Brüel & Kjær A/S, Naerum, 28-44.
Gauthier, C., E. Reynauda, R. Vassoillea, and L. Ladouce-Ste-
landreb, 2004, Analysis of the non-linear viscoelastic behavior
of silica filled styrene butadiene rubber, Polymer 45, 2761-
2771.
Ge, L., X. Gong, Y. Fan, and S. Xuan, 2013, Preparation and
mechanical properties of the magnetorheological elastomer
based on natural rubber/rosin glycerin hybrid matrix, Smart
Mater. Struct. 22, 115029.
Ginic-Markovic, M, N.K. Dutta, M. Dimopoulos, N. Roy Choud-
hury, and J.G. Matisons, 2000, Viscoelastic behaviour of filled,
and unfilled, EPDM elastomer, Thermochim. Acta 357-358,
211-216.
Gong, X., Y. Xu, S. Xuan, C. Guo, L. Zong, and W. Jiang, 2012,
The investigation on the nonlinearity of plasticine-like magne-
torheological material under oscillatory shear rheometry, J.
Rheol. 56, 1375-1391.
Gunasekaran, S. and M.M. Ak, 2000, Dynamic oscillatory shear
testing of foods-selected application, Trends Food Sci. Technol.
11, 115-127.
Guo, F., C.B. Du, and R.P. Li, 2014, Viscoelastic parameter
model of magnetorheological elastomers based on abel dash-
pot, Adv. Mech. Eng., 629386.
Hegde, S., K. Kiran, and K.V. Gangadharan, 2015, A novel
approach to investigate effect of magnetic field on dynamic
properties of natural rubber based isotropic thick magnetorhe-
ological elastomers in shear mode, J. Cent. South Univ. 22,
2612-2619.
Hegde, S., U.R. Poojary, and K.V. Gangadharan, 2014, Experi-
mental investigation of effect of ingredient particle size on
dynamic damping of RTV silicone base magnetorheological
elastomers, International Conference on Advances in Manu-
facturing and Materials Engineering (ICAMME 2014), Man-
galore, India, 2301-2309.
Umanath R Poojary, Sriharsha Hegde and K.V. Gangadharan
312 Korea-Australia Rheology J., 28(4), 2016
Höfer, P. and A. Lion, 2009, Modelling of frequency-and ampli-
tude-dependent material properties of filler-reinforced rubber,
J. Mech. Phys. Solids 57, 500-520.
ISO 10846-1, 2008, Acoustics and vibration-Laboratory mea-
surement of vibro-acoustic transfer properties of resilient ele-
ments-Part 01: Principles and guidelines, International Standard
Organization, Geneva.
ISO 10846-2, 2008, Acoustics and vibration-Laboratory mea-
surement of vibro-acoustic transfer properties of resilient ele-
ments-Part 02: Dynamic stiffness of elastic supports for
translator motion-direct method, International Standard Orga-
nization, Geneva.
ISO 10846-3, 2002, Acoustics and vibration-Laboratory mea-
surement of vibro-acoustic transfer properties of resilient ele-
ments-Part 3: Indirect method for determination of the
dynamic stiffness of resilient supports for translatory motion,
International Standard Organization, Geneva.
Jolly, M.R., J.D. Carlson, and B.C. Muñoz, 1996, A model of the
behaviour of magnetorheological materials, Smart Mater.
Struct. 5, 607-614.
Jong, L., 2005, Viscoelastic properties of ionic polymer compos-
ites reinforced by soy protein isolate, J. Polym. Sci. Pt. B-
Polym. Phys. 43, 3503-3518.
Ju, B.X., M. Yu, J. Fu, Q. Yang, X.Q. Liu, and X. Zheng, 2012,
A novel porous magnetorheological elastomer: Preparation and
evaluation, Smart Mater. Struct. 21, 035001.
Kim, Y.K., J.H. Koo, K.S. Kim, and S. Kim, 2010, Vibration iso-
lation strategies using magneto-rheological elastomer for a
miniature cryogenic cooler in space application, 2010 IEEE/
ASME International Conference on Advanced Intelligent
Mechatronics, Montreal, Canada, 1203-1206.
Koblar, D. and M. Boltežar, 2016, Evaluation of the frequency-
dependent Young's modulus and damping factor of rubber
from experiment and their implementation in a finite-element
analysis, Exp. Tech. 40, 235-244.
Koo, J.H., A. Dawson, and H.J. Jung, 2012, Characterization of
actuation properties of magnetorheological elastomers with
embedded hard magnetic particles, J. Intell. Mater. Syst. Struct.
23, 1049-1054.
Kumar, A., A.D. Stickland, and P.J. Scales, 2012, Viscoelasticity
of coagulated alumina suspensions, Korea-Aust. Rheol. J. 24,
105-111.
Lakes, R., 2009, Viscoelastic Materials, Cambridge University
Press, New York.
Leng, D., L. Sun, F. Gordaninejad, A. Bayat, and Y. Lin, 2015,
The dynamic performance of magnetic-sensitive elastomers
under impact loading, Smart Mater. Struct. 24, 045023.
Leopoldes, J., C. Barres, J.L. Leblanc, and P. Georget, 2004,
Influence of filler-rubber interactions on the viscoelastic prop-
erties of carbon-black-filled rubber compounds, J. Appl. Polym.
Sci. 91, 577-588.
Li, J.F. and X.L. Gong, 2008, Dynamic damping property of
magnetorheological elastomer, J. Cent. South Univ. 15, 261-
265.
Li, R. and L.Z. Sun, 2011, Dynamic mechanical behavior of
magnetorheological nanocomposites filled with carbon nano-
tubes, Appl. Phys. Lett. 99, 131912.
Li, W., X. Zang, and H. Du, 2012, Development and simulation
evaluation of a magnetorheological elastomer isolator for seat
vibration control, J. Intell. Mater. Syst. Struct. 23, 1041-1048.
Li, W.H., Y. Zhou, and T.F. Tian, 2010a, Viscoelastic properties
of MR elastomers under harmonic loading, Rheol. Acta 49,
733-740.
Li, W.H., Y. Zhou, T. Tian, and G. Alici, 2010b, Creep and recov-
ery behaviors of magnetorheological elastomers, Front. Mech.
Eng. China 5, 341-346.
Li, Y., J. Li, T. Tian, and W. Li, 2013, A highly adjustable mag-
netorheological elastomer base isolator for applications of real-
time adaptive control, Smart Mater. Struct. 22, 095020.
Liao, G., X. Gong, S. Xuan, C. Guo, and L. Zong, 2012, Mag-
netic-field-induced normal force of magnetorheological elasto-
mer under compression status, Ind. Eng. Chem. Res. 51, 3322-
3328.
Lin, T.R., N.H. Farag, and J. Pan, 2003, Evaluation of frequency
dependent rubber mount stiffness and damping by impact test,
Appl. Acoust. 66, 829-844.
Lion, A. and C. Kardelky, 2004, The Payne effect in finite vis-
coelasticity: Constitutive modelling based on fractional deriv-
atives and intrinsic time scales, Int. J. Plast. 20, 1313-1345.
Lokander, M. and B. Stenberg, 2003, Performance of isotropic
magnetorheological rubber materials, Polym. Test 22, 245-251.
Lu, X., X. Qiao, H. Watanabe, X. Gong, T. Yang, W. Li, K. Sun,
M. Li, K. Yang, H. Xie, Q. Yin, D. Wang, and X. Chen, 2012,
Mechanical and structural investigation of isotropic and aniso-
tropic thermoplastic magnetorheological elastomer composites
based on poly(styrene-b-ethylene-co-butylene-b-styrene) (SEBS),
Rheol. Acta 51, 37-50.
Luo, W., X. Hu, C. Wang, and Q. Li, 2010, Frequency- and
strain-amplitude-dependent dynamical mechanical properties
and hysteresis loss of CB-filled vulcanized natural rubber, Int.
J. Mech. Sci. 52, 168-174.
Mallik, A.K., V. Kher, M. Puri, and H. Hatwal, 1999, On the
modelling of non-linear elastomeric vibration isolators, J.
Sound Vibr. 219, 239-253.
Martinelli, A.E.B., 2005, Rubber Bearings for Precision Positioning
Systems, M.S. Thesis, Massachusetts Institute of Technology.
McConnel, K.G., 1995, Vibration Testing: Theory and Practice,
John Wiley & Sons, New York.
Medalia, A.I., 1978, Effect of carbon black on dynamic proper-
ties of rubber vulcanizates, Rubber Chem. Technol. 51, 437-
523.
Nadeau, S. and Y. Champoux, 2000, Application of the direct
complex stiffness method to engine mounts, Exp. Tech. 24, 21-
23.
Ooi, L.E. and Z.M. Ripin, 2011, Dynamic stiffness and loss fac-
tor measurement of engine rubber mount by impact test, Mater.
Des. 32, 1880-1887.
Opie, S. and W. Yim, 2011, Design and control of a real-time
variable modulus vibration isolator, J. Intell. Mater. Syst. Struct.
22, 113-125.
Osman, M.A. and A. Atallah, 2006, Effect of the particle size on
the viscoelastic properties of filled polyethylene, Polymer 47,
2357-2368.
Padalka, O., H.J. Song, N.M. Wereley, J.A. Filer II, and R.C.
Dynamic blocked transfer stiffness method of characterizing dynamic viscoelastic properties of MRE
Korea-Australia Rheology J., 28(4), 2016 313
Bell, 2010, Stiffness and damping in Fe, Co, and Ni nanowire-
based magnetorheological elastomeric composites, IEEE Trans.
Magn. 46, 2275-2277.
Payne, A.R., 1966, Physical Properties of Natural Rubber, M.S.
Thesis, Durham University.
Qiao, X., X. Lu, W. Li, J. Chen, X. Gong, T. Yang, W. Li, K. Sun,
and X. Chen, 2012, Microstructure and magnetorheological
properties of the thermoplastic magnetorheological elastomer
composites containing modified carbonyl iron particles and
poly(styrene-b-ethylene-ethylenepropylene-b-styrene) matrix,
Smart Mater. Struct. 21, 115028.
Ramier, J., C. Gauthier, L. Chazeau, L. Stelandre, and L. Guy,
2006, Payne effect in silica filled styrene butadiene rubber:
Influence of surface treatment, J. Pol. Sci. Part B Pol. Phy. 45,
286-297.
Ramorino, G., D. Vetturi, D. Cambiaghi, A. Pegoretti, and T.
Ricco, 2003, Developments in dynamic testing of rubber com-
pounds: Assessment of non-linear effects, Polym. Test 22, 681-
687.
Song, H.J., O. Padalka, M. Werely, and R.C. Bell, 2009, Impact
of nanaowire versus spherical microparticles in magnetorheo-
logical elastomer composites, 50th AIAA/ASME/ASCE/AHS/
ASC Structures, Structural Dynamics, and Materials Confer-
ence, Palm Springs, USA, AIAA 2009-2118.
Stacer, R.G., C. Hübner, and D.M. Husband, 1990, Binder/filler
interaction and the nonlinear behavior of highly-filled elasto-
mers, Rubber Chem. Technol. 63, 488-502.
Stelandre, L.L., Y. Bomal, L. Flandin, and D. Labarre, 2003,
Dynamic mechanical properties of precipitated silica filled rub-
ber: Influence of morphology and coupling agent, Rub. Chem.
Technol. 76, 145-160.
Stelzer, G.J., M.J. Schulz, J. Kim, and R.J. Allemang, 2003, A
magnetorheological semi-active isolator to reduce noise and
vibration transmissibility in automobiles, J. Intell. Mater. Syst.
Struct. 14, 743-765.
Stepanov, G.V., A.V. Chertovich, and E.Y. Kramarenko, 2012,
Magnetorheological and deformation properties of magneti-
cally controlled elastomers with hard magnetic filler, J. Magn.
Magn. Mater. 324, 3448-3451.
Stepanov, G.V., D.Y. Borin, Y.L. Raikher, P.V. Melenev, and N.S.
Perov, 2008, Motion of ferroparticles inside the polymeric
matrix in magnetoactive elastomers, J. Phys.-Condes. Matter
20, 204121.
Sun, T.L., X.L. Gong, W.Q. Jiang, J.F. Li, Z.B. Xu, and W.H. Li,
2008, Study on the damping properties of magnetorheological
elastomers based on cis-polybutadiene rubber, Polym. Test 27,
520-526.
Thompson, D.J., W.J. van Vliet, and J.W. Verheij, 1998, Devel-
opments of the indirect method for measuring the high fre-
quency dynamic stiffness of resilient elements, J. Sound Vibr.
213, 169-188.
Tian, T.F., X.Z. Zhang, W.H. Li, G. Alici, and J. Ding, 2013,
Study of PDMS based magnetorheological elastomers, J.
Phys.-Conf. Ser. 412, 012038.
Tsai, M.H., S.L Huang, P.C. Chiang, and C.J. Chen, 2007, Mor-
phology, dynamic mechanical properties, and gas separation of
crosslinking silica-containing polyimide nanocomposite thin
film, J. Appl. Polym. Sci. 106, 3185-3192.
Tsai, M.H. and W.T. Whang, 2001, Dynamic mechanical prop-
erties of polyimide/poly(silsesquioxane)-like hybrid films, J.
Appl. Polym. Sci. 81, 2500-2516.
Ungar, E.E. and E.M. Kerwin Jr., 1962, Loss factors of visco-
elastic systems in terms of energy concepts, J. Acoust. Soc. Am.
34, 954-957.
Wang, Y., Y. Hu, L. Chen, X. Gong, W. Jiang, P. Zhang, and Z.
Chen, 2006, Effects of rubber/magnetic particle interactions on
the performance of magnetorheological elastomers, Polym.
Test 25, 262-267.
Yang, J., X. Gong, H. Deng, L. Qin, and S. Xuan, 2012, Inves-
tigation on the mechanism of damping behavior of magneto-
rheological elastomers, Smart Mater. Struct. 21, 125015.
Yurkeli, K., R. Krishnamoorti, M.F. Tse, K.O. McElrath, A.H.
Tsou, and H.C. Wang, 2001, Structure and dynamics of carbon
black-filled elastomers, J. Polym. Sci. Pt. B-Polym. Phys. 39,
256-275.
Zhu, J.T., Z.D. Xu, and Y.Q. Guo, 2012, Magnetoviscoelasticity
parametric model of an MR elastomer vibration mitigation
device, Smart Mater. Struct. 21, 075034.
Zhu, J.T., Z.D. Xu, and Y.Q. Guo, 2013, Experimental and mod-
eling study on magnetorheological elastomers with different
matrices, J. Mater. Civ. Eng. 25, 1762-1771.