Vibration Isolation Performance of an Adaptive ... - MDPI

Citation: Choi, Y.; Wereley, N.M.

Vibration Isolation Performance of an

Adaptive Magnetorheological

Elastomer-Based Dynamic Vibration

Absorber. Actuators 2022, 11, 157.

https://doi.org/10.3390/act11060157

Received: 15 April 2022

Accepted: 23 May 2022

Published: 12 June 2022

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actuators

Article

Vibration Isolation Performance of an AdaptiveMagnetorheological Elastomer-Based DynamicVibration AbsorberYoung Choi and Norman M. Wereley *

Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA;[email protected]* Correspondence: [email protected]; Tel.: +1-301-405-1927

Abstract: This study evaluates the vibration isolation performance of an adaptive magnetorheologicalelastomer (MRE)-based dynamic vibration absorber (MRE-DVA) for mitigating the high frequencyvibrations (100–250 Hz) of target devices. A simple and effective MRE-DVA design was presentedand its vibration isolation performance was experimentally measured. A cylindrical shaped MREpad was configured to be operated in shear mode and also worked as a semi-actively tunable springfor achieving adaptive DVA. A complex stiffness analysis for the damper force cycle was conductedand it was experimentally observed that the controllable dynamic stiffness range of the MRE-DVAwas greater than two over the tested frequency range. The transmissibility of a target system wasmeasured and used as a performance index to evaluate its vibration isolation performance. It wasalso experimentally demonstrated that a better vibration isolation performance of the target deviceexposed to the high frequency vibrations could be achieved by using the adaptive MRE-DVA.

Keywords: adaptive vibration isolation; magnetorheological elastomer (MRE); dynamic vibrationabsorber (DVA); high frequency vibration

1. Introduction

Since structures and systems are inevitably exposed to undesirable vibrations, vi-bration isolation technology has been an important research topic for several decades toprotect them. One effective way of achieving vibration isolation is to use dynamic vibrationabsorbers (DVAs) because of their simplicity and low cost [1,2]. Typically, DVAs consist of astiffness, a damping, and an oscillating mass, but can effectively reduce the forced vibrationof host structures and systems excited by external harmonic excitations with a specificfrequency [3–5]. However, passive DVAs typically have a narrow working frequency band-width only focused at their resonant frequency. Thus, they lack adaptability to changesin the excitation harmonic frequency [6,7]. As a result, even a slight mistuning of passiveDVAs can result in poor vibration isolation performance. To broaden the working frequencybandwidth, adaptive DVAs that can adjust their resonant frequency via external controlinputs have been recently developed in order to cope with shifting harmonic excitation.Several studies using electromagnets [8,9], piezoelectric materials [10,11], shape memoryallosy [12,13], and magnetorheological elastomer (MRE) [14–33] have been reported toimplement adaptive DVAs.

Among these adaptive DVAs, this study focused on the MRE-based adaptive DVA,or MRE-DVA because it can provide a continuously controllable stiffness and damping.Such an adaptability of the MRE-DVA is attributed with MREs, which are smart particlereinforced composites [34,35]. MREs can significantly change their physical or mechanicalproperties by adjusting an external magnetic field, similar to magnetorheological fluids(MRFs). However, unlike MRFs [36–40], MREs are immune to sedimentation becausethe micron-sized iron particles are permanently dispersed in an elastomeric matrix. In

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Actuators 2022, 11, 157 2 of 18

the absence of a magnetic field, MREs are generally designed to show the behavior ofpassive rubbers with lower stiffness and lower damping. However, when a magneticfield is applied, the stiffness and damping of MREs are substantially increased. Suchan increment is rapid and continuous, and also simply achieved by applying a currentto an electromagnet. Thus, MREs have been applied to various engineering applicationsespecially for vibration isolation such as engine mounts [18,41] and seismic isolators [42–46].In this study, an MRE was applied to implement adaptive DVA that can adjust its resonantfrequency and, hence, has adaptability on vibration isolation performance.

On the other hand, from the perspective of vibration isolation, the vibrations below100 Hz can be considered as low frequency vibrations. Most of the semi-active and activevibration isolation devices and systems have been developed to reduce such low frequencyvibrations. High frequency vibrations for vibration isolation are usually higher than 100 Hz.For the vibration isolation of high frequency vibrations above 100 Hz, passive vibrationisolation methods such as elastomers and DVAs have been the most feasible and reliablesolutions because many semi-active and active actuators do not have a sufficiently fastenough response time for handling such high frequency vibrations. Thus, even thoughmany studies on adaptive MRE-DVAs have been reported, most of them had focused onthe low frequency vibration reduction of a target system as shown in Figure 1. Thus, thisstudy proposed a simple and effective semi-active MRE-DVA design to cope with the highfrequency vibrations (100–250 Hz) of target devices and experimentally investigate its vi-bration isolation performance. To this end, an MRE (circular cylindrical) pad was designedand fabricated to be operated in shear mode. This MRE pad operated as a semi-activelytunable spring for achieving an adaptive DVA. First, the damper force controllability of theadaptive MRE-DVA with respect to applied current inputs was experimentally confirmedusing a material testing system. The vibration testing setup for the frequency responsemeasurement of a target device with the adaptive MRE-DVA was constructed. The trans-missibility in the frequency domain was measured under different magnetic field inputs inorder to evaluate the vibration isolation performance of the MRE-DVA. The feasibility ofthe adaptive MRE-DVA for the vibration isolation of target devices exposed to the highfrequency vibrations was then experimentally validated.

Table: Comparison on Peak first mode frequency and adjustable first mode frequency range of a target system using MRE-based DVAs.

Peak first mode frequency of

a target system, !!,# (Hz) Adjustable first mode frequency

range of a target system, !!,#-!!,$% (Hz)

Reference

11.77 2.14 Bian et al.[1] 12 7 Yang et al.[2] 19 15.8 Sun et al.[3] 21 10 Liao et al.[4] 24 6 Komatsuzaki et al. [5]

31.9 9.2 Xin et al.[6] 40 12.5 Deng et al.[7]

40.09 4.77 Gao et al.[8] 44 2 Sinko et al.[9] 45 17 Xu et al.[10]

46.8 26.8 Komtsuzaki et al.[11] 56.88 13.79 Liu et al.[12] 63.75 22.75 Deng et al.[13]

65 15 Komatsuzaki et al.[14] 65 15 Komatsuzaki et al.[15] 67 30 Sun et al.[16] 74 5 Kumbhar et al.[17]

81.25 26.25 Deng et al.[18] 90 30 Liao et al.[19]

131 21 Jeong[20] 170 35 UMD

0 10 20 30 40Adjustable first mode frequency range (Hz)

0

50

100

150

200

Peak

firs

t mod

e fre

quen

cy (H

z) UMDOther Researchers

High frequency vibration

Figure 1. Peak first mode frequency versus adjustable first mode frequency range of a target systemof most reported studies on adaptive MRE-DVAs (refer to Table 1). Here, “UMD” implies this study.

Actuators 2022, 11, 157 3 of 18

Table 1. Comparison on the peak first mode frequency and adjustable first mode frequency range ofa target system in most reported studies on adaptive MRE-DVAs.

Peak First Mode Frequencyof a Target System (Hz)

Adjustable First Mode FrequencyRange of a Target System (Hz) References

11.77 2.14 [20]12 7 [21]19 15.8 [17]21 10 [14]24 6 [22]

31.9 9.2 [18]40 12.5 [23]

40.09 4.77 [24]44 2 [25]45 17 [26]

46.8 26.8 [16]56.88 13.79 [27]63.75 22.75 [28]

65 15 [29]65 15 [30]67 30 [31]74 5 [13]

81.25 26.25 [32]90 30 [14]

131 21 [33]

2. Magnetorheological Elastomer-Based Dynamic Vibration Absorber (MRE-DVA)2.1. Electromagnetic Analysis

Figure 2 presents a schematic of the adaptive MRE-DVA used in this study. TheMRE-DVA consisted of the electromagnetic coil wound around the bobbin, two MRE pads,and an outer cylinder. The outer cylinder provided the magnetic flux return guides for themagnetic field produced from the electromagnetic coil in the bobbin. The MRE pads, in theshape of a circular tube, were sandwiched between the bobbin and the outer cylinder andattached using adhesive. At stationary status shown in Figure 2a, the MRE pads were notnearly deformed by the magnetic core consisting of the bobbin and electromagnetic coil.However, when a disturbance is applied through the bottom frame or base, the magneticcore is vibrated and the MRE pads are deformed as shown in Figure 2b. On the otherhand, in the absence of magnetic field, the MRE pad behaves as a soft (i.e., low springand low damping) passive rubber isolator. However, when a current input is applied tothe electromagnetic coil, the magnetic field generated from the magnetic core activatesthe MRE pad. The micron-sized iron particles suspended in the activated MRE pad tendto align with the magnetic flux direction. The magnetic interactions between carbonyl Feparticles primarily induce an increase in the stiffness and damping of the MRE pad. Suchincrements of the stiffness and damping can be rapidly and continuously controlled by themagnetic field strength. Because of this feature of the MRE pad, the MRE-DVA can changeits resonant frequency so as to match with the resonant frequency of the target system byadjusting the magnetic field strength.

In order to analytically evaluate the electromagnetic characteristics of the MRE-DVA,a finite element method (FEM) was used in this study. Figure 3 presents one example ofthe analytical electromagnetic characteristics of the MRE-DVA at an applied current inputof 0.7 A. In this design, the outer diameter and height of the DVA were 1.64 inches and1.25 inches, respectively. The top and bottom active lengths were 0.2 inches that wereselected to achieve the desired stiffness of the MRE-DVA and the electromagnetic coilheight was 0.7 inches. Two MRE pads were placed at the top and bottom active lengths andeach MRE pad height was 0.45 inches. The coil turn number of the electromagnetic coil was625 and the coil wire was 28 AWG (American wire gauge). The maximum applied currentinput was 0.7 A that was selected by the maximum allowable current not to burn out the

Actuators 2022, 11, 157 4 of 18

electromagnetic coil wire. The magnetic behavior of the bobbin and the outer cylinder wasemulated by the nonlinear B− H saturation curve of a low-carbon steel. The magneticbehavior of the MRE pad was assumed to be linear and its relative magnetic permeabilitywas chosen to be three, which was the measured magnetic property for an isotropic MREwith the volume fractions (percentage by volume, vol%) of 30–40% carbonyl Fe particlesreported in the reference [47]. As seen in Figure 3a, the magnetic flux generated from theelectromagnetic coil was well circulated through a closed path in the confined area. Themagnetic flux leakage to the air space surrounding this MRE-DVA was insignificant becausethere was a significantly large magnetic permeability difference between the low-carbonsteel (e.g., µsteel ≈ 2000) and the air (e.g., µair = 1). Thus, the magnetic flux density waswell concentrated at the active length areas and its magnetic flux density level was almostuniformed. Three different MRE pad gaps such as 1 mm, 2 mm, and 3 mm were consideredin this study. As seen in Figure 3b, the 1 mm gap case presented the highest magnetic fluxdensity over the active length areas. In addition, the magnetic flux density decrement fromthe 2 mm to the 3 mm gap case was larger than the decrement from the 1 mm to the 2 mmgap case, because the magnetic flux density is inversely proportional to the gap squared.As a result, the lowest magnetic flux density level over the active length areas was obtainedin the 3 mm gap case.

Magnetorheological Elastomer-Based Dynamic Vibration Absorber

Figure 1 presents the schematic of the adaptive MRE-based used in this study. The MRE-

based DVA consisted of the electromagnetic coil wound around the bobbin, MRE pad, and

outer cylinder. The outer cylinder work as magnetic flux return guides for the magnetic field

produced from the electromagnetic coil in the bobbin. The MRE pad was in cylindrical shape

and sandwiched between the bobbin and the outer cylinder by using adhesive. This MRE pad

worked as semi-actively controlled spring component so as to make the DVA tunable by

applied current input. When a disturbance is applied through the bottom frame, the magnetic

core that consists of the bobbin and electromagnetic coil is vibrated. In the absence of

magnetic field, the MRE pad works as soft (i.e., low spring and low damping) passive rubber.

But, when a current input is applied to the electromagnetic coil, the magnetic field generated

from the magnetic core activates the MRE pad. The micron-sized iron particles inside the

activated MRE pad tend to be aligned with the magnetic flux direction. This magnetic

interactions between iron particles mainly causes to increase the stiffness and damping of the

Figure 1: Schematic of the magnetorheological elastomer (MRE)-based dynamic

vibration absorber (DVA).

Outer cylinder

Top active length

Bobbin

Electromagnetic coil

Bottom frame

Magnetorheological elastomer (MRE) pad

Magnetic flux path

Bottom active length

(a)

Figure 1: Schematic of the magnetorheological elastomer (MRE)-based dynamic vibration absorber (DVA).

Outer cylinder

Top active length

Bobbin


Bottom frame


Magnetic flux path


Outer cylinder

Bobbin


Bottom frame


(b)

Figure 2. Schematic of the magnetorheological elastomer (MRE)-based dynamic vibration absorber(MRE-DVA): (a) at stationary status and (b) at dynamic status.

Figure 4 presents the analytical magnetic flux densities on the active lengths of theMRE-DVA with respect to the applied current inputs. For the 2 mm and 3 mm gap cases,the magnetic flux density increased almost linearly in response to the applied current input.However, for the 1 mm gap case, the magnetic flux density started to be saturated forapplied current inputs above 0.6 A. On the other hand, the magnetic flux density levels

Actuators 2022, 11, 157 5 of 18

for the top and bottom active lengths, as well as their field-dependent behaviors, werevery similar.

MRE pad and such an increment can be rapidly and continuously controlled by adjusting the

magnetic field strength. Because of this feature of the MRE pad, the MRE-based DVA can

change its resonant frequency so as to be match with the resonant frequency of the target

system by adjusting the magnetic field strength.

Figure 2 presents the electromagnetic analysis of the MRE-based DVA at an applied

current input of 0.7 A. In this study, the outer diameter and height of the DVA were 1.64”

and 1.25”, respectively. The top and bottom active lengths were 0.2” and the electromagnetic

coil height was 0.7”. Two MRE pads were placed at the top and bottom active lengths and

each MRE pad height was 0.45”. The coil turn number of the electromagnetic coil was 625

and the coil wire was 28 AWG (American wire gauge). The maximum applied current input

was 0.7 A. The magnetic behavior of the bobbin and the outer cylinder was emulated by the

nonlinear B-H saturation curve of a low-carbon steel. The magnetic behavior of the MRE

pad was assumed to linear and its relative magnetic permeability was chosen to be 3. As seen

in Fig. 2, the magnetic density was concentrated at the active length areas and its magnetic

(a) magnetic field contour (2 mm gap case) (b) magnetic density versus bobbin length

Figure 2: Electromagnetic analysis of the MRE-based DVA at an applied current input of

0.7 A.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Length (in)

0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm

Top active length


Electromagnetic coil length

(a)

MRE pad and such an increment can be rapidly and continuously controlled by adjusting the

magnetic field strength. Because of this feature of the MRE pad, the MRE-based DVA can

change its resonant frequency so as to be match with the resonant frequency of the target

system by adjusting the magnetic field strength.

Figure 2 presents the electromagnetic analysis of the MRE-based DVA at an applied

current input of 0.7 A. In this study, the outer diameter and height of the DVA were 1.64”

and 1.25”, respectively. The top and bottom active lengths were 0.2” and the electromagnetic

coil height was 0.7”. Two MRE pads were placed at the top and bottom active lengths and

each MRE pad height was 0.45”. The coil turn number of the electromagnetic coil was 625

and the coil wire was 28 AWG (American wire gauge). The maximum applied current input

was 0.7 A. The magnetic behavior of the bobbin and the outer cylinder was emulated by the

nonlinear B-H saturation curve of a low-carbon steel. The magnetic behavior of the MRE

pad was assumed to linear and its relative magnetic permeability was chosen to be 3. As seen

in Fig. 2, the magnetic density was concentrated at the active length areas and its magnetic

(a) magnetic field contour (2 mm gap case) (b) magnetic density versus bobbin length

Figure 2: Electromagnetic analysis of the MRE-based DVA at an applied current input of

0.7 A.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Length (in)

0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm

Top active length


Electromagnetic coil length

(b)

Figure 3. One example of the analytical electromagnetic characteristics of the MRE-DVA at an appliedcurrent input of 0.7 A: (a) magnetic field contour (2 mm gap case) and (b) magnetic density versusbobbin length.

density level was almost uniformed. Three different MRE pad gaps such as 1 mm, 2 mm, and

3 mm were considered in this study. As seen in Fig.2(b), 1 mm gap case showed a largest

magnetic density level over the active length areas. In addition, the magnetic density

increment from 3 mm gap case to 2 mm gap case was larger than the increment from 2 mm

gap case to 1 mm gap case.

Figure 3 presents the analytical magnetic densities on the active lengths of the MRE-

based DVA with respect to the applied current inputs. As seen in this figure, for 2 mm gap

and 3 mm gap cases, the magnetic density was almost linearly increased by the applied

current input. But, for 1 mm gap case, the magnetic density started to be saturated at applied

current input of above 0.6 A.

(a) for the top active length (b) for the active length

Figure 3: Analytical magnetic densities on the active lengths of the MRE-based DVA.

Figure 4 presents the photograph of the fabricated MRE-based DVA. The bobbin and

the outer cylinder were made of a low-carbon 12L14 steel and the bottom frame was made

of 3D printing plastic material. The isotropic MRE pad sample was fabricated by randomly

dispersing micron-sized iron particles into liquid silicone rubber in the absence of magnetic

field. The rapid curing process in room temperature was used. As iron particles for the MRE

pad samples, Carbonyl iron powders was used and its volume fraction was 35%. The shore

number of the liquid silicone rubber was as soft as 00-20 and its volume fraction was 30%.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Applied current (A)

0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm


0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm

(a)

density level was almost uniformed. Three different MRE pad gaps such as 1 mm, 2 mm, and

3 mm were considered in this study. As seen in Fig.2(b), 1 mm gap case showed a largest

magnetic density level over the active length areas. In addition, the magnetic density

increment from 3 mm gap case to 2 mm gap case was larger than the increment from 2 mm

gap case to 1 mm gap case.

Figure 3 presents the analytical magnetic densities on the active lengths of the MRE-

based DVA with respect to the applied current inputs. As seen in this figure, for 2 mm gap

and 3 mm gap cases, the magnetic density was almost linearly increased by the applied

current input. But, for 1 mm gap case, the magnetic density started to be saturated at applied

current input of above 0.6 A.

(a) for the top active length (b) for the active length

Figure 3: Analytical magnetic densities on the active lengths of the MRE-based DVA.

Figure 4 presents the photograph of the fabricated MRE-based DVA. The bobbin and

the outer cylinder were made of a low-carbon 12L14 steel and the bottom frame was made

of 3D printing plastic material. The isotropic MRE pad sample was fabricated by randomly

dispersing micron-sized iron particles into liquid silicone rubber in the absence of magnetic

field. The rapid curing process in room temperature was used. As iron particles for the MRE

pad samples, Carbonyl iron powders was used and its volume fraction was 35%. The shore

number of the liquid silicone rubber was as soft as 00-20 and its volume fraction was 30%.


0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm


0

0.1

0.2

0.3

0.4

0.5

Mag

netic

den

sity

(T)

1 mm2 mm3 mm

(b)

Figure 4. Analytical magnetic flux density as a function of the applied current for the top and bottomactive lengths of the MRE-DVA: (a) for the top active length (upper MRE pad) and (b) for the bottomactive length (lower MRE pad).

2.2. MRE Pad Material

The isotropic MRE pad sample was fabricated by randomly dispersing micron-sizedcarbonyl Fe particles into liquid silicone rubber (Ecoflex, Smooth-On Inc., Macungie, PA,USA) in the absence of a magnetic field. A rapid curing process at room temperature (curetime: 4 h) was used. The composition of the MRE pads was as follows. The Shore numberof the liquid silicone rubber was in the range of 0–20 and its volume fraction was 30 vol%.To adjust (for mainly softening purpose) the stiffness of the MRE pad, a 1000 cSt viscosity ofsilicone oil was added and its volume fraction was 35%. This mixture of the liquid siliconerubber and the silicone oil were mixed and served as the matrix of the MRE composite. Thesolids loading of the carbonyl Fe powder dispersant was 35 vol%.

Actuators 2022, 11, 157 6 of 18

2.3. Fabrication of the MRE-DVA

Figure 5 presents a photograph of the fabricated MRE-DVA. The bobbin and the outercylinder were made of a low-carbon 12L14 steel and the bottom frame was made of 3Dprinted plastic material (ABS-P430, Stratasys). In this study, MRE pads with three differentthicknesses (i.e., 1 mm, 2 mm, and 3 mm) were fabricated and their effects on the vibrationisolation performance of the MRE-DVA were experimentally investigated. To this end,three different MRE-DVAs with different MRE pad thicknesses were fabricated and tested.

Figure 4: Photograph of the fabricated MRE-based DVA.

MRE pad Bobbin

Outer cylinder

D: 1.44”

Figure 5. Photograph of the fabricated MRE-DVA.

3. Damper Force Characteristics of the MRE-DVA3.1. Complex Stiffness Analysis Method

In order to evaluate the damper force behavior of the MRE-DVA, an Instron materialtesting system (model: DynaMight 8841) shown in Figure 6 was used. The bottom of theDVA was connected to the fixed load cell and the magnetic core (i.e., bobbin) was attachedto the hydraulic actuator. When a sinusoidal excitation displacement was applied to themagnetic core, the damper force of the MRE-DVA was measured by the load cell withrespect to different current inputs. The excitation displacement was measured by a linearvariable differential transformer (LVDT) built into the hydraulic actuator. The commandedamplitude of the excitation displacement was ±0.3 mm and the excitation frequencies were0.1 Hz and 150 Hz. The sampling frequency for the data acquisition in this study was5 kHz.

On the other hand, complex stiffness analysis was selected for evaluating the damperforce characteristics of the MRE-DVA in this study because it has been widely used tocharacterize the mechanical behaviors of the vibration isolation materials and devices. Thiscomplex stiffness analysis is a linearization technique in the frequency domain, whichreplaces the nonlinear hysteresis damper force loop by an equivalent elliptical viscoelasticdamper force loop. In this analysis, the complex stiffness, K∗(ω, i) is expressed as [48]

K∗(ω, i) = K′(ω, i) + jK′′(ω, i) (1)

Here, ω is the frequency, i is the current input, and j is the imaginary unit. K′(ω, i) isthe storage stiffness, which is a measure of the energy stored over a cycle and K′′(ω, i) is theloss stiffness, which is a measure of the energy dissipated over a period. The magnitude ofthe complex stiffness implies the dynamic stiffness, Kd(ω, i) in this study. That is given by

Kd = |K∗(ω, i)| (2)

Using the storage stiffness and the loss stiffness, the loss factor, η is given by

η =K′′(ω, i)K′(ω, i)

(3)

Actuators 2022, 11, 157 7 of 18

This loss factor was used to evaluate the linearized damping capability of the MRE-DVA corresponding to the nonlinear hysteresis damper force loop. On the other hand, theloss factor, η, is similar to the damping ratio, ζ, of a system at resonance such as

η = 2ζ =C√KM

(4)

Here, K, C, and M are the stiffness, viscous damping, and mass of a system. FromEquation (4), the loss factor increment implies the increment of the effective viscous damping.

Figure 5: Experimental setup for the damper force testing of the MRE-based DVA.

Figure 6 presents the measured damper force of the DVA with MRE pad only versus

the displacement. In this case, the MRE thickness was 3 mm. As seen in this figure, the

damper force of the DVA increased as the applied current input increased. At 0.1 Hz

excitation input, the shape of the damper force cycle was similar to the rectangle. This

physically implies that the MRE pad produced the damper force like coulomb type frictional

force. The inclined slope of the damper force cycle physically implies the stiffness. As the

current increased, the inclined slope became steeper. In addition, the enclosed area of the

damper force cycle also increased. The enclosed area physically implies the damping. In

response to the applied current input, the MRE pad-embedded DVA could increase the

damping as well as the stiffness. On the other hand, at 150 Hz excitation input, the shape of

the damper force turned into the elliptical shape. This physically implies that the MRE pad-

embedded DVA at much higher frequency showed adjustable viscoelastic damping behavior.

Figure 6. Experimental setup for the damper force testing of the MRE-DVA.

3.2. Experimental Results for the Damper Force Behavior

Figure 7 presents one example of the measured damper force of the MRE-DVA versusthe displacement. In this case, the MRE-DVA with 3 mm MRE pad thickness was selectedbecause as observed in the electromagnetic analysis in chapter 2, the lowest magnetic fluxdensity in the active lengths was obtained in the 3 mm MRE pad thickness case. Thus, it wasneeded to confirm if the MRE-DVA with 3 mm MRE pad thickness produced sufficientlylarge damper force increment. As seen in Figure 7, the measured excitation displacementat 0.1 Hz was almost the same as the command signal (i.e., ±0.3 mm), but it reduced toalmost ±0.03 mm at 150 Hz because of the performance limitation of the hydraulic actuatorof the Instron testing machine. On the other hand, the damper force of the MRE-DVAincreased as the applied current input increased. At 0.1 Hz excitation input, the shapeof the field-on damper force cycle was similar to the rectangle. This physically impliesthat the MRE-DVA produced the damper force like nonlinear Coulomb friction dampingforce due to the yield stress of the MRE. In addition, the inclined slope of the damperforce cycle physically implies the stiffness. As the current increased, the inclined slopebecame steeper. In addition, the enclosed area of the damper force cycle also increased. Theenclosed area physically implies the viscous damping. In response to the applied currentinput, the MRE-DVA could increase the damping as well as the stiffness at the same time.On the other hand, at as high as 150 Hz excitation input, the shape of the field-on damperforce turned into the elliptical shape. This physically implies that the MRE-DVA at a muchhigher frequency showed adjustable viscoelastic damping behavior. In addition, the initialtwist at both ends of the force-displacement plot at 150 Hz excitation input was observed.This phenomenon may result from the occurrence of other dynamics by not only verticalmotion, but also rocking motion due to the high frequency vibration.

Figure 8 presents the complex stiffness analysis of the MRE-DVA in the frequencydomain. In this case, the excitation frequencies were changed to 0.1, 25, 50, 75, 100, 125,150 Hz. As seen in this figure, the dynamic stiffness, Kd(ω, i), showed linear behavior with

Actuators 2022, 11, 157 8 of 18

the frequency in the frequency range of 0–50 Hz, but started to exponentially increase withthe frequency after 50 Hz. On the other hand, the loss factor, η, at the frequency range of0–50 Hz increased with the applied current input. At the frequency range of 50–100 Hz, theloss factor was hardly changed by the applied current input. However, after 100 Hz, theloss factor decreased with the applied current input. This phenomenon implies that theloss stiffness, K′′(ω, i) increment was larger than the storage stiffness, K′(ω, i) incrementin response to the applied current input until the frequency reached 50 Hz. In other words,the damping increment of the MRE-DVA by the applied current input was larger than itsstifness increment. However, at the frequency range of 50–100 Hz, the storage stiffnessincrement with respect to the applied current inputs was almost similar to the loss stiffnessincrement. Finally, after 100 Hz, the storage stiffness increment by the applied currentinputs was larger than the loss stiffness increment. In other words, the stiffness increment ofthe MRE-DVA by the applied current was larger than the damping increment after 100 Hz.Such trends can be also observed in the studies published by other researchers [49–51]. Thisphenomenon may result from the interaction between the iron particles and the matrix [52].At the lower current input and high frequency vibration, the particle-particle interactioninduced by the magnetic field can increase the interfacial friction between the particles andthe matrix, thereby increasing the loss factor. However, at the higher current input andhigh frequency vibration, the stronger magnetic fields hold the iron particles very tightly inparallel to the magnetic flux direction, thus decreasing the interaction between the particlesand the matrix. This caused an increase in the dynamic stiffness of the MRE-DVA but adecrease in the loss factor at the high current input and high frequency vibration. Figure 8eshowed the dynamic range, DR, which is defined as the ratio of the dynamic stiffness at acurrent input to the dynamic stiffness at no current input, Kd(ω, i = 0A), mathematicallyrepresented by

DR =Kd(ω, i)

Kd(ω, i = 0A)(5)

As seen in Figure 8e, the dynamic range over the tested frequency range was DR ≥ 2at relatively higher current inputs (above 0.5 A). This implies that the dynamic stiffness atthe current input above 0.5 A was at least two times as large as that at no current input.In addition, this dynamic range is related to the resonant frequency adaptability of theMRE-DVA. Using this dynamic range value, DR ≥ 2, the resonant frequency, ωn, i=0.5A ofthe MRE-DVA at the current input of above 0.5 A was estimated to be shifted from ωn, i=0Ato ωn, i=0.5A ≥

√2ωn, i=0A. Here, ωn, i=0A is the resonant frequency of the MRE-DVA at no

current input.

(a) at 0.1 Hz (b) at 150 Hz

Figure 6: Measured damper force of the MRE-based DVA versus the displacement.

Figures 7 presents the complex stiffness of the DVA with MRE pad only in frequency

domain. In this case, the DVA with the unformed gap design was used and excitation

frequencies were changed to 0.1, 25, 50, 75, 100, 125, 150 Hz. As seen in this figure, at the

lower current inputs of below 0.3 A, the storage stiffness and loss stiffness were almost in

linear relationship with the excitation frequency. But, at relatively higher current inputs, they

were exponentially increased as the excitation frequency increased. If using the curve-fitting

method with second order polynomial equations, the storage stiffness and loss stiffness as a

function of excitation frequency could be obtained:

-0.5 -0.25 0 0.25 0.5Displacement (mm)

-15

-10

-5

0

5

10

15

Forc

e (N

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A0.4A0.45A0.5A0.55A0.6A0.65A0.7A

-0.04 -0.02 0 0.02 0.04Displacement (mm)

-8

-4

0

4

8

Forc

e (N

)


0 50 100 150Frequency (Hz)

0

50

100

150

200

250

Dyn

amic

stif

fnes

s (N

/mm

)



0

0.2

0.4

0.6

0.8

1

Loss

fact

or (-

)

(a)

(a) at 0.1 Hz (b) at 150 Hz


Figures 7 presents the complex stiffness of the DVA with MRE pad only in frequency

domain. In this case, the DVA with the unformed gap design was used and excitation

frequencies were changed to 0.1, 25, 50, 75, 100, 125, 150 Hz. As seen in this figure, at the

lower current inputs of below 0.3 A, the storage stiffness and loss stiffness were almost in

linear relationship with the excitation frequency. But, at relatively higher current inputs, they

were exponentially increased as the excitation frequency increased. If using the curve-fitting

method with second order polynomial equations, the storage stiffness and loss stiffness as a

function of excitation frequency could be obtained:

-0.5 -0.25 0 0.25 0.5Displacement (mm)

-15

-10

-5

0

5

10

15

Forc

e (N

)


-0.04 -0.02 0 0.02 0.04Displacement (mm)

-8

-4

0

4

8

Forc

e (N

)



0

50

100

150

200

250

Dyn

amic

stif

fnes

s (N

/mm

)



0

0.2

0.4

0.6

0.8

1

Loss

fact

or (-

)

(b)

Figure 7. Measured damper force of the MRE-DVA versus the displacement (for a 3 mm padthickness): (a) at 0.1 Hz and (b) at 150 Hz.

Actuators 2022, 11, 157 9 of 18

(a) dynamic stiffness (b) loss factor

Figure 7: Dynamic stiffness and loss factor of the MRE-based DVA in frequency domain.

Figure 8: Testing setup for frequency response measurement of the target system with the MRE-embedded DVA.


0

50

100

150

200

Dyn

amic

stif

fnes

s (N

/mm

)0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

0.2

0.4

0.6

0.8

1

Loss

fact

or (-

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A

Rubber mounts

Accelerometer for the ground, Xg

Accelerometer for the target system, Xh

MRE-embedded DVA

DC vibration motor with eccentric mass

(a)

(a) dynamic stiffness (b) loss factor

Figure 7: Dynamic stiffness and loss factor of the MRE-based DVA in frequency domain.

Figure 8: Testing setup for frequency response measurement of the target system with the MRE-embedded DVA.


0

50

100

150

200

Dyn

amic

stif

fnes

s (N

/mm

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

0.2

0.4

0.6

0.8

1

Loss

fact

or (-

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A

Rubber mounts



MRE-embedded DVA


(b)

(a) at 0.1 Hz (b) at 150 Hz


-0.5 -0.25 0 0.25 0.5Displacement (mm)

-15

-10

-5

0

5

10

15

Forc

e (N

)


-0.04 -0.02 0 0.02 0.04Displacement (mm)

-8

-4

0

4

8

Forc

e (N

)



0

1

2

3

4

5

Dyn

amic

rang

e (-)

0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

50

100

150

200

Stor

age

stiff

ness

(N/m

m)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

50

100

150

200

Loss

stif

fnes

s (N

/mm

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A

(c)

(a) at 0.1 Hz (b) at 150 Hz


-0.5 -0.25 0 0.25 0.5Displacement (mm)

-15

-10

-5

0

5

10

15

Forc

e (N

)


-0.04 -0.02 0 0.02 0.04Displacement (mm)

-8

-4

0

4

8

Forc

e (N

)



0

1

2

3

4

5D

ynam

ic ra

nge

(-)0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

50

100

150

200

Stor

age

stiff

ness

(N/m

m)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

50

100

150

200

Loss

stif

fnes

s (N

/mm

)

0A0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A

(d)

(a) at 0.1 Hz (b) at 150 Hz


-0.5 -0.25 0 0.25 0.5Displacement (mm)

-15

-10

-5

0

5

10

15

Forc

e (N

)


-0.04 -0.02 0 0.02 0.04Displacement (mm)

-8

-4

0

4

8

Forc

e (N

)



0

1

2

3

4

5

Dyn

amic

rang

e (-)

0.05A0.1A0.15A0.2A0.25A0.3A0.35A

0.4A0.45A0.5A0.55A0.6A0.65A0.7A


0

50

100

150

200

Stor

age

stiff

ness

(N/m

m)



0

50

100

150

200

Loss

stif

fnes

s (N

/mm

)


(e)

Figure 8. Complex stiffness analysis of the MRE-DVA in the frequency domain (3 mm pad thickness): (a) dynamic stiffness, Kd(ω, i), (b) loss factor, η, (c) storagestiffness, K′(ω, i), (d) loss stiffness, K′′(ω, i) and (e) dynamic range, DR.

Actuators 2022, 11, 157 10 of 18

4. Vibration Isolation Performance of the MRE-DVA4.1. Experimental Setup and Results

Figure 9 presents the testing setup for measuring the frequency response of the targetsystem with the MRE-DVA. The mass of the target system was 1,027 g and the rubbermounts worked as a supporter of the target mass and also the stiffness and dampingcomponents of the target system. To excite the target mass, the eccentric vibrating motorwith an eccentric mass of 4 g was configured at the bottom base. The rpm of the eccentricvibrating motor was swept by using the DC motor controller to excite the target massup to 250 Hz. To measure the vibrations of the target mass and the bottom base, theaccelerometers were placed atop the target mass and also the bottom base. The measuredaccelerations of the target mass and the bottom base were stored at the computer throughthe data acquisition device. In Figure 9, the displacement of the bottom base was denoted byXg, and the displacement of the target mass was denoted by Xh. In this study, the excitationamplitude of Xg was about ±0.75 G at 150 Hz. Here G is the gravitational acceleration.This corresponds to the displacement amplitude of about ±8.3 µm at 150 Hz.

Figure 9 presents effect of the MRE pad thickness on the vibration isolation

performance. In this case, the uniformed gap design was used and three different gaps (i.e.,

1 mm, 2 mm, and 3 mm) were tested. As seen in this figure, the case of 1 mm thickness did

not show the vibration isolation improvement than the case without DVA because the passive

(i.e., zero current input) stiffness of the DVA at 1 mm MRE pad thickness became initially

too larger. But, the cases of 2 mm thickness and 3mm thickness showed nice vibration

isolation performances. It should be noted that these tests in this figure were reconducted

after reseating the testing setup shown in Fig. 3. But, since the excitation level of this testing

setup was a few micron meter, the table supporting this testing setup can be considered as

flexible ground at such a small vibration level. As a result, the vibration isolation

Figure 8: Testing setup for frequency response measurement of the target system with

the MRE-embedded DVA.


MRE-embedded DVA


Rubber mounts


Figure 9. Testing setup for frequency response measurement of the target system with the MRE-DVA.

Figure 10 presents the vibration isolation performance of the MRE-DVA for a 3 mm padthickness. Testing was conducted for current ranging in the electromagnet from 0 to 0.7 A.As seen in this figure, the MRE-DVA could improve the vibration isolation performanceover the baseline system with no DVA. Initially, the target system with the MRE-DVA atzero current input had a resonance frequency of about 170 Hz, and a nominal crossoverfrequency of about 220 Hz. As the current increased, the vibration at the resonant frequencyof around 170 Hz was significantly reduced. However, for current inputs larger than 0.35 A,the resonant frequency significantly shifted to a lower frequency of about 135 Hz. As thecurrent increased further, the vibration at the resonant frequency of about 135 Hz becamelarger and the resonant frequency slightly shifted again to the right side (i.e., toward ahigher frequency) in the frequency domain.

Actuators 2022, 11, 157 11 of 18

performance of the DVA could be slightly varied by the reseating condition of this testing

setup.

(a) 1 mm thickness (b) 2 mm thickness

(c) 3 mm thickness

Figure 9: Effect of the MRE pad thickness on vibration isolation performance of the MRE-

based DVA.

Figure 10 presents the comparison on the minimum envelopes of the vibration isolation

performances for three different MRE pad thicknesses. As clearly observed in this figure, the 2

mm thickness and 3 mm thickness improved the vibration isolation performance of the case

100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)

without DVAwith DVA (0A)with DVA (0.05A)with DVA (0.1A)with DVA (0.15A)with DVA (0.2A)with DVA (0.25A)with DVA (0.3A)with DVA (0.35A)with DVA (0.4A)with DVA (0.45A)with DVA (0.5A)with DVA (0.55A)with DVA (0.6A)

100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)

without DVAwith DVA (0A)with DVA (0.05A)with DVA (0.1A)with DVA (0.15A)with DVA (0.2A)with DVA (0.25A)with DVA (0.3A)with DVA (0.35A)with DVA (0.4A)with DVA (0.45A)with DVA (0.5A)with DVA (0.55A)with DVA (0.6A)with DVA (0.65A)with DVA (0.7A)

100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


Figure 10. Vibration isolation performance of the MRE-DVA (3 mm pad thickness).

4.2. Equivalent Mechanical Model of the MRE-DVA

Figure 11 presents the equivalent mechanical model of the MRE-DVA. As seen in thisfigure, the MRE-DVA consisted of a stiffness Ka, a viscous damping Ca and a Coulombfriction damping force (i.e., yield force) Fy. The damper force of the MRE-DVA, Fa is given.

Fa = Ka(Xa − Xh) + Ca(Xa − Xh) + Fysign(Xa − Xh) (6)

Here, Xa and Xa are the displacement and velocity of the MRE-DVA, respectively. Xhis the velocity of the target system. sign(·) is the signum function. The governing equationof a motion for the equivalent mechanical model of the MRE-DVA is obtained as follows:

MaXa = −Fa (7)

MhXh = Fa − Kh(Xh − Xg)− Ch(Xh − Xg) (8)

Here, Kh and Ch are the stiffness and viscous damping of the target system, respectively.Xg is the velocity of the excitation.

Figure 4: Mechanical model of the MAD-LRA in the absence of magnetic field input.

100 150 200 250Frequency (Hz)

0.5

1

1.5

2

2.5

3

3.5

4|X

h/Xg|(-

)without DVAwith DVA (case1)with DVA (case2)with DVA (case3)with DVA (case4)with DVA (case5)with DVA (case6)with DVA (case7)with DVA (case8)with DVA (case9)with DVA (case10)with DVA (case11)with DVA (case12)with DVA (case13)with DVA (case14)with DVA (case15)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Simulated Parameter Cases

0

2

4

6

8

10

12

14

Nor

mal

ized

Val

ue (-

)

Ka/Ka0Ca/Ca0Fy/Fy0

Dynamic vibration absorber, Ma

Ca Ka

Ch Kh

Target system mass, Mh

Xa

Xh

Xg

Fy MRE-based DVA

Figure 11. Equivalent mechanical model of the MRE-DVA.

Figure 12 presents the simulated vibration isolation performance and identified systemparameters of the MRE-DVA using the equivalent mechanical model. As seen in this figure,the simulated vibration isolation performance could well capture the behavior of themeasured vibration isolation performance shown in Figure 10. The normalized systemparameters identified through this simulated vibration isolation responses are presented

Actuators 2022, 11, 157 12 of 18

in Figure 12b. In this figure, Ka0 and Ca0 are the stiffness and viscous damping at nocurrent input. Fy0 is the Coulomb friction damping force at a current input of 0.05 A. Usingthese values, the identified system parameters shown in Figure 12b were normalized. Theidentified system parameters are listed in Table 2. As expected from the experimentalbehavior of the MRE-DVA shown in Figure 10, the stiffness and Coulomb friction dampingforce of the MRE-DVA increased when the current input increased. Especially, the Coulombfriction damping force increment was significantly larger than the stiffness increment.However, the viscous damping of the MRE-DVA was kept constant. Thus, the stiffnessand Coulomb friction damping force increments caused to significantly shift the resonantfrequency of the MRE-DVA toward lower frequency ranges. The identified stiffness, viscousdamping, and Coulomb friction damping force of the MRE-DVA can be expressed as alinear function of current input as follows:

Ka = 79, 573 i + Ka0 [N/m] (9)

Ca = Ca0 [N · s/m] (10)

Fy = 5.14 i [N] (11)

As seen in Figure 12b, the curve-fitted functions well captured the identified systemparameters of the MRE-DVA. From Equations (9)–(11), it was again confirmed that thestiffness and Coulomb friction damping force of the MRE-DVA were proportional to thecurrent input. However, the viscous damping of the MRE-DVA did not depend on thecurrent input. This behavior of the MRE-DVA used in this study is similar to an idealBingham plastic damper force model in which a viscous damping force is independentwith the current input but a yield force is a function of the current input.

3 mm

100 150 200 250Frequency (Hz)

0.5

1

1.5

2

2.5

3

3.5

4

|Xh/X

g|(-)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Current input (A)

0

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

Val

ue (-

)

Ka/Ka0Ca/Ca0Fy/Fy0curve fittingcurve fittingcurve fitting

(a)

3 mm

100 150 200 250Frequency (Hz)

0.5

1

1.5

2

2.5

3

3.5

4

|Xh/X

g|(-)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Current input (A)

0

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

Val

ue (-

)


(b)

Figure 12. Simulated vibration isolation performance and identified system parameters of the MRE-DVA using the equivalent mechanical model: (a) simulated vibration isolation performance and(b) identified system parameters.

Table 2. The identified system parameters for the MRE-DVA.

Variables Values

Mass of the target system, Mh 1027 gStiffness of the target system, Kh 1005 kN/mViscous damping of the target system, Ch 274.3 N · s/mMoving mass of the MRE-DVA, Ma 122 gStiffness of the MRE-DVA at no current input, Ka0 60.9 kN/mViscous damping of the MRE-DVA at no current input, Ca0 34.5 N · s/mCoulomb friction damping force (i.e., yield force), Fy0 0.26 Nof the MRE-DVA at a current input of 0.05 A

Actuators 2022, 11, 157 13 of 18

4.3. Effect of the MRE Pad Thickness

Figure 13 presents the effect of the MRE pad thickness on the vibration isolationperformances of the MRE-DVAs. In this case, three different MRE pad thicknesses suchas 1 mm (seen in Figure 13a), 2 mm (seen in Figure 13b), and 3 mm (seen in Figure 10)were tested. As seen in these figures, the case of 1 mm thickness did not particularly showthe vibration isolation improvement over the baseline system with no DVA because thepassive (i.e., zero current input) stiffness of the DVA at 1 mm MRE pad thickness becametoo large (please refer to Appendix A) As a result, the moving mass of the DVA workedlike an almost lumped mass attached to the target mass and could not much improve thevibration isolation performance of the baseline system with no DVA. On the other hand,as seen in these figures, the resonant frequency of the MRE-DVA with 1 mm MRE padthickness shifted only to the right side in the frequency domain, as the applied currentinput increased. However, for the cases of 2 mm and 3 mm MRE pad thicknesses, theresonant frequency of the MRE-DVA initially shifted to the right side at current inputslower than 0.4 A. However, at a current input of 0.4 A, the resonant frequency jumpedto the left side (i.e., from about 170 Hz to about 135 Hz). For further current inputs, theresonant frequency shifted again to the right side.


setup.


(c) 3 mm thickness


based DVA.




100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


(a)


setup.


(c) 3 mm thickness


based DVA.




100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)


(b)

Figure 13. Effect of the MRE pad thicknesses on the vibration isolation performances of the MRE-DVAs: (a) 1 mm thickness and (b) 2 mm thickness.

Figure 14 presents the comparison on the minimum envelopes of the vibration isolationperformance for three different MRE pad thicknesses. First, it should be noted that theseminimum envelopes in the frequency domain were extracted from Figures 10 and 13 underthe assumption that optimal current inputs at each frequency were applied to the MRE-DVAs. As clearly observed in this figure, the 2 mm and 3 mm MRE pad thickness improvedthe vibration isolation performance of the baseline system with no DVA over most of itstested frequency range. However, if considering the vibration magnitude reduction aroundthe resonant frequency, the 2 mm thickness case showed a slightly better performancethan the 3 mm thickness case. In contrast, the 1 mm thickness case showed good vibrationisolation performance around the resonant frequency of the target system. However,because of the too stiff system, the vibration isolation performance was deteriorated atthe frequency range below the resonant frequency of the target system. On the otherhand, it should be noted that the MRE-DVA used in this study was aimed at reducingthe steady-state vibration of the target system at a periodic excitation condition, not fortransient and random vibrations. In addition, this MRE-DVA is not an active actuator buta semi-active actuator, in which its stiffness and damping can be adjusted by an appliedcurrent input. Thus, the response time of this MRE-DVA was not an important factor forthis study.

Actuators 2022, 11, 157 14 of 18

without the DVA over most of tested frequency ranges. From this result, 3 mm MRE pad

thickness was chosen in this study for further research.

Figure 10: Comparison on the minimum envelopes of the vibration isolation performances

for three different MRE pad gaps.

Figure 11 presents the power consumption of the DVA with MRE pad and wave spring.

Sample #1 used about 12W of power consumption to achieve great vibration isolation

performance. But, sample #5 needed only about 2 W.

100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)

Without DVAMRE only (uniformed gaps, 1mm)MRE only (uniformed gaps, 2mm)MRE only (uniformed gaps, 3mm)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Current input (A)

0

1

2

3

4

5

6

7

Pow

er c

onsu

mpt

ion

(W)

Figure 14. Comparison of the minimum envelopes of the vibration isolation performances of theMRE-DVAs for three different MRE pad thicknesses.

Figure 15 presents the power consumption of the MRE-DVA. The maximum powerconsumption of the MRE-DVA used in this study was as small as nominally 6.1 W at acurrent input of 0.7 A.

without the DVA over most of tested frequency ranges. From this result, 3 mm MRE pad

thickness was chosen in this study for further research.

Figure 10: Comparison on the minimum envelopes of the vibration isolation performances

for three different MRE pad gaps.

Figure 11 presents the power consumption of the DVA with MRE pad and wave spring.

Sample #1 used about 12W of power consumption to achieve great vibration isolation

performance. But, sample #5 needed only about 2 W.

100 150 200 250Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

3.5

4

|xh /x

g/| (-)

Without DVAMRE only (uniformed gaps, 1mm)MRE only (uniformed gaps, 2mm)MRE only (uniformed gaps, 3mm)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Current input (A)

0

1

2

3

4

5

6

7

Pow

er c

onsu

mpt

ion

(W)

Figure 15. Power consumption of the MRE-DVA.

5. Conclusions

In this study, the vibration isolation performance of the magnetorheological elastomer(MRE)-based dynamic vibration absorber (MRE-DVA) for mitigating the high frequencyvibrations (100–250 Hz) was experimentally investigated. From the results presented inthis study, the following conclusions were obtained.

1. To soften the stiffness of the MRE pads, a silicone oil was added to the mixture of theliquid silicone rubber and carbonyl Fe particles before curing.

2. From the complex stiffness analysis for the damper force cycle, it was confirmed thatthe dynamic range (DR) was DR ≥ 2 at a relatively higher current input of above 0.5A over the tested frequency range.

3. From the vibration isolation testing, it was observed that the resonant frequenciesof the MRE-DVAs could be substantially adjusted using an applied current input.For the 2 mm and 3 mm MRE pad thickness cases, the adjustable resonant frequencyrange by the current input was about 135–170 Hz. However, for the 1 mm MRE padthickness case, the resonant frequency change was small because it was initially toostiff for no current input (0 A).

Actuators 2022, 11, 157 15 of 18

4. From the minimum envelopes shown the in vibration frequency response plots for thetested frequency range from 100 Hz to 250 Hz, it was demonstrated that the systemwith the MRE-DVAs achieved much better vibration isolation performance than thebaseline system with no DVA.

5. It was confirmed that the design of the MRE-DVAs used in this study was simple buteffective to reduce the vibration of the target system for the high frequency vibrations(i.e., 100–250 Hz).

As a future work, the reliability and endurability of the MRE-DVA need to be investi-gated. In addition, an appropriate control algorithm for this adaptive MRE-DVA will bedeveloped in future.

Author Contributions: All authors equally contributed. All authors have read and agreed to thepublished version of the manuscript.

Funding: This research received no external funding.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable.

Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

Figure A1 presents the simulated vibration isolation performances of the MRE-DVAsusing the equivalent mechanical model for the 1 mm and 2 mm MRE pad thickness cases.In this figure, the curves of the normalized system parameters were exactly the same as thecurve of Figure 12b, but the values of the identified system parameters were different asshown in Table A1. If comparing Figure A1 to Figure 13, the equivalent mechanical modelcould still capture the behaviors of the measured vibration isolation performance of theMRE-DVAs with the 1 mm and 2 mm MRE pad thicknesses well.

1mm

100 150 200 250Frequency (Hz)

0.5

1

1.5

2

2.5

3

3.5

4

|Xh/X

g|(-)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Current input (A)

0

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

Val

ue (-

)


(a)

2 mm

100 150 200 250Frequency (Hz)

0.5

1

1.5

2

2.5

3

3.5

4

|Xh/X

g|(-)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Current input (A)

0

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

Val

ue (-

)


(b)

Figure A1. Simulated vibration isolation performances of the MRE-DVAs using the equivalentmechanical model: (a) 1 mm thickness and (b) 2 mm thickness.

Actuators 2022, 11, 157 16 of 18

Table A1. The identified system parameters for the MRE-DVAs with the 1 mm, 2 mm and 3 mm MREpad thicknesses.

Variables Values

For the 1 mm MRE pad thickness caseStiffness of the MRE-DVA at no current input, Ka0 107.8 kN/mViscous damping of the MRE-DVA at no current input, Ca0 45.9 N · s/mCoulomb friction damping force (i.e., yield force), Fy0 0.51 Nof the MRE-DVA at a current input of 0.05 A



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