VIBRATION ANALYSIS OF FULLY AND PARTIALLY FILLED ...
Transcript of VIBRATION ANALYSIS OF FULLY AND PARTIALLY FILLED ...
Journal of Engineering Science and Technology Vol. 15, No. 5 (2020) 3162 - 3177 © School of Engineering, Taylor’s University
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VIBRATION ANALYSIS OF FULLY AND PARTIALLY FILLED SANDWICHED CANTILEVER BEAM
WITH MAGNETORHEOLOGICAL FLUID
N. SRINIVASA, GURUBASAVARAJU T.M., H. KUMAR*, ARUN M.
Department of Mechanical Engineering, National Institute of Technology Karnataka,
Surathkal, Mangalore, 575025, Karnataka, India
*Corresponding Author: [email protected]
Abstract
This paper presents the experimental and computational study on damping
effect of the fully and partially filled sandwich cantilever beams. The sandwich
beams referred as adaptive beams have a core layer filled with
magnetorheological fluid (MRF) between two aluminium face plates. Forced
vibration tests were conducted under different magnetic fields with the
application of external force in the form of sinusoidal sweep excitation using
an electrodynamic shaker. Effect on damping and natural frequency due to
change in MR fluid core thickness of 2 mm, 4 mm and 6 mm for the fully filled
beam and fluid core length of 75 mm, 150 mm and 250 mm for partially filled
beam were investigated. Modal and harmonic analysis of the MR sandwich
beams were carried out using FE analysis. The results indicated that in the case
of the fully filled beam, a reduction in the natural frequency with the increase
in MR fluid core thickness and a better damping at 2 mm fluid core thickness
were observed. Also, in the case of the partially filled beam a reduction in
natural frequency and improvement in damping is found with the increase in
core length and magnetic field. The results of these analyses can be useful in
designing the sandwich beams for structural application.
Keywords: Damping ratio, Magneto rheological fluid (MRF), Modal and harmonic
analysis, Sandwich beam.
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1. Introduction
In the case of structural applications, it is important to control vibration. This can
be controlled by modifying mechanical properties or by applying passive, semi-
active or active damping inputs. Undesirable vibration in beams can be supressed
by incorporating a damping layer, either over the surface or stacked between two or
more layers of plates or laminates. Use of viscoelastic damping layers like rubber,
shape memory alloys, piezoelectric materials, electrorheological (ER) fluids, MRF
and magnetorheological elastomer (MRE) help in stabilizing the vibration.
Nowadays, MRF is widely used in many applications and it is well known that its
property changes with the influence of external magnetic field. An MR fluid
comprises of soft ferromagnetic particles (0.03-10-micron) such as pure iron,
carbonyl iron powder, cobalt, ceramic metal, or alloys, dispersed in a carrier liquid
namely mineral oil, synthetic oil or silicone oil. The MR particles present in the fluid
then forms a chain like structure along the magnetic field lines.
The MR fluid changes from liquid state to semi-solid state within a fraction of
milliseconds in the presence of magnetic field and retains its fluid form in the absence
of the magnetic field [1]. The semi-solid state is represented as a viscoelastic material
in the pre-yield region in the form of complex shear modulus, and as non-Newtonian
behaviour model in the post yield region [2]. Sun et al. [3] stated that MRF has higher
stiffness values compared to ERF in adaptive structure applications. Yeh et al. [4] and
Yeh and Chen [5] investigated the outcome of the structural stiffness, natural
frequencies and loss factors of the sandwich beam with ER fluid and used FEM to
evaluate the same. Yalcintas and Dai [6] studied the vibration characteristics of ER
and MR fluid filled simply supported beams and found that the beam filled with MR
fluid has better stiffness under magnetic field as compared to the beam with ER fluid
under electric field. Yeh and Chen [7] presented the effect of electric field on damping
of a sandwich beam through experimentation.
Limitations in the use of ERF led some of the researchers to develop a smart
fluid called magnetorheological fluid, where the electric field is replaced by the
use of permanent magnets or electromagnet. Hirunyapruk et al. [8] investigated
the use tuned vibration absorber (TVA) to control the vibration of the system
using magnetorheological fluid layer between the structure. Lara-Prieto et al. [9]
discussed the vibration characteristics of the poly-ethylene terephthalate (PET)
and aluminium sandwiched beam filled with MRF. Rajamohan et al. [10] carried
out studies on vibration responses of multi-layered MRF beam. Rajamohan et al.
[11] investigated vibration analysis using developed FE formulations to find the
effect of partial treatment of MRF sandwich beam and the tests were validated
through experimental studies.
Further, Rajamohan et al. [12] utilized an optimization technique to study the
optimal position of MRF partial treatment of a partially-treated MR sandwich
beam. Li et al. [13] studied the dynamic responses of a rectangular plate with
MRF and isotropic face plates using FEM. Investigations on fully and partially
treated laminated beams with MR fluid were carried out by Rajamohan et al. [14]
and they observed from the experimental investigation that the frequency and the
displacement response of the system is strongly influenced by the applied
magnetic field, pocket position and size of the partial fluid filling. Vibration
parameters like frequency and damping coefficients were investigated for two
types of MR fluids [15].
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Rajamohan et al. [16] developed a finite element model to perform vibration
analysis of a sandwich beam filled with MRF. They developed a mathematical
model for the beam and validated the experimental results with the FE method and
Ritz method. Romaszko and Węgrzynowski [17] modelled a three-layered
sandwich beam with MRF core and conducted FEM analysis.
The study carried out by recent researchers mainly emphasizes on experiments
conducted with free vibration and analytical formulations for the MR sandwich beam.
But there is limited study on experiments considering forced vibration. The work
carried out in this paper mainly focuses on the use of MR fluid as a semi-active core
layer to determine its vibration isolation capability. The variation of natural frequency,
vibration amplitude and damping effect with MR fluid thickness, length and their
positions under different magnetic fields were investigated using forced vibration tests
and finite element analysis in ANSYS software.
2. Fabrication of MR Sandwich Beams
2.1. Fabrication of fully filled MR sandwich beam
An MR sandwich cantilever beam consists of three layers namely two solid face
layers (plates) and an MR fluid core layer. The rheology of the fluid and the
behaviour of the beam is controlled by the application of an external magnetic field.
Geometric models of the fully filled MR sandwich beam with different fluid core
thickness are shown in Fig. 1(a). Exploded view of parts of the MR sandwich beam
is shown in Fig. 1(b).
Aluminium was used as face plates as it has a relative permeability equal to
unity and does not affect the distribution of magnetic field. The face plates were
fabricated to a dimension of 290 mm span length and 2 mm thickness. An
aluminium square piece of 20 mm length, 25 mm width and 2 mm thickness were
riveted and glued to the upper and lower face plates at their ends to give a stiff
support and to maintain an equal MRF core layer thickness along the length of the
MR sandwich beam. The MR fluid core length is 250 mm for all the fully filled
beams. The same is done for 4 mm and 6 mm MR fluid core thickness. The width
of the beam is 25 mm and the gaps are sealed with silicone sealant to avoid MR
fluid leaks. A small gap of 5 mm was left on one side of the beam to fill the core
with MR fluid and the gap was properly sealed with silicone sealant. Later the
sealant was set to dry.
2.2. Fabrication of partially filled MR sandwich beam
The fluid core thickness was maintained constant at 2 mm for the partially filled beams
and the position of the fluid core and its length was varied. The fluid core was
considered at three different positions. This is shown in Figs. 2 and 3. The face plates
and the middle plate made of aluminium are glued and riveted together to form a rigid
beam with required fluid core length. During this process, the middle layer was cut in
different dimensions depending upon the fluid core position required. The fluid core
lengths considered are 75 mm and 150 mm with locations named as P1 near clamped
end, P2 for middle and P3 near the free end of the beam.
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(a) Geometric model.
(b) Exploded view of parts.
Fig. 1. Geometric models of MR sandwich beam with
different core thickness and fabricated MR sandwich beams.
(a) P1.
(b) P2.
(c) P3.
Fig. 2. Geometric models of partially filled MRF
beam with 75 mm fluid core length at different positions.
4 mm8 mm
250 mm
290 mm
2mm
6 mm
250 mm
290 mm
250 mm
290 mm
6 mm10 mm
MRF Aluminium face plates (2 mm)
2mm
MRFAluminium face plates (2 mm)
6 mm
75 mm
290 mm
P1
6 mm
75 mm
290 mm
P2
2mm
P3
2mm
6 mm
75 mm
290 mm
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(a) P1.
(b) P2.
(c) P3.
Fig. 3. Geometric models of partially filled MRF
beam with 150 mm fluid core length at different positions.
3. Experimental Setup
Based on the size of the test specimen, an experimental test setup was built to clamp the
beam and mount the permanent magnets as shown in Fig. 4. The setup consists of
various components such as beam fixture, magnet support, electrodynamic shaker,
permanent magnets, power amplifier, data acquisition (DAQ) system, accelerometer
and force sensor. An electrodynamic shaker was used to provide forced excitation to
the beam. Permanent magnets were mounted on upper and lower plates having north
pole and south pole respectively. The magnetic field was varied by changing the
distance between the upper and lower plates. The magnetic field was measured using a
gauss meter of Lakeshore model 410. The magnetic field was applied in the range from
0 T to 0.1 T in steps of 0.025 T. Permanent magnet arrangement for fully and partially
filled MR sandwich beams are shown in Fig. 5.
Fig. 4. Vibration test setup for MR sandwich beam.
2mm
P1MRF
Aluminium face plates (2 mm)
6 mm
150 mm
290 mm
6 mm
290 mm2mm
150 mm
P2
2mm
6 mm
290 mm
150 mm
P3
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(a) 250 mm.
(b) 75 mm. (c) 150 mm.
Fig. 5. Permanent magnet positions for fully and partially treated beams.
A stinger of 6 mm diameter was fabricated using brass and was used to
connect the free end of the beam with the shaker. The power amplifier was used
to amplify the voltage output to the electrodynamic shaker. A LabVIEW program
was developed to send and acquire the signals through DAQ cards to the beam.
A National Instruments (NI) DAQ card 9264 was used to supply power to the
amplifier in the form of voltage. The amplified voltage signal was given in the
form of sine sweep ranging from 10 Hz to 100 Hz. Uniaxial accelerometer and
force sensor were placed on the beam and stinger respectively to measure the
frequency response of the beam. These sensor signal data were acquired using
NI DAQ 9234 and fed to the computer through LabVIEW software for
further processing. The forced vibration tests were carried out for different
magnetic fields.
4. Results and Discussions
A set of experiments were conducted on fully and partially filled MR sandwich beams
to study the influence of different magnetic field intensities on displacement response,
natural frequency and the damping ratio. The amplitude and frequency of vibration of
the beam at different magnetic fields were obtained from the data acquired using
LabVIEW software. Initially, a general study was conducted to check the effect of
magnetic field on fully filled MR sandwich beam with 2 mm fluid core thickness. Figs.
6(a) and 6(b) show the time domain and frequency domain plots of the beam before and
after application of magnetic field respectively. From the acquired signals it can be
observed that the magnetic field has a significant effect on the natural frequency and
amplitude of vibration. This is due to the increase in stiffness and damping of MR beam
with the application of magnetic field.
MRF
N NN
S S S Lower support
plate
Upper support
plate
Free
endClamped
end
Magnets
N
S
P1
N
S
P1
N
S S
N
S
P2
N
P2
N
S S
N
P3
S
N
P3
N
S S
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(a) Time domain. (b) Frequency domain.
Fig. 6. Free vibration response of the sandwich beam
with 2 mm fluid core thickness without and with magnetic field.
4.1. Fully filled MR sandwich beam
The frequency response for 2 mm, 4 mm and 6mm MR fluid core sandwich beams is
calculated as ratio of the acceleration (output) to the force (input) and are shown in Fig. 7.
The peak amplitude and the corresponding frequencies were obtained from the plot of the
forced vibration test in LabVIEW software. The shift in frequency and improvement in
damping is observed when the magnetic field is gradually increased. Comparing the
frequency shift and amplitude reduction between the off state (0 T) and 0.1 T magnetic
field, the 2 mm MR core shows 9.53% increase in frequency and 72.986% reduction in
amplitude, whereas 4 mm MR core shows 5.77% increase in frequency and 18.18 %
reduction in amplitude. Then finally 6 mm MR core shows 6.65% reduction in frequency
and 59.39% reduction in amplitude.
(a) 2 mm. (b) 4 mm.
(c) 6 mm.
Fig. 7. Frequency response of the MR sandwich
beams with varying core thickness at different magnetic fields.
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To determine damping ratio at different magnetic fields for the MR sandwiched
beam, half-power bandwidth method was used. Damping ratio is calculated using
Eq. (1):
n
2
12
(1)
The damping ratio at 0.1T increased by 676.36%, 11.11 % and 231.48% MR
for sandwich beams with 2 mm, 4 mm and 6 mm MRF core thickness respectively,
as compared to that obtained at 0 T.
4.2. Partially filled MR sandwich beam
The study was carried out for the partially filled beam with 2 mm fluid core
thickness and fluid core length of 75 mm and 150 mm at different positions. The
test results for partially treated beams are presented in Table 1. For the 75 mm MR
beam at the P1 position, there is a small shift in natural frequency and a significant
increase in damping with the increase in magnetic field. MR sandwich beam with
75 mm core length at P3 position shows a negative shift in frequency, which is due
to change in stiffness and the location of the fluid core. Since the stiffness may vary
at any point on the beam, the frequency may shift in positive nature or in negative
nature [18].
Table 1. Natural frequency and damping ratio
at different core lengths and positions under different magnetic fields.
Partially
filled MRF
sandwich
beam
Magnetic
Field (T)
Natural frequency
(Hz) Damping ratio
P1 P2 P3 P1 P2 P3
75 mm
0 29.66 27.99 36.33 0.011 0.010 0.012
0.025 30.66 34.66 35.99 0.020 0.018 0.017
0.05 27.66 28.66 34.99 0.023 0.025 0.032
0.075 30.42 29.99 35.34 0.042 0.034 0.031
0.1 30.33 34.66 30.66 0.027 0.052 0.039
150 mm
0 24.66 27.99 28.66 0.020 0.023 0.013
0.025 24.99 26.99 28.66 0.024 0.029 0.027
0.05 25.33 29.33 28.99 0.034 0.033 0.027
0.075 25.36 27.99 28.99 0.048 0.043 0.035
0.1 26.33 28.99 29.33 0.061 0.082 0.039
Therefore, as the fluid core length gets reduced and is placed farther away from the
fixed end, the frequency of the MR beam reduces. The next test was conducted for the
sandwich beams with 150 mm fluid core length. As the fluid core length increased, an
increase in frequency was observed. Results obtained for 150 mm fluid core length
shows increase in damping effect with the increase in magnetic field.
From the study, it was observed that there was a maximum shift in frequency
and increase in damping at P2 position for both 75 mm and 150 mm fluid core
lengths and the frequency shift was not profound at P1 and P3 positions. The
damping ratio at 0.1 T increased by 144%, 406.3% and 224.25% for the MR
sandwich beams with 75 mm core length at P1, P2 and P3 positions respectively as
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compared to those at 0 T. In case of MR sandwich beam with 150mm fluid core
length, the damping ratio at 0.1 T increased by 195.64%, 258.69% and 210.08% at
P1, P2 and P3 positions respectively as compared to those at 0 T. It is evident that
the MR sandwich cantilever beam with 150 mm fluid core length gives better
damping at all the magnetic fields than the beam with 75 mm core length.
4.3. Effect of magnetic field on frequency for different fluid core
lengths considered from centre of beam
The effect of magnetic field on the frequency with increasing magnetic field and
fluid core length was studied. The partially filled fluid core length of 75 mm and
150 mm at P2 position were considered along with fully filled beam. It was
observed that as the fluid core length increased, the frequency of the beam tends to
decrease as shown in Fig. 8.
Fig. 8. Effect of fluid core
length on frequency for different magnetic fields.
This clearly shows that the magnetic field and fluid core length of the fully filled
and partially filled MR beam plays a significant effect on frequencies. Also, the
frequency increases with increase in the applied magnetic field which is in
agreement with the results of earlier studies of fully filled and partially filled
sandwich MR fluid beams. The results indicate that the damping ratio for the fully
filled beam is higher than those of the partially filled MR sandwich beam
irrespective of different configurations.
5. Finite Element Analysis
MRF sandwich cantilever beam is modelled in ANSYS software by creating a
geometry for aluminium face plates with corresponding cores for MR fluid layer
for fully filled and partially filled beams of different lengths and positions. The
shear stress and shear modulus of the MR fluids are highly influenced with the
application of magnetic fluid [19].
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Table 2 shows the comparison of first natural frequency obtained from the
experimental and FEA modal analysis as well as their percentage deviation. The
material properties of aluminium and MR fluid [20] are specified in Table 3. Modal
analysis helps in calculating dynamic behaviour parameters like natural frequencies
and mode shapes of the structure. This is considered as a basis for transient and
harmonic analysis.
Table 2. Comparison of natural frequencies computed from FEA
with experimental tests for fully and partially filled MR sandwich beams.
Fluid core
thickness
Experimental
(Hz)
FEA
(Hz)
Percentage deviation
(%)
2 mm 26.88 28.07 4.24
4 mm 25.6 25.74 0.54
6 mm 24.32 25.36 4.1
Fluid core length
75 mm
P1 43.52 54.28 19.82
P2 48.64 55.34 12.11
P3 53.76 56.2 4.34
150 mm
P1 34.56 41.35 16.42
P2 38.4 43.92 12.57
P3 43.52 47.47 8.32
Table 3. Material properties of
Aluminium and MRF in MRF sandwich beam.
Properties Aluminium MRF
Density (kg/m3) 2700 3500
Young’s Modulus (Pa) 69x109 -
Poisson’s Ratio 0.3 0.3
Shear Modulus (Pa) 26.53x109 0.5x106
5.1. Harmonic analysis
Once the dominant natural frequencies and their corresponding mode shapes were
obtained, finding the steady state response of the structures for a sinusoidal varying
load is the main objective of the harmonic analysis. The force applied to the
structure varies sinusoidally for different frequencies and the structural response
also shows a variation in the similar manner. Using this analysis, the natural
frequency of the structure can be computed by plotting the amplitudes at any point
on the structure as a function of forcing frequency. In this case, 1 N force was
applied at the free end of the beam for a harmonic frequency range varying between
1 to 100 Hz.
The mesh properties and the boundary conditions are defined for the geometric
model of MR sandwich beam. The number of elements of MR sandwich beam is
7059 and the mesh type is hexa-mesh. The corresponding conditions are shown in
Fig. 9.
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(a) Mesh model. (b) Boundary conditions.
Fig. 9. Mesh model and boundary
conditions of the MR sandwiched cantilever beam
5.1.1. Fully filled MR sandwich beam
The MR fluid layer is considered as a viscoelastic material. The structure is modelled
similar to that as the fully filled fabricated beams of different fluid core thicknesses.
The magnetic field is indirectly specified as an input in terms of shear modulus for
the MR fluid layer in the ANSYS software. This shear modulus is calculated based
on the relation between the storage modulus and magnetic field and the loss modulus
and magnetic field. The shear modulus for the MR fluid is found out by using the
equation developed by Manoharan et al. (2016) as given in Eqs. (2) to (4).
𝐺∗(𝐵) = 𝐺′(𝐵) + 𝑖𝐺"(𝐵) (2)
8.858355.42805035.0 2 BBBG (3)
35.848105.452057.0 2 BBBG (4)
where, B is the magnetic flux intensity in Gauss, G'(B) is the storage modulus and
G"(B) is the loss modulus of MR fluid. Substituting Eqs. (3) and (4) in Eq. (2) gives
the complex shear modulus G*(B) for the MR fluid. The shear modulus is computed
by taking the magnitude of the complex value. The computed first natural frequency
at different magnetic fields are compared with that of the experimental ones as shown
in Table 4.
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Table 4. Natural frequency for fully filled sandwich MR
beam with different fluid core thickness by experiment and FEA.
Natural frequencies (Hz)
2 mm 4 mm 6 mm
Magnetic Field (T) Experiment FEA Experiment FEA Experiment FEA
0 20.33 27.05 17.33 24.01 19.99 21.49
0.025 20.33 27.96 18.66 25.13 17.99 22.86
0.05 20.33 28.72 18.66 26 16.99 23.81
0.075 20.99 29.39 17.99 26.76 17.33 24.66
0.1 22.99 29.98 18.66 27.43 18.66 25.4
From harmonic analysis, it is observed that for all the beams with different fluid
core thickness, the frequency increases with increase in the magnetic field as
compared to the beam without magnetic field and the same can also be observed from
experimental study.
5.1.2. Partially filled MR sandwich beam
The geometry for harmonic analysis is modelled similar to that of the partially filled
fabricated beam. The analysis is performed for partially filled MR sandwich beam of
different fluid core lengths of 75 mm and 150 mm at P1, P2 and P3 positions. The
results are represented in Fig. 10, which shows vibration amplitude in terms of
acceleration vs frequency.
From the plots, it is evident that the frequency change is not that significant as
compared to that obtained from experimental study. Though there is minor shift in
the frequency, the magnitude of the harmonic response tends to reduce with increase
in the magnetic field. The shift in frequency is notable with increasing fluid core
length, i.e., from 75 mm to 150 mm. When the fluid core is increased to 250 mm, it
can be observed that the frequency shift is more. From the plots of 75 mm and 150
mm fluid core length at P2 position and 250 mm fully treated beams, it is also
observed that as the fluid core length is increased, the natural frequency of the
sandwich MR beam is decreased. This is because of change in properties of the MR
sandwich beam. A similar trend is observed from the experimental study. The
damping values are increasing with increasing fluid core length for the beam partially
filled at the P2 position of the MR sandwich beam.
(a) 75 mm, P1 position. (d) 150 mm, P1 position.
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(b) 75 mm, P2 position. (e) 150 mm, P2 position.
(c) 75 mm, P3 position. (f) 150 mm, P3 position.
Fig. 10. Harmonic response for partially filled beams at
different magnetic fields for different fluid core lengths and positions.
5.2. Effect of magnetic field on frequency for different fluid core length
considered from centre of the beam
Figure 11 shows the effect of magnetic field intensity for fluid core length of 75
mm, 150 mm and 250 mm (fully filled) considered from centre of beam. It can
be observed that for 75 mm fluid core length there is no change in natural
frequency with increase in magnetic field intensity. This may be due to lower MR
fluid core length and the rest of the core layer being covered with aluminium. For
150 mm MR fluid core length, it can be observed that there is a slight increase in
frequency with increase in magnetic field. This increase in frequency is observed
only at 0.025 T and 0.1 T, but there is no change at 0.05 T and 0.075 T. For fully
filled MR beam, it is observed that there is increase in frequency with increase in
the magnetic field intensity. Also, there is a decrease in frequency with increase
in fluid core length because of increase in mass of the structure which is more
evident to the effect of stiffness.
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Fig. 11. Effect of fluid core length on frequency
for different magnetic fields from harmonic analysis.
6. Conclusions
This research study presents vibration analyses of fully filled and partially filled
MR fluid aluminium sandwich beam of different fluid core thickness, fluid core
lengths and their positions under different magnetic fields. Based on the
experimental tests and FE analyses performed in ANSYS software, following
conclusions were drawn.
The MR fluid in the sandwich beam has a better ability of reduction in the
magnitude of the peak response. The MR beam has better stiffening effect with
the application of an external magnetic field.
The frequencies and the damping ratios of the MR sandwich beam are mainly
affected by varying the fluid core size both in terms of thickness and length. It was
observed that the frequency decreased with increase in MR fluid core thickness.
With the advantage of design possibilities for partially filled beams, different
configurations were considered with 75 mm and 150 mm fluid core length at
different positions. It was seen that the fluid core length and its position have a
significant effect on frequencies and damping ratios with the increase in
magnetic field.
Finite element analysis study was performed in ANSYS software for the fully
filled and partially filled sandwich MR beams. The analysis shows a similar
trend of the shift in natural frequency, reduction in the magnitude of peak
response and damping with increase in magnetic field when compared with the
experimental results.
Nomenclatures
G' Storage modulus, Pa
G" Loss modulus, Pa
G* Complex shear modulus, Pa
B Magnetic field, T
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Greek Symbols
ζ Damping ratio
Natural frequency, Hz
Abbreviations
DAQ Data Acquisition
ER Electrorheological
ERE Electrorheological Elastomer
ERF Electrorheological Fluid
FEM Finite Element Method
MR Magnetorheological
MRE Magnetorheological Elastomer
MRF Magnetorheological Fluid
NI National Instruments
PET Polyethylene Terephthalate
TVA Tuned Vibration Absorber
References
1. Jolly, M.R.; Carlson, J.D.; and Munoz, B.C. (1996). A model of the behaviour
of magnetorheological materials. Smart Materials and Structures, 5(5), 607-614.
2. Carlson, J.D.; Matthis, W.; and Toscano, J.R. (2001). Smart prosthetics based
on magneto rheological fluids. Proceedings of. SPIE, 4332, 308-316.
3. Sun, Q.; Zhou, J.X.; and Zhang, L. (2003). An adaptive beam model and
dynamic characteristics of magnetorheological materials. Journal of Sound
and Vibration, 261(3), 465-481.
4. Yeh, J.Y.; Chen, L.W.; and Wang, C.C. (2004). Dynamic stability of a
sandwich beam with a constrained layer and electrorheological fluid core.
Composite Structures, 64(1), 47-54.
5. Yeh, J.Y.; and Chen, L.W. (2004). Vibration of a sandwich plate with a
constrained layer and electrorheological fluid core. Composite Structures,
65(2), 251-258.
6. Yalcintas, M.; and Dai, H. (2003). Vibration suppression capabilities of
magnetorheological materials based adaptive structures. Smart Materials and
Structures, 13(1), 1-11.
7. Yeh, J.Y.; and Chen, L.W. (2006). Dynamic stability analysis of a rectangular
orthotropic sandwich plate with an electrorheological fluid core. Composite
Structures, 72(1), 33-41.
8. Hirunyapruk, C.; Brennan, M.J.; Mace, B.R.; and Li, W.H. (2010). A tunable
magneto-rheological fluid-filled beam-like vibration absorber. Smart
Materials and Structures, 19(5), 055020.
9. Lara-Prieto, V.; Parkin, R.; Jackson, M.; Silberschmidt, V.; and Kęsy, Z.
(2010). Vibration characteristics of MR cantilever sandwich beams:
experimental study. Smart Materials and Structures, 19(1), 015005.
10. Rajamohan, V.; Sedaghati, R.; and Rakheja, S. (2010). Vibration analysis of a
multi-layer beam containing magnetorheological fluid. Smart Materials and
Structures, 19(1), 015013.
Vibration Analysis of Fully and Partially Filled Sandwiched . . . . 3177
Journal of Engineering Science and Technology October 2020, Vol. 15(5)
11. Rajamohan, V.; Rakheja, S.; and Sedaghati, R. (2010). Vibration analysis of a
partially treated multi-layer beam with magnetorheological fluid. Journal of
Sound and Vibration, 329(17), 3451-3469.
12. Rajamohan, V.; Sedaghati, R.; and Rakheja, S. (2010). Optimum design of a
multilayer beam partially treated with magnetorheological fluid. Smart
Materials and Structures, 19(6), 065002-15.
13. Li, Y.H.; Fang, B.; Li, F.M.; Zhang, J.Z.; and Li, S. (2011). Dynamic analysis
of sandwich plates with a constraining layer and a magnetorheological fluid
Core. Polymers and Polymer Composites, 19(4-5), 295-302.
14. Rajamohan, V.; Sedaghati, R.; and Rakheja, S. (2011). Optimal vibration
control of beams with total and partial MR-fluid treatments. Smart Materials
and Structures, 20(11), 115016.
15. Romaszko, M.; Pakuła, S.; Sapiński, B.; and Snamina, J. (2011). Vibration
parameters of sandwich beams with two types of MR fluid. Mechanics and
Control, 30(3), 151-156.
16. Rajamohan, V.; Sundararaman, V.; and Govindarajan, B. (2013). Finite
element vibration analysis of a magnetorheological fluid sandwich beam.
Procedia Engineering, 64, 603-612.
17. Romaszko, M.; and Węgrzynowski, M. (2014). FEM Analysis of a
cantilever sandwich beam with MR fluid based on ANSYS. Journal Solid
State Phenomena, 208, 63-69.
18. Hu, G.; Guo, M.; Li, W.; Du, H.; and Alici, G. (2011). Experimental
investigation of the vibration characteristics of a magnetorheological elastomer
sandwich beam under non-homogeneous small magnetic fields. Smart
Materials and Structures, 20(12), 127001.
19. Gurubasavaraju, T.M.; Kumar, H.; and Arun, M. (2017). Evaluation of optimal
parameters of MR fluids for damper application using particle swarm and
response surface optimisation. Journal of the Brazilian Society of Mechanical
Sciences and Engineering, 39(9), 3683-3694.
20. Ramamoorthy, M., Rajamohan, V., and AK, J. (2016). Vibration analysis of a
partially treated laminated composite magnetorheological fluid sandwich
plate. Journal of Vibration and Control, 22(3), 869-895.