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Vibration characteristics of MR cantilever sandwich
beams: Experimental study
Vianney Lara-Prieto
1
, Rob Parkin
1
, Mike Jackson
1
, Vadim Silberschmidt
2
and Zbigniew
Kęsy
3
1
Mechatronics Research Group, Wolfson School of Mechanical and Manufacturing Engineering,
Loughborough University, UK
2
Mechanics of Advanced Materials, Wolfson School of Mechanical and Manufacturing Engineering,
Loughborough University, UK
3
Institute of Applied Mechanics, Technical University of Radom, Poland
Abstract.
The concept of vibration controllability with smart fluids within flexible structures has been in the
centre of interest in the past two decades. Although much research has been done on structures with
embedded electrorheological (ER) fluids, there has been little investigation of magnetorheological (MR)
fluid adaptive structures. In particular, a body of research on experimental work of cantilever MR
beams is still lacking. This experimental study investigates controllability of vibration characteristics of
magnetorheological cantilever sandwich beams. These adaptive structures are produced by embedding
an MR fluid core between two elastic layers. The structural behaviour of the MR beams can be varied
by applying an external magnetic field to activate the MR fluid. The stiffness and damping structural
characteristics are controlled, demonstrating vibration suppression capabilities of MR fluids as
structural elements. MR beams were fabricated with two different materials for comparison purposes.
Diverse excitation methods were considered as well as a range of magnetic field intensities and
configurations. Moreover, the cantilever MR beams were tested in horizontal and vertical
configurations. The effects of partial and full activation of the MR beams were outlined based on the
results obtained. Controllability of the beam’s vibration response was observed in the form of
variations in vibration amplitudes and shifts in magnitudes of the resonant natural frequency.
1. Introduction
One of the main issues in various structures is the undesirable excessive vibration. The
control of structural vibrations can be implemented different ways such as modifying stiffness,
mass, damping and shape, and by providing passive or active counter forces. The work
presented in this paper constitutes the initial study of a magnetorheological (MR) fluid-based
actuator as a structural element for vibration mitigation applications. An underpinning
principle for the proposed MR actuator is tuning the total structure’s stiffness and damping
properties by means of the MR fluid effect. The changes in stiffness and damping are
observed in the form of shifts in magnitudes of the resonant natural frequency and variations
in vibration amplitudes, respectively.
As well known, MR fluids change from a fluid state to a quasi-solid one when activated by a
magnetic field. Such a behaviour is linked to their structure: MR fluids contain magnetic
particles (usually iron) in a carrier liquid; the size of the particles ranges typically from 1 to
10 μm. Under the application of a magnetic field, the particles magnetise and form chains in
the direction of the field lines. This rearrangement causes a non-linear increase in the apparent
yield stress. With increasing field strength, MR fluids exhibit increasing resistance to flow
(apparent viscosity) or increasing stiffness (elastic modulus) depending on deformation. It is
generally assumed that MR fluids behave as non-Newtonian fluids in the absence of field.
Under the effect of magnetic field, two types of their rheological behaviour in the pre-yield
and post-yield regimes are modelled. In the pre-yield regime, MR fluids show linear
viscoelastic behaviour that can be characterised by the complex shear modulus G* with the
storage modulus G’ and loss modulus G” being its real and imaginary parts, respectively. On
the other hand, the post-yield behaviour can be approximated by the Bingham plastic model.
MR fluids have a short response time, of the order of a few milliseconds, and are thus suitable
for real-time applications. [1]
During the last two decades, smart fluids have been investigated as structural elements for
vibration mitigation. However, much research has focused on ER fluid adaptive structures
compared to the work done on structures embedded with MR fluids.
The damping characteristics of ER fluid-filled cantilevered beams in free oscillation were
theoretically and/or experimentally investigated by several researchers [2-6]. Other
investigations on ER sandwich structures include an ER filled insert in a solid beam [7], an
ER beam embedded with a fibre optic sensor [8], and cantilever ER beams rotating in the
horizontal plane [9]. In all these cases, the ER structures were fully activated by
homogeneous fields. Furthermore, research was done on clamped-clamped ER beams with
cavities which were tested with different volumes of filling of ER fluid [10] and by activating
the ER fluid in different regions of the beam [11]. In general, controllability of the ER beam
was shown by changing its stiffness and damping characteristics. However, the degree of
tunability was limited by the properties of the used ER fluid and hardware constraints to
achieve high voltages.
Unlike the extensive literature that can be found for ER fluids structures, research on MR
fluids structures is more limited. This is surprising since MR fluids have higher stiffness
compared to ER fluids and therefore can facilitate higher controllability. While ER fluids
achieve a yield stress between 2-5 kPa, MR fluids achieve 50-100 kPa [12]. Besides, MR
fluids do not need high voltage sources and have a wider range of operating temperatures.
Still, an experimental work with MR fluids can be quite challenging. In ER fluid sandwich
beams, the external layers of the beam (face plates) are the electrodes generating the electric
field; whereas in MR fluid beams, the magnetic poles are not a part of the beam, and the
magnetic field is generated externally. In a steady-state position, the magnetic field lines are
perpendicular to the MR beam. However, once the MR beam is excited, it vibrates within the
static magnetic field, continuously changing the angle between the magnetic field lines and
the beam’s axis. Moreover, since the magnetic poles are outside the beam, it might be rather
demanding to generate a strong and homogeneous magnetic field at the fluid gap. In addition,
the material of the outer faces should be non-magnetic so that the MR effect can be studied.
Moreover, it is important to remember that the MR fluid contains magnetic particles and
therefore is attracted to the magnetic poles. This could cause bending of the beam depending
on the thickness and stiffness of the face plates and magnetic field strength.
Analytical models and simulations of composite structures containing MR fluids enclosed
between layers can be found in literature [13-14]. The vibration characteristics of ER and MR
fluid simply supported sandwich beams were experimentally investigated [15-16]. Results
showed that MR materials have higher stiffness values and are recommended for vibration
suppression of structures, which operate with high frequencies. However, their work
presented some difficulties since their MR beam bended with the presence of magnetic field
and they failed to achieve the expected magnetic field intensities. Similarly, sandwich beams
with MR elastomer cores have been studied to create devices with controllable stiffness [17].
While simply-supported MR sandwich beams have been experimentally investigated before,
there still lacks a body of experimental research on cantilever MR beams. So, the objective of
the present work is to analyze experimentally the controllability of cantilever MR sandwich
beams under different magnetic field configurations, face plates materials and amplitudes of
excitation. The maximum relative change in natural frequency, and therefore in stiffness,
obtained by adjusting the applied magnetic field is here referred as controllability. The
achieved magnetic fields are stronger than those reported in literature [16]. Furthermore, this
study also aims to investigate the partial activation of cantilever MR beams in specific regions.
2. Sandwich beam design and manufacture
A simple sandwich cantilever beam system is selected to study the performance of MR fluids
in adaptive structures. Cantilever beams are frequently used to study different behaviours
because of their relatively simple mechanical model and as a basis for more complex
structures. In this case, the controllable capabilities of MR fluids in adaptive structures were
analysed in real time. The studied cantilever beam is formed by three layers: two elastic face
plates and an MR fluid core. An external magnetic field controls the rheological properties of
the fluid, and hence the dynamic characteristics of the structure. Modal analysis was
conducted to obtain the natural frequencies of vibration of the cantilever beam in the absence
and presence of magnetic field.
It was decided to use different materials for the face plates: aluminium and polyethylene
terephthalate (PET). The middle frame, made of PET in both cases, keeps a uniform MR fluid
layer inside the beam. The specimens are referred to as ‘aluminium beam’ and ‘PET beam’ in
this paper. Table 1 shows the general properties of the employed materials.
Table 1. Material properties
Density (ρ) [kg/m
3
] Young's Modulus (E) [GPa]
Aluminium 2710 70
PET 1370 3
MR fluid 3000 -
The MR fluid selected for this study was MRF-132DG manufactured by LORD Corporation.
This hydrocarbon-based fluid has a viscosity of 0.092 Pa·s at 40°C and 80.98% of solids
content. It contains carbonyl iron particles, which are widely used for MR fluids due to their
high magnetic permeability and low coercivity, making the fluid suitable for reversible
systems. Since in this specific application of the sandwich beam, the MR fluid is always in
the pre-yield region, it is considered as a linear viscoelastic material.
It was decided to employ aluminium in one of the beams due to its light weight, low damping
and relative high stiffness (compared to PET). Since its relative magnetic permeability is
equal to unity, aluminium does not affect the strength and distribution of the magnetic field.
On the other hand, the transparency of the PET face plates and frame, allowed ensuring that
no air bubbles were left within the fluid during the fabrication process. Besides, the MR beam
with all three layers made of PET has some benefits, such as similarity in mechanical
properties of the plastic parts, glue and sealant.
Each of the two MR sandwich beams is composed of three 1 mm thick layers. The aluminium
plates were machined and the PET parts were laser-cut to the dimensions shown in figure 1.
The manufactured layers were glued together with Super Glue and sealed to avoid any
leakage. Next, to be able to fill the cavity of the sandwich beam, a hole of 0.6 mm diameter
was drilled in each side of the beam. One hole was drilled in the free end of the beam and the
other one in the opposite side, very close to the clamping part. Then, the MR fluid was
injected in the beam using a hypodermic syringe. Figure 2 shows a schematic of the glued
MR beam and the location of the drilled holes. The hole close to the clamping part was used
to let the MR fluid in and the hole in the free end was used to let the air go out. This method
of filling the beam worked well without any air bubbles trapped inside. Finally, the two holes
were sealed and allowed to dry.
Figure 1. Design of the aluminium MR beam
Figure 2. Glued MR beam with measurement positions 1-5 and drilled holes for injecting the MR
fluid
3. Experimental setup
It was necessary to build a structure to clamp the MR beam for the tests. Aluminium profiles
were used for a rigid base to support and hold two lines of permanent magnets and the MR
beam between these magnets (figure 3). Permanent magnets were chosen for their versatility
to create different magnetic field configurations (homogeneous and non-homogeneous) along
the MR beam. The entire unit was mounted on a granite base for maximum measurement
stability.
The main elements of the employed test rig are the structure with the cantilever MR beam and
permanent magnets, an impact hammer, an amplifier, a shaker, an oscillator, a laser
vibrometer, a data acquisition card and a dynamic signal analyzer. Permanent magnets
generate a magnetic field, which goes through the MR beam; this field is controlled by
changing the distance between the magnets. Once the MR beam is excited, the laser
vibrometer measures its vibration response. The data acquisition card collects the signals from
the impact hammer (if necessary) and the laser vibrometer and sends them to the dynamic
signal analyzer software. Finally, the signals are processed and Fourier transformed to get the
natural frequencies of the beam. A schematic of the rig is presented in figure 3.