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Numerical Analysis Of Magnetorheological Fluid Damper Using FEM full report
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[attachment=2564]

MAGNETORHEOLOGICAL FLUID DAMPER
1.INTRODUCTION
Vibration isolators or dampers are commonly used to mitigate vibrations in structures or machines. The isolators are typically passive and they are designed to reduce the vibration of the most undesired frequency. However, in many applications, the excitation frequency varies across a large range. In a semi-active device, the stiffness or damping can be adjusted during operation. Changing the stiffness of the support device can be exploited by moving the eigenfrequency of the system to bypass the resonance. Reliable control of the support device requires monitoring of a critical point of structure and knowledge about the frequency response of the system. This kind of adaptive isolator can change operation conditions according to dominant loading resulting in improved vibration isolation capability compared to passive systems. Undesired vibrations are reduced in different loading conditions, i.e. a large frequency range is covered.
Several concepts have been studied recently to utilize smart materials in adaptive structures. Magnetorheological (MR) fluids and elastomers, shape memory alloys (SMA) and piezoelectric materials comprise a class of smart materials whose properties can be controlled. The constitutive behaviour of smart materials couples their mechanical response (stress and strain) with other physical fields like magnetic or electric field or heat, which makes it possible to develop an adaptive structure without complicated mechanisms.
Magnetorheological materials (MR) are a class of materials whose rheological properties are rapidly varied by applying a magnetic field. This change is in proportion to the magnetic field applied and is immediately reversible. MR-materials exhibit rapid, tuneable and reversible transition from a free-flowing state to a semi-solid state upon the application of an external magnetic field. MR-material provides simple, quiet and rapid-response interface between the electronic control and mechanical system to mitigate the vibration of the host structure (Li et al., 2000). MR-materials are useful in many applications because the change in their material properties is large.
2.MAGNETORHEOLOGICAL FLUID
A magnetorheological fluid (MR fluid) is a type of smart fluid. It is a suspension of micrometer-sized magnetic particles in a carrier fluid, usually a type of oil. When subjected to a magnetic field, the fluid greatly increases its apparent viscosity, to the point of becoming aviscoelastic solid. Importantly, the yield stress of the fluid when in its active ("on") state can be controlled very accurately by varying the magnetic field intensity. The upshot of which is that the fluid's ability to transmit force can be controlled with an electromagnet, which gives rise to its many possible control-based applications. It is important to note the difference between MR fluid and ferrofluid. MR fluid particles primarily consist of micrometre-scale particles which are too heavy for Brownian motion to keep them suspended, and thus will settle over time due to the inherent density difference between the particle and its carrier fluid. The particles in a ferrofluids primarily consist of nanoparticles which are suspended by Brownian motion and generally will not settle under normal conditions. As a result, these two fluids have very different applications.
2.1 HOW ITS WORK
The magnetic particles, which are typically micrometer or nanometer scale spheres or ellipsoids, are suspended within the carrier oil are distributed randomly and in suspension under normal circumstances, as below.
Figure 1: Magnetic particles suspended in oil
When a magnetic field is applied, however, the microscopic particles (usually in the 0.1-10 m range) align themselves along the lines of magnetic flux, see below. When the fluid is contained between two poles (typically of separation 0.5-2 mm in the majority of devices), the resulting chains of particles restrict the movement of the fluid, perpendicular to the direction of flux, effectively increasing its viscosity. Importantly, mechanical properties of the fluid in its on state are anisotropic. Thus in designing a magnetorheological (or MR) device, it is crucial to ensure that the lines of flux are perpendicular to the direction of the motion to be restricted.
Figure 2: Direction of magnetic flux
2.2 MATERIAL BEHAVIOR
MR-materials usually consist of micron-sized (3 8 m) magnetizeable particles suspended in a liquid. A typical MR-fluid consists of 20 40% by volume of relatively pure iron particles suspended in a carrier liquid such as mineral oil, synthetic oil, water, or glycol. A variety of proprietary additives similar to those found in commercial lubricants are used to discourage gravitational settling and promote particle suspension, enhance lubricity, change initial viscosity, and inhibit wear (Encyclopedia of Smart Materials). The MR-effect does not increase much with increasing particle content above the CPVC.
To understand and predict the behavior of the MR fluid it is necessary to be able to model the fluid mathematically, a task slightly complicated by the varying material properties (such as yield stress), but is possible. As mentioned above, smart fluids are such that they have a low viscosity in the absence of an applied magnetic field, but become quasi-solid with the application of such a field. In the case of MR fluids (andER), the fluid actually assumes properties comparable to a solid when in the activated ("on") state, up until a point of yield (the shear stress above which shearing occurs). This yield stress (commonly referred to as apparent yield stress) is dependent on the magnetic field applied to the fluid, but will reach a maximum point after which increases in magnetic flux density have no further effect, as the fluid is then magnetically saturated. The behavior of a MR fluid can thus be considered similar to a Bingham plastic, a material model which has been well-investigated.
However, a MR fluid does not exactly follow the characteristics of a Bingham plastic. For example, below the yield stress (in the activated or "on" state), the fluid behaves as a viscoelastic material, with a complex modulus that is also known to be dependent on the magnetic field intensity. MR fluids are also known to be subject to shear thinning, whereby the viscosity above yield decreases with increased shear rate. Furthermore, the behavior of MR fluids when in the "off" state is also non-Newtonian and temperature dependent, however it deviates little enough for the fluid to be ultimately considered as a Bingham plastic for a simple analysis.
Thus our model of MR fluid behavior becomes:
Where t = shear stress; ty = yield stress; H = Magnetic field intensity = Newtonian viscosity; is the velocity gradient in the z-direction.
2.3 PARTICLE SEDIMENTATION
Ferroparticles settle out of the suspension over time due to the inherent density difference between the particles and their carrier fluid. The rate and degree to which this occurs is one of the primary attributes considered in industry when implementing or designing an MR device.Surfactants are typically used to offset this effect, but at a cost of the fluid's magnetic saturation, and thus the maximum yield stress exhibited in its activated state.
2.4 COMMON MR FLUID SURFACTANTS
MR fluids often contain surfactants including, but not limited to:
oleic acid
tetramethylammonium hydroxide
citric acid
soy lecithin
These surfactants serve to decrease the rate of ferroparticle settling, of which a high rate is an unfavorable characteristic of MR fluids. The ideal MR fluid would never settle, but developing this ideal fluid is as highly improbable as developing a perpetual motion machine according to our current understanding of the laws of physics. Surfactant-aided prolonged settling is typically achieved in one of two ways: by addition of surfactants, and by addition of spherical ferromagnetic nanoparticles. Addition of the nanoparticles results in the larger particles staying suspended longer since to the non-settling nanoparticles interfere with the settling of the larger micrometre-scale particles due to Brownian motion. Addition of a surfactant allows micelles to form around the ferroparticles. A surfactant has a polar head and non-polar tail (or vice versa), one of which adsorbs to a nanoparticle, while the non-polar tail (or polar head) sticks out into the carrier medium, forming an inverse or regular micelle,respectively, around the particle. This increases the effective particle diameter. Steric repulsion then prevents heavy agglomeration of the particles in their settled state, which makes fluid remixing (particle redispersion) occur far faster and with less effort. For example, magnetorheological dampers will remix within one cycle with a surfactant additive, but are nearly impossible to remix without them. While surfactants are useful in prolonging the settling rate in MR fluids, they also prove detrimental to the fluid's magnetic properties (specifically, the magnetic saturation), which is commonly a parameter which users wish to maximize in order to increase the maximum apparent yield stress. Whether the anti-settling additive is nanosphere-based or surfactant-based, their addition decreases the packing density of the ferroparticles while in its activated state, thus decreasing the fluids on-state/activated viscosity, resulting in a "softer" activated fluid with a lower maximum apparent yield stress. While the on-state viscosity (the "hardness" of the activated fluid) is also a primary concern for many MR fluid applications, it is a primary fluid property for the majority of their commercial and industrial applications and therefore a compromise must be met when considering on-state viscosity, maximum apparent yields stress, and settling rate of an MR fluid.
2.5 MODES OF OPERATION AND APPLICATIONS
A MR fluid is used in one of three main modes of operation, these being flow mode, shear mode and squeeze-flow mode. These modes involve, respectively, fluid flowing as a result of pressure gradient between two stationary plates; fluid between two plates moving relative to one another; and fluid between two plates moving in the direction perpendicular to
Figure 3: FLOW MODE
their planes. In all cases the magnetic field is perpendicular to the planes of the plates, so as to restrict fluid in the direction parallel to the plates.
Figure 4:SHEAR MODE Figure 5: Squeeze flow mode
The applications of these various modes are numerous. Flow mode can be used in dampers and shock absorbers, by using the movement to be controlled to force the fluid through channels, across which a magnetic field is applied. Shear mode is particularly useful in clutches and brakes - in places where rotational motion must be controlled. Squeeze-flow mode, on the other hand, is most suitable for applications controlling small, millimeter-order movements but involving large forces. This particular flow mode has seen the least investigation so far. Overall, between these three modes of operation, MR fluids can be applied successfully to a wide range of applications. However, some limitations exist which are necessary to mention here.
2.6 LIMITATIONS
1.Although smart fluids are rightly seen as having many potential applications, they are
limited in commercial feasibility for the following reasons:
2.High density, due to presence of iron, makes them heavy. However, operating volumes are small, so while this is a problem, it is not insurmountable.
3.High-quality fluids are expensive.
4.Fluids are subject to thickening after prolonged use and need replacing.
Commercial applications do exist, as mentioned, but will continue to be few until these problems (particularly cost) are overcome.
3.MR-DAMPER
A principal sketch is shown in Fig. 1 and detailed information is found in Table 1. When a magnetic field is applied to the MR-fluid inside the cylinder, the damping characteristics of the fluid increase rapidly since the response time is very short (under 10 milliseconds).
Fig :6 MR-fluid inside the cylinder in addition, the fast damping control is practically achieved accurately. The main cylinder houses the piston, the magnetic circuit, an accumulator Figure
and MR- fluid. The magnetic field is generated by a small electromagnet integrated in the piston head.
1. Principal sketch of MR-damper
An external power source, less than 10 W, is needed for continuous operation. The simplified structure of the RD-1005-3 with main components is shown in Figure 1. The volume of MR fluid portion in the gap, flux guide (piston, ring) and coil create the magnetic circuit (see dash line) in which the magnetic field is produced by the input current.
If external forces act on the piston
Table 1. Typical data of MR-damper
in the absence of a magnetic field, the damping force depends, above all, on the rate of MR fluid flow through the gap, resulting from the pressure differences between the cells. The RD-1005-3 behaves then like a viscous damper. If a magnetic field is applied, the shear stress and the MR fluid viscosity increase the restricting motion of the piston head. As a result, the fluid flow through the gap becomes limited, which produces increased hydraulic resistance to the piston movement and creates a controlled component of the damping force depending on the applied magnetic field.,
4.EXPERIMENTS AND PHENOMENOLOGICAL MODELS
4.1BINGHAM SMODEL
Based on the Bingham s rheological model, one can idealize a simplified mechanical model to simulate the MR-damper. The parallel friction and dashpot elements illustrated in Fig. 4 can be applied to simulate the force-displacement behaviour reasonably, but the force-velocity behaviour is not captured, especially for the velocities close to zero. In addition, this kind of model does not exhibit the non-linear force-velocity behaviour.
Therefore, a more advanced model is needed.
f u(t)
1 2
c
Figure 4. Mechanical model containing a friction and dashpot element to simulate
Bingham s model.
4.2 BOUC-WEN MODEL
The most extensive model for modelling a hysteretic system is the Bouc-Wen model, as shown in Fig. 5 and Eq. (4). It is a versatile but also complicated model that needs a closed-loop control algorithm (Dyke et al., 1998, Yang et al., 2002, Liao and Lai, 2002).
Figure 5. Mechanical model of the MR-damper based on the Bouc-Wen model (Dyke et
al., 1998).
5.NUMERICAL SIMULATIONS
5.1DYNAMIC ANALYSIS
The goal was to study the feasibility of different models of MR-materials to be implemented into the finite element method (FEM) for structural dynamic analysis purposes in the time domain. ABAQUS/Standard software was used for the numerical simulation. A controllable MR-damper was introduced as a User Element subroutine (UEL). The basis of this routine was developed earlier by the author (Heinonen, 2002). As described in the previous chapters, the Bouc-Wen model is versatile for modelling hysteresis. One disadvantage is that it needs a closed-loop control algorithm and several parameters need to be calibrated. Therefore, in this study, a simpler open-loop model was implemented to simulate the hysteresis behaviour. Both dynamic and quasi-static simulations were carried out. The simulations were based on the model and parameters proposed by Oh and Onoda (2002) and the model verification was based on the experimental test shown in that paper. Verification of the FEM-model was made by comparison to the simpler Matlab routine.
5.2 EQUIVALENT MODEL FOR FEM
Oh and Onoda (2002) presented an equivalent structural model based on the springs, dashpot and friction elements, as shown in Fig. 15 (see also Fig. 12). The model with lumped mass was implemented into ABAQUS/Standard with the User Element
subroutine "Smart connector".
smart connector
u(t)
fc
m
c
1 2 k 3
k
Figure 15. Equivalent model of MR-damper. Sequential smart connector and ordinary
spring elements are coupled together with a mass element between them.
The mathematical model of the smart connector, which is a part of the total damper, consists of a spring, a variable viscous damper and a variable friction element. A magnetic field is applied to adjust the viscous and frictional element behaviour. The
internal nodal force Fint for the smart connector is defined as follows:
Fint Fs Fd Fc (7)
The elastic force Fs for the linear spring with a spring stiffness k is
Fs ku (8)
where u is the relative displacement between nodes 1 and 2. The damping force Fd
according to Oh and Onoda (2002) in the adjustable viscous element is defined as

n 1
Fd c H
u u
(9)
in which the damping coefficient c depends on the magnetic field H and n is a fitting
parameter. The force-velocity relation is presented in Fig. 16.
Damping force, Oh and Onoda
10
8
6
4
2
0
-2
-4
-6
-8
-10
-500 -400 -300 -200 -100 0 100 200 300 400 500
velocity (mm/s)
Figure 16. Damping force versus velocity according Oh and Onoda (2002).
Hysteresis caused by the frictional mechanism is described with an incremental solution
procedure. The friction force Fc in the adjustable element at time t1 is modelled as
follows:
F t Fc t0 ks u
; Fc
fc (10)
c 1 f
H sgnu
;
else
in which the ks is a stick stiffness chosen to have a high value ks = 100k
and u ut1 ut0 . fc is the threshold value describing the friction force.
The values c and fc are based on the numerical calibration. The experimental results shown in Fig. 17 indicate that c and fc are almost independent of frequency. The data for c and fc corresponding to the frequency equal to 0.5 Hz is shown in Table 3. All other parameters are presented in Table 4.

Figure 17. Estimated values c and fc of MR-damper as a function of input magnetic field
and frequency (Oh and Onoda, 2002).
Table 3. Field-dependent parameters and resulting displacement amplitude umax used in
the simulations with 0.5 Hz excitation frequency. umax is determined from Fig. 13.
Case # H (mT) c (N/ (mm/s)0.4) fc (N) umax (mm)
1 0 0.68 0 0.39
2 10 1.20 0 0.38
3 20 1.51 0.82 0.35
4 30 2.10 2.18 0.31
5 40 2.45 3.61 0.27
5.3RESULTS
The harmonic excitation in the dynamic analysis was conducted by displacement control. The displacement amplitude at node 1 in Fig. 15 varied for each test case, see Table 3. The hysteresis phenomenon in both the displacement and the velocity domain
is presented in Fig. 18.
10 h = 0 mT
h = 10 mT
h = 20 mT
h = 30 mT
5 h = 40 mT
0
-5
-10
-4 -3 -2 -1 0 1 2 3 4
displacement (m) x 1 -4
0
10
5
0
-5
-10
-1 -0.5 0 0.5 1
velocity (m/s)
-3
x 10
Figure 18. Simulated force-displacement and force-velocity relation in the MR-damper
at different values for the magnetic field.
The simulated results in the displacement domain are very similar compared to the experimental results (Figs. 13 and 18). The friction element controls the operation range. With a low or zero friction, the MR-fluid operates mostly at the post-yield range having lower stiffness, and the damping is mainly caused by the fluid resistance. During the reversal, the stiffness is much higher due to frictional behaviour if the frictional force is adjusted at high level by the magnetic field. In this case, the dissipation energy is mainly generated by friction.
6.QUASI-STATIC ANALYSIS
A simplified quasi-static model is created by Matlab to study the effect of each individual component more closely, especially how the different properties influence the hysteresis phenomenon. The model is a simplified version of the previous model (Oh and Onoda, 2002), containing only a spring, a dashpot and a friction element, all of which are connected together in parallel, as shown in Fig. 19. The mass element is not used in the quasi-static analysis. The damper was loaded by a sinusoidal displacement at node 2. The force components were computed according to Eq. (7). The same simulations were also carried out with ABAQUS/Standard to verify the UEL
subroutine.
f u(t)
1 c 2
k

Figure 19. Simplified model of the MR-element.
6.1EFFECT OF FORCE COMPONENTS
The first Matlab simulation is approximately the same as case #5 in the dynamic FEM- simulations (see Table 3). The serial springs are replaced by one spring with a stiffness coefficient of 26.87 kN/m. The hysteresis phenomenon for each individual force
component as well the total effect is characterized in Figs. 20 23.
Elastic spring
10
5
0
-5
-10
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
10
5
0
-5
-10
-3 -2 -1 0 1 2 3 4
displacement (m)
10
-4
x 10
5
0
-5
-10
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
velocity (m/s)
-3
x 10
Figure 20. Force time history and hysteresis loop in displacement and velocity domain
Viscous damping
4
2
0
-2
-4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
4
2
0
-2
-4
-3 -2 -1 0 1 2 3 4
displacement (m)
4
-4
x 10
2
0
-2
-4
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
velocity (m/s)
-3
x 10
Figure 21. Force time history and hysteresis loop in displacement and velocity domain
for the viscous damping element.
Friction element
4
2
0
-2
-4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
4
2
0
-2
-4
-3 -2 -1 0 1 2 3 4
displacement (m)
4
-4
x 10
2
0
-2
-4
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
velocity (m/s)
-3
x 10
Figure 22. Force time history and hysteresis loop in displacement and velocity domain
for the friction component.
Due to non-sinusoidal friction and damping forces, the resulting connector force was no
longer sinusoidal, although the prescribed displacement was sinusoidal.
Total force
20
10
0
-10
-20
Total
fs fd fc
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
20
10
0
-10
-20
-3 -2 -1 0 1 2 3 4
displacement (m)
20
-4
x 10
10
0
-10
-20
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
velocity (m/s)
-3
x 10
Figure 23. Time history of the total force and components. Total hysteresis effect in
displacement and velocity domain.
Table 4. Constant parameters used in the simulations (see Fig. 12 for definitions).
k1 (kN/m) k2 (kN/m) m (kg) n
222.2 30.57 50 0.4
6.2 DISSIPATION ENERGY
Dissipation energy WD during the cyclic oscillation is defined from the force- displacement curve. The enclosed area describes the energy lost in one cycle and it is defined by the following equivalent formulas (Thomson, 1998):
WD F d x
2 /
Fx d t (11)
0
A loss factor is defined as the ratio between the dissipation energy per radian and the
peak potential energy U = kX2 (X is the peak displacement).
WD
2U
(12)
The equivalent viscous damping factor ceq, determines a linear relation between the velocity and the damping force ( Fd ceq v ). It is defined to create equal damping energy in comparison to the dissipation energy produced by other damping elements, such as friction and non-linear viscous damping.
WD F d x ceq x d x (13)
By assuming a sinusoidal excitation, a solution for the equivalent viscous damping
factor is found:
(13)

c WD
(14)
eq X 2
In this model, the dissipation energy is created by the viscous damping element and the
friction element demonstrated in Figs. 20 22.
The dissipation energy caused by the individual components and altogether in one cycle for cases #5 and #10 is shown in Fig. 26. The loss factors and equivalent viscous damping coefficient are given in Table 6.
Table 6. Loss factors and equivalent damping coefficient in cases #5 and #10.
Case
# Loss factor Equivalent damping ceq (Ns/m)

Viscous
Friction
Total
5 0.358 0.600 0.958 8.19e3
10 3.581 5.769 9.350 80.0e3
-3
x 10
6
5
W total
d
Wd ring
Dissipation energy, Case # 5
damp
d
Wd ic
3
2
1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
0.06
0.05
W total
d
Wd ring
Dissipation energy, Case # 10
damp
d
Wd ic
0.03
0.02
0.01
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (s)
Figure 26. Dissipated energy caused by different force components in cases #5 and #10. The latter has increased values for friction and viscous damping parameters.
6.3 MODEL VERIFICATION
The verification of the FEM-model with the User Element subroutine was made by
comparing the results of the hysteresis loops between ABAQUS and Matlab. The
hysteresis plots in the quasi-static analysis are shown in Fig. 27. The Matlab model was
based on the analytical equations yielding correct results.
Abaqus UEL vs. Matlab
80
60
40
20
0
-20
-40
-60
-80
Abaqus
Matlab
-3 -2 -1 0 1 2 3 4
displacement (m)
-4
x 10
80
60
40
20
0
-20
-40
-60
-80
Abaqus
Matlab
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
velocity (m/s)
-3
x 10
Figure 27. Hysteresis plots created by ABAQUS and Matlab in the quasi-static analysis.
The results from both models are very close together. Some difference is found due to some numerical adjustments around the zero velocity in ABAQUS model. The error in the ABAQUS results is insignificant, but if desired it can be decreased by using a shorter time incrementation.
7.CONCLUSIONS
The FEM-model was verified by quasi- static studies using a single degree of freedom model and compared to the Matlab model. It was observed by numerical simulations that the smart connector element could be applied to simulate a similar dynamic response to that measured in the experiments. The relation between different force components is the most important factor in determining the force-velocity relationship in the MR-damper. Both the friction force and the viscous damping force need to be high compared to the elastic force to simulate similar hysteresis phenomena observed in the experiments.
The "smart connector element" is a promising element for structural dynamic analysis purposes in the time domain. It can be employed to analyze adaptive structures in which the MR-damper is utilized for the control of dynamic properties. Further studies are needed to characterize both the stiffness and damping characteristics instead of studying only the force and displacement responses of MR-devices. The stiffness and damping are the main variables of an individual MR-component as part of a vibrating structure.
8. REFERENCES
Carlson, J.D. & Jolly, M.R. MR-fluid, foam and elastomer devices, Mechatronics 10 (2000) p. 555 569.
Choi, S.-B. & Lee, S.-K. A Hysteresis Model for the Field-Dependent Damping Force
of a Magnetorheological Damper, Journal of Sound and Vibration (2001) 245(2), p.
375 383.
Dyke, S.J., Spencer, B.F. Jr., Sain, M.K. & Carlson, J.D. An experimental study of MR
dampers for seismic protection, Smart Mater. Struct. 7 (1998) p. 693 703.
Encyclopedia of Smart Materials,
http://mrw.interscience.wileyesm/index.html.
Heinonen, J. Simulating Smart Connector by ABAQUS/Standard, VTT Internal Report prepared for the topic Embedded structural intelligence in VTT s technology theme Intelligent Products and Systems, 2002, 16 p.
ABAQUS Theory Manual Version 5.7. Hibbitt, Karlsson, Sorensen.
ABAQUS/Standard User Manual Vol. 1, 2 and 3, Version 6.2. Hibbitt, Karlsson, Sorensen.
Genc, S. & Phul P.P. Rheological properties of magnetorheological fluids, Smart Mater. Struct. 11 (2002) p. 140 146.
Jolly, M.R., Carlson, J.D. & Munoz, B.C. A model of the behaviour of
magnetorheological materials, Smart Mater. Struct. 5 (1996) p. 607 614.
Li, W.H., Yao, G.Z., Chen, G., Yeo, S.H. & Yap, F.F. Testing and steady state modeling of a linear MR damper under sinusoidal loading, Smart Mater. Struct. 9 (2000) p. 95 102.
Liao, W.H. & Lai, C.Y. Harmonic analysis of a magnetorheological damper for
vibration control, Smart Mater. Struct. 11 (2002) p. 288 296.
Lokander, M. & Stenberg, B. Performance of Isotropic Magnetorheological Rubber Materials, Polymer Testing, Volume 22, Issue 3, May 2003, p. 245 251.
Lord Corporation (http://mrfluid.com).
Oh, H-U. & Onoda, J. An experimental study of a semiactive magneto-rheological fluid variable damper for vibration suppression of truss structures, Smart Mater. Struct. 11 (2002) 156 162.
Thomson, W. T. Theory of Vibration with Applications, 4th Edition, Stanley Thornes Publishers Ltd., 1998 (reprinted), 546 p., ISBN 0-7487-4380-4.
Yang, G., Spencer, B.F. Jr., Carlson, J.D. & Sain, M.K. Large-scale MR fluid dampers:
modeling and dynamic performance considerations, Engineering Structures 24 (2002) p.
309 323.
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#2
[attachment=7129]
MAGNETORHEOLOGICAL FLUID DAMPER

INTRODUCTION
Vibration isolators or dampers are commonly used to mitigate vibrations in structures or machines. The isolators are typically passive and they are designed to reduce the vibration of the most undesired frequency. However, in many applications, the excitation frequency varies across a large range. In a semi-active device, the stiffness or damping can be adjusted during operation. Changing the stiffness of the support device can be exploited by moving the eigenfrequency of the system to bypass the resonance. Reliable control of the support device requires monitoring of a critical point of structure and knowledge about the frequency response of the system. This kind of adaptive isolator can change operation conditions according to dominant loading resulting in improved vibration isolation capability compared to passive systems. Undesired vibrations are reduced in different loading conditions, i.e. a large frequency range is covered.
Several concepts have been studied recently to utilize smart materials in adaptive structures. Magnetorheological (MR) fluids and elastomers, shape memory alloys (SMA) and piezoelectric materials comprise a class of smart materials whose properties can be controlled. The constitutive behaviour of smart materials couples their mechanical response (stress and strain) with other physical fields like magnetic or electric field or heat, which makes it possible to develop an adaptive structure without complicated mechanisms.
Magnetorheological materials (MR) are a class of materials whose rheological properties are rapidly varied by applying a magnetic field. This change is in proportion to the magnetic field applied and is immediately reversible. MR-materials exhibit rapid, tuneable and reversible transition from a free-flowing state to a semi-solid state upon the application of an external magnetic field. MR-material provides simple, quiet and rapid-response interface between the electronic control and mechanical system to mitigate the vibration of the host structure (Li et al., 2000). MR-materials are useful in many applications because the change in their material properties is large.
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