Topical Review

Review of magnetostrictive materials forstructural vibration control

Zhangxian Deng and Marcelo J Dapino

NSF IUCRC Smart Vehicle Concepts Center, Department of Mechanical and Aerospace Engineering, TheOhio State University, Columbus, OH 43210, United State of America

E-mail: dapino.1@osu.edu

Received 4 April 2018, revised 11 June 2018Accepted for publication 10 September 2018Published 23 October 2018

AbstractExcessive vibrations in civil and mechanical systems can cause structural damage or detrimentalnoise. Structural vibrations can be mitigated either by attenuating energy from vibration sourcesor isolating external disturbance from target structures. Magnetostrictive materials couplingmechanical and magnetic energies have provided innovative solutions to vibration controlchallenges. Depending on the system’s tunability and power consumption, the existing vibrationcontrol strategies are categorized into active, passive, and semi-active types. This article firstsummarizes the unique properties of magnetostrictive materials that lead to compact and reliablevibration control strategies. Several magnetostrictive vibration control mechanisms together withtheir performance are then studied using lumped parameter models. Finally, this article reviewsthe current state of vibration control applications utilizing magnetostrictive materials, especiallyTerfenol-D and Galfenol.

Keywords: magnetostrictive materials, vibration control, damping, stiffness tuning

(Some figures may appear in colour only in the online journal)

1. Introduction

Low-frequency seismic impacts can cause devastating struc-ture damage in buildings. Structural vibrations in mechatronicsystems, on the other hand, exhibit a broader frequency rangeand may cause excessive detrimental noise. For certainapplications, such as surgical equipment and atomic forcemicroscopy, structural vibrations can lead to undesirablefluctuation and degrade motion control accuracy. The afore-mentioned negative effects can be mitigated by variousvibration control mechanisms.

The vibration control systems can be categorized asvibration compensation, frequency tuning, structural damp-ing, vibration isolation, and vibration absorption [1]. Avibration compensation system (e.g., vibration compensationlens) directly generates a force or varying stiffness thatcounteracts the external disturbance. Frequency tuningmethod controls the system natural frequencies and avoidsresonance due to external excitations. The frequency can be

tuned either by changing the mass m or stiffness k. The fre-quency tuning usually targets a specific system resonance;introducing structural damping c to the system (e.g., hydraulicdashpots) can convert vibration energy to heat and thusreduce the vibration amplitude over a broad frequency range.Vibration isolation either separates vibration sources fromprimary structures (e.g., car engine mounts) or protects theprimary structure from base excitation (e.g., car suspension).Vibration absorbers, on the other hand, suppress structuralvibration by attaching a damped vibration neutralizer ordamped dynamic vibration absorber, which is simply anadditional spring-damper-mass system.

Smart materials coupling mechanical energy with otherenergy forms have been investigated in vibration control.Depending on system tunability and power consumption, theexisting smart vibration control systems can be categorizedinto three different types: active, passive, and semi-active.Active isolators or absorbers, as shown in figure 1, generate aforce F(t) that counteracts the disturbances [2, 3]. Unlike

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conventional passive servo-hydraulic actuators or electricalmotors, smart materials enable vibration control strategieswith small packaging size, broad frequency bandwidth, andhigh reliability. Shape memory alloys, which typically exhibitlarge deformation (up to 6%) but low operation frequencies,have been implemented to reduce seismic vibrations inbuildings [4]. Piezoelectric materials, which provide largeforces and moderate displacements at extremely high fre-quencies, have been utilized to design lightweight anddynamic actuators for mechatronic systems [5, 6] or civilapplications [7]. But piezoelectric materials suffer fromdepolarization and brittleness thus exhibiting limitedreliability.

Smart active vibration control requires external powersources and sometimes complex controllers which are notalways available in practice. Thus, smart passive vibrationcontrol shown in figure 1(b), which is more convenient hasbeen studied. Conventional passive vibration control can beachieved by adding damping materials, such as fluids andviscoelastic materials, to the primary structure. These passivematerials provide a large damping coefficient c while exhi-biting low stiffness and introducing redundant mass. Smartmaterials have been implemented as passive damping mate-rials either through energy coupling or superelasticity.Piezoelectric materials [8] and piezoelectric polymers [9]attenuate vibration energy via intrinsic hysteresis and electro-mechanical energy coupling in shunt circuits. However, thepiezoelectric materials are not suitable for complex loadingsdue to their brittleness. Shape memory alloys, which exhibitsuperelasticity during phase transition, are able to providelarge damping but extremely low stiffness [10].

Smart active vibration control requires large controlefforts and may cause control-induced instability. Smartpassive vibration control, on the other hand, is not adaptive tothe variation of system parameters and uncertainties invibration sources. Semi-active vibration control lifts theselimitations by creating tunable springs or dampers, as shownin figure 1(c). Since the semi-active mechanisms do notdirectly act against the vibration sources, little or no externalpower is required [11]. Smart materials integrated with pas-sive mechanisms have been implemented in semi-activevibration control. Giurgiutiu et al [12] connected shapememory alloys with morphing mechanisms to mitigatestructural vibrations in helicopter blades. However, shapememory alloys exhibit a low operating frequency and need a

mechanism to provide restoring forces. Recent studies havepresented other possible semi-active vibration control meth-ods by directly tuning the material properties of smart mate-rials. Magnetorhelogical (MR) materials, which are ironparticles embedded elastomers or fluids, are able to providemagnetically-tunable stiffness and damping coefficient[13, 14]. Asnaniet al [15] showed that the stiffness anddamping coefficient of piezoelectric materials can be con-tinuously tuned by adjusting electrical shunts.

Table 1 summarizes the merits and drawbacks of selectedsmart materials in three different types of vibration controlstrategies. Magnetostrictive materials coupling mechanicaland magnetic energies are able to tackle the drawbacksassociated with the existing smart solutions. This articlereviews the state of the art of magnetostrictive materials,especially Terfenol-D and Galfenol, in structural vibrationcontrol. The unique material properties of magnetostrictivematerials and the resulting vibration control strategies arediscussed in section 2. The vibration control systems areinvestigated following lumped parameter modeling insection 3. Configurations of magnetostrictive devices forvibration control are summarized and compared in section 4.

2. Properties of magnetostrictive materials

Magnetostrictive materials can be approximated by a collec-tion of magnetic domains whose orientations depend on theinterplay of magnetic and mechanical energies. The magneto-mechanical coupling induces several unique behaviors thatare relevant to structural vibration control: the Joule effect, theVillari effect, material hysteresis, and the Delta-E effect.

2.1. Joule magnetostriction

As the applied magnetic field increases, magnetic domainstend to rotate toward the field direction, resulting in adimensional change. The field-induced strain, or magnetos-triction, includes the longitudinal component λP and thetransverse component l̂ . To maintain volume consistency,

0.5l l= -^ . All magnetic materials demonstrate magneto-mechanical coupling, but a few materials containing rare earthelements show significant magnetostriction. Terbium, iron,and dysprosium alloys, or Terfenol-D, are able to generate amaximum magnetostriction of 1600×10−6 while requiring ahigh excitation magnetic field (≈160 kA/m) [16]. Terfenol-Dis brittle and can only withstand compressive axial loads.Iron-gallium alloys, known as Galfenol, exhibit moderatemagnetostriction and mechanical robustness [17]. The mag-netostriction of Galfenol varies with respect to gallium con-tent, peaking around 18.6% gallium [18]. A maximummagnetostriction of 350×10−6 and 400×10−6 can beachieved from polycrystalline and single crystal Galfenol,respectively. Galfenol has high tensile strength of about500MPa and thus is able to support shear and tensile loads.Similar to steel, Galfenol can be machined, welded, andformed without the loss of magnetostriction. Figure 2 showsthe field-induced magnetostriction of a polycrystalline

Figure 1. Lumped parameter model of (a) active, (b) passive, and (c)semi-active vibration control strategies. F(t) is the actuation force, k(t) is a tunable spring, and c(t) is a tunable damper.

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Smart Mater. Struct. 27 (2018) 113001 Topical Review

Fe Ga81.4 18.6 Galfenol rod under various mechanical stres-ses [19].

Compared with traditional electric motors and hydraulicactuators, magnetostrictive materials are able to provide ahigh energy density of 1.4–2.5 10 J m4 3´ while maintainingsystem stiffness [20]. Magnetostrictive materials react toexternal magnetic field excitations instantaneously and thusare suitable for dynamic operation. The frequency bandwidthof magnetostrictive actuators is mainly constrained by eddycurrents. By creating laminated or particulate magnetos-trictive composites, recent magnetostrictive actuators haveshown an operating frequency above 20kHz [21]. Withoutundergoing permanent depolarization that exists in piezo-electric materials, magnetostrictive materials can also with-stand harsh temperature. For instance, the maximumoperating temperatures for Terfenol-D and Galfenol are350°C and 700°C, respectively [22, 23]. Due to the mag-netically-induced operation, non-contact and wireless opera-tions are possible for rotating machinery and inaccessiblestructures. Due to the aforementioned merits, magnetos-trictive materials have been studied to configure compact andefficient actuators for active vibration control. Magnetos-trictive actuators exhibit a frequency response comparable topiezoelectric, electrostatic, or electromagnetic actuators [24].Unlike their electrically-activated counterparts, magnetos-trictive materials operate at dc frequency: a static magnetic

field induces a static and stable response in these materials.Although, in principle, magnetostrictive materials can operatein the tens of thousands of Hertz, in practical actuator systemstheir response is limited by eddy currents (skin depth effect),electrical inductance, and mechanical resonance [21]. Com-mercial Terfenol-D-based actuators have been implementedin ultrasonic systems that operate at 20kHz [25, 26].

2.2. Villari effect

As the mechanical load on the magnetostrictive materialincreases, all magnetic domains tend to be aligned in the basalplane perpendicular to the load. The domain rotation inducesmagnetization change, or known as the Villari effect. Figure 3shows the flux density versus stress curves under variousmagnetic fields [19].

The stress-induced magnetization variation can even-tually generate electrical energy on coils wound around themagnetostrictive materials following Faraday’s law. Notabledamping coefficients are available by dissipating the electricalenergy on a shunt circuit. The Villari effect can also inducesignificant eddy current loss in electrically-conductive mag-netostrictive materials [27, 28]. The stress-induced eddycurrents provide a compact damping mechanism that convertsmechanical energy to Joule heat without introducing bulkyshunt circuits.

Table 1. Comparison of smart materials in vibration control. (*Only applies to certain magnetostrictive materials, such as Galfenol andAlfenol).

Active Passive Semi-active

Shape memory alloy Thermally-activated Large strainLow frequency

Superelasticity Large dampingLow stiffness

With tuning mechanism Large packa-ging size

MR elastomer N/A Magnetically-tunable Wireless and non-contact Low stiffness

Piezoelectric Voltage activated Hysteresis and energy coupling Electrically-tunableHigh frequency and stiffness Moderate strain Brittleness and low reliability

Magnetostrictive Magnetically-activated Hysteresis, eddy currents, andenergy coupling

Magnetically-, mechanically-, or elec-trically-tunable

High stiffness and moderate strain Machinable and non-contact Mechanically-robust and reliable

Figure 2. Magnetostriction versus magnetic field curves of a ⟨100⟩-oriented and polycrystalline Fe Ga81.4 18.6 Galfenol rod [19]. Theapplied bias stresses are −1.64, −10.23, −20.44, −30.65, −40.88,−51.10, and −61.31MPa. The arrow indicates the increasing biasmechanical stress.

Figure 3. Flux density versus stress curves of 100á ñ-oriented andpolycrystalline Fe Ga81.4 18.6 Galfenol rod [19]. The bias magneticfields are 0.73, 1.42, 2.41, 3.88, 5.50, 7.17, 8.84, 10.51, 12.19, and13.76kA/m. The arrow indicates the increasing bias magnetic field.

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Smart Mater. Struct. 27 (2018) 113001 Topical Review

2.3. Hysteresis

Figure 4 presents typical strain versus stress curves of mag-netostrictive materials under various magnetic fields. Due tothe material impurities, material anisotropy, and crystalimperfections, magnetostrictive materials exhibit significanthysteresis loss during domain rotation. The hysteresis can bequantitatively described by the area enclosed by the strainversus stress loops. The hysteresis loss has been experimen-tally characterized for Terfenol-D and Galfenol under differ-ent types of magnetic excitations and stress amplitudes [29].Constitutive models describing the nonlinear hysteresis havebeen developed and validated in previous studies [30]. Hys-teresis presents chanllenges for actuator development; it alsoprovides an intrinsic damping effect that can be beneficial forvibration attenuation.

2.4. Delta-E effect

The strain versus stress curves of Galfenol, shown in figure 4,are nonlinear due to additional magnetostriction. TheYoung’s modulus E of a magnetostrictive material, which isthe inverse of the slope of the strain versus stress curve, isestimated by piecewise linearization as

E H TT

S H T,

,. 1

e l=

+( )

( )( )

Here, H and T are the uniaxial magnetic field and stress,respectively; the total strain is the superposition of the elasticstrain Se and magnetostriction λ. Figure 5 shows the nonlinearYoung’s modulus of a polycrystalline Fe Ga81.4 18.6 Galfenolsample under various magnetic fields and mechanical stresses.The value of E is stress- and field-dependent. The Delta-Eeffect, or the change in quasi-static Young’s modulus withrespect to external excitations, has been documented forTerfenol-D [16, 31–34] and Galfenol [19, 35–39]. Thevarying Young’s modulus can be implemented in active orsemi-active vibration isolation.

3. Theory

3.1. Vibration compensation

Active vibration compensation mechanisms directly generatea force or continuously adjust system stiffness to act againstexternal disturbances or adjust system stiffness, as illustratedin figure 6. For vibration compensation, the actuation forceFm should be negative when the mass is above the equili-brium position. Otherwise, Fm>0 when the mass is belowthe equilibrium position. For stiffness tuning, the springshould have a large stiffness kmax when the mass moves awayfrom the equilibrium position, while the spring takes a smallstiffness when the mass moves towards the static equilibriumposition (S.E.P.).

3.2. Frequency tuning

As the frequency of external excitation coincides with one ofthe system’s natural frequencies, resonance occurs. Inmechanical systems, resonance is associated with extremelylarge strain energy and thus can lead to system failure. Toavoid resonance, figure 7 shows a frequency tuning mech-anism whose natural frequencies can be tuned by changing m

Figure 4. Strain versus stress curves of a 100á ñ-oriented andpolycrystalline Fe Ga81.4 18.6 Galfenol rod. The bias magnetic fieldsare 2.41, 3.88, and 5.50kA/m [19]. The arrow indicates theincreasing bias magnetic field.

Figure 5. Young’s modulus variation of a 100á ñ-oriented andpolycrystalline Fe Ga81.4 18.6 Galfenol rod with respect to (a) amagnetic field of 2.41, 3.88, and 5.50kA/m and (b) a mechanicalstress of −5.73, −27.2, and −41.6MPa [19]. The arrows indicatethe increasing magnetic field and stress.

Figure 6. Lumped parameter model for active vibration compensa-tion [40]. The blue arrow indicates the motion of the moving mass;the solid purple arrow indicate the actuation force Fm.

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Smart Mater. Struct. 27 (2018) 113001 Topical Review

or c. In most cases, the mass cannot be easily changed. Forexample, the mass of a flywheel is determined by the energystorage requirement [1]. Hence, frequency tuning in practiceis often equivalent to stiffness tuning.

3.3. Structural damping

Accurate positioning systems (e.g., antennas, microscopes)should be able to resist external impact excitations, such as agust of wind. The lumped parameter model is presented infigure 8, in which the transfer function is written as

T sX

Fs

ms cs k

1, 2a

d

s2

= =+ +

( ) ( ) ( )

where Xd is the corresponding displacement due to an impactexcitation Fs(t). The transfer function can be normalized as

T sm s s

1 1

2, 3a

n n2 2w z w

=+ +

( ) ( )

where the fundamental radial frequency is k mnw = andc mk0.5z = is the damping ratio.

Figure 9 shows the impact response of under-damped,critically-damped, and over-damped systems. The vibrationamplitude reduces with respect to increasing damping ratio. In

practice, the large damping ratio is typically provided byviscoelastic or superelastic materials. However, these passivedamping materials exhibit relative low stiffness and thusdramatically reduce the system resonant frequency. Rigiddampers with large loss factors that can be directly installed inthe load path are desirable for future applications.

3.4. Vibration isolation

Figure 10 presents two different configurations of vibrationisolators. The first configuration, shown in figure 10(a),reduces the force transmitted from the vibration source Fs(t)to the primary structure. The other configuration, shown infigure 10(b), protects the primary structure from base vibra-tions Xs(t). The performance of the vibration isolators isdescribed by the force or displacement transmissibility TI(s),where

T sF

Fs

X

Xs

cs k

ms cs k. 4I

b

s

b

s2

= = =+

+ +( ) ( ) ( ) ( )

Here, m is the system mass; Fb and Xd are the force anddisplacement transmitted to the primary structure,

Figure 7. Lumped parameter model for frequency tuning.

Figure 8. Lumped parameter model for structural damping.

Figure 9. Time-domain responses under a unit impact excitation(Fs(t)=δ(t)) for under-damped (ζ=0.1), critically-damped(ζ=1), and over-damped (ζ=2) systems. (m=1 kg and k=4π2

N·m).

Figure 10. Lumped parameter model for (a) source vibrationisolation and (b) base vibration isolation.

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respectively. The normalized expression for T sI ( ) is

T ss

s s

2

2. 5I

n n

n n

2

2 2

w z ww z w

=+

+ +( ) ( )

Figure 11 shows the amplitude of the transmissibilitytransfer function TI w∣ ( )∣ with respect to varying excitationfrequencies. When the excitation frequency is near DC,T 1I w =∣ ( )∣ . Thus, the stiffness k should be as soft as possible.However, a soft spring may not able to provide enoughsupport. The effect of damping ratio is also presented infigure 11. Under-damped (ζ=0.1), critically-damped(ζ=1), and over-damped (ζ=2) conditions are investi-gated. A large damping reduces TI w∣ ( )∣ around the systemresonance but degrades the performance at high frequencies.Hence, the values of k and c need to be selected accordinglybased on the desired system response [11].

3.5. Vibration absorption

The damped vibration absorber presented in figure 12 is ableto suppress the resonance of the primary structure. The dis-placement transmissibility between the base excitation Xb andthe vibration of the primary structure Xp is

T sX

Xs

c s k

DEN s, 6md

p

b

p p= =+

( ) ( )( )

( )

where

DEN s mm s cm cm c m s

cc km km k m s k c kc s kk .

7

p p p

p p p p p p

4 3

2

= + + +

+ + + + + + +

( ) ( )

( ) ( )( )

Here, the subscription p denotes the primary structure. Opti-mal stiffness kopt and damping coefficient copt have beenselected empirically for harmonic excitations following [41],where

kmm

m m

c mk

m m

,

3

2. 8

optp n

p

optopt

p

2 2

2

w=

+

=+

( )

( )( )

Figure 13 presents the displacement transmissibility of a2nd order system. The tuned vibration absorber designedfollowing equation (8) is able to reduce the transmissibilityamplitude around the system’s resonance. When the resonantfrequency of the primary structure reduces by 5%, the per-formance of the vibration absorber deteriorates dramatically.The parameters of the vibration absorber are preferred to beadjustable to follow the system variations.

4. Vibration control

Due to the unique material properties discussed in section 2,magnetostrictive materials have been widely investigated in

Figure 11. Amplitude of the transmissibility transfer function TI w∣ ( )∣with respect to normalized excitation frequency f f0, wheref0=ωn/2π. (m k1 kg and 4 N2p= = /m).

Figure 12. Lumped parameter model for a damped vibrationabsorber.

Figure 13. Amplitude of the displacement transmissibility Tmd w∣ ( )∣with respect to normalized excitation frequency for a 2nd ordersystem, where m=1 kg, mp=100 kg, kp=400π2 N/m, andcp=0.05. (black: no vibration absorber; blue: undamped vibrationabsrober; green: tuned and damped vibration absorber; red: de-tunedand damped vibration absorber when the resonance of the primarystructure reduces by 5%).

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structural vibration control. This section reviews the currentstate of magnetostrictive materials in active, passive, andsemi-active vibration control.

4.1. Active vibration control

Taking advantage of the Joule magnetostriction, previousstudies have developed magnetostrictive actuators that areable to generate dynamic forces or motions to counteractexternal vibrational disturbance. Figure 2 shows that thedeformation of magnetostrictive materials is maximized whenthey operate around the center of the burst region or when theinput mechanical energy balances with the magnetic energy.To maximize the stroke, figure 14 shows a typical config-uration of a magnetostrictive actuator. The bias stress isusually applied by a pre-stress spring or Belleville washer.The bias magnetic field is applied by a DC current through thesolenoid [42]. In practice, the bias magnetic field can also begenerated by a cylindrical permanent magnet to avoid headbuild up as is the case with DC currents.

The effectiveness of active control strategies depends onhow the magnetostrictive actuators are integrated with theprimary structure. Various actuator placement strategies havebeen studied for helicopter struts to attenuate longitudinal andflexural vibrations transmitted from main gearbox to thefuselage. As shown in figure 15, Mahapatraet al [43] pro-posed four different actuator configurations. The performanceof each configuration was validated numerically by theoreti-cally designing a feedback control algorithm together with anactive spectral element model. The serial configuration, infigure 15(a), can achieve considerable reduction in long-itudinal vibrations throughout the frequency range of interest[44]. By orienting the magnetostrictive actuator perpendicularto the strut, as shown in figure 15(b), the flexural vibrationwaves can be significantly attenuated. Figure 15(c) proposes ahybrid configuration targeting the coupled longitudinal-flex-ural vibrations. Magnetostrictive actuators in figures 15(a)and (c) have to be placed in the load path and thus may not befeasible in practice. Thus, an alternate, shown in figure 15(d),implements a pair of magnetostrictive actuators in parallel to

attenuate longitudinal vibrations. The parallel configurationhas been validated experimentally.

Suttonet al [45] placed three actuators in parallel to ahelicopter gearbox support strut, as shown in figure 16. Bydriving the three actuators in phase, the active strut attenuatedby 30–40dB the kinetic energy measured on the fuselageconnection side over a frequency range of 250–1250Hz.Attenuation in flexural wave transmission is possible bydriving the three actuators out-of-phase.

Similar to the vertical orientation proposed infigure 15(c), several experimental studies have been con-ducted to suppress flexural vibrations. As shown in figure 17,Prattet al [46] installed a Terfenol-D actuator at the base of acantilever beam. A feedback control loop was designed to

Figure 14. Schematic of a magnetostrictive actuator.

Figure 15. Placements of magnetostrictive actuators in helicopterstruts: (a) serial orientation, (b) vertical orientation, (c) hybridorientation, and (d) parallel orientation [43].

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attenuate the tip acceleration induced by the external dis-turbance applied in the middle of the beam. The actuator wascontrolled to suppress the first and second modes. Utilizing asimilar experimental setup, Flatauet al [47] actively drove aTerfenol-D actuator such that its deformation amplitude wasproportional to the tip acceleration and its phase was 180°out-of-phase. The simple controller attained a −23dBreduction in tip acceleration at frequencies up to 4kHz.Theoretical analysis presented a frequency limit of more than10kHz. Moonet al [48] implemented a pair of Terfenol-Dactuators to support both ends of a simple aluminum beam.Together with a linear quadratic feedback controller, theactive vibration control was able to reduce the flexural

vibrations by 12–20dB up to a frequency of 500Hz sup-pressing the first four modes of vibrations.

Besides helicopter gearbox struts, magnetostrictiveactuators have been applied to attenuate vibrations induced bygear meshing. Rebbechiet al [49] configured four Terfenol-Dactuators distributed circumferentially around a rotating shaft,as shown in figure 18. Two actuators were normal to thecontact point of the meshing gears. The other pair wasinstalled perpendicular to the first pair. Each pair of actuatorswas driven 180° out-of-phase and operated in push-pullmode. Both the acceleration on the gearbox housing and thesound pressure outside of the gearbox were measured. Bysimultaneously minimizing the first three modes of the gearpair via an adaptive feedforward controller, the accelerationamplitude was reduced by 20–28dB, 5–10dB, and 0–2dBfor 1×, 2×, and 3×of the gear mesh frequency, respectively.Guanet al [50] later proposed several actuator configurationsto attenuate gear pair vibrations using less number ofactuators.

Figure 16. Active helicopter strut with three parallel orientedmagnetostrictive actuators [45].

Figure 17. Magnetostrictive actuator configuration to attenuateflexural vibrations in a cantilever beam [47].

Figure 18. Gearbox with two pairs of magnetostrictive actuatorssupporting the bearing [49].

Figure 19. Hybrid magnetostrictive actuators incorporated with (a) alever mechanism [51] and (b) a hydraulic cylinder [53].

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Magnetostrictive actuators exhibit a large energy densitybut a relatively small stroke. For vibration control systemsthat requires large deformation, hybrid actuators have beendeveloped. Bartlettet al [51] combined a lever mechanismwith a Terfenol-D actuator, as shown in figure 19(a). TwoTerfenol-D rods (Φ30 mm by 254 mm long) were connectedin series. With a lever gain of 6, the hybrid actuator generateda maximum displacement of 4mm and an associated zero-displacement force of 0.5kN. This actuator is only suitablefor civil engineering structures (e.g., bridge cables) due to itsnarrow frequency bandwidth. Vibrations in automobile sys-tems span a much wider frequency range. For instance, theengine vibrations ranges from 20Hz to 400Hz, depending onthe number of cylinders, the engine speed, and the strokenumber [52]. Commercial electrodynamic engine mountactuators can provide a stroke in the millimeter range with anarrow frequency range up to 110 Hz [53]. Chakrabarti and

Dapino [53–55] incorporated a hydraulic cylinder with aTerfenol-D actuator, as shown in figure 19(b). The hybridactuator is able to improve the maximum frequency to 280Hzwhile meeting the displacement requirement and lowering thepower consumption. Nakamuraet al [56] developed anotherhybrid actuator combining an air actuator and a Terfenol-D-based actuator, as shown in figure 20. The air actuator has arelatively large displacement in the low frequency range,while the magnetostrictive actuator is able to provide sig-nificant displacement at high frequencies.

By arranging several actuators in particular patterns,multiple degrees of freedom (DOFs) vibration control plat-forms have been developed. Bryantet al [57] installed threeTerfenol-D actuators in parallel, as shown in figure 21(a), andthe performance of the 3-DOF vibration isolation platformwas evaluated by measuring the vibration power transmittedfrom the base to the stage. For a 70Hz base excitation, a PIDcontroller and a neural network controller attenuated thevibration power by 6.9dB and 15dB, respectively. Geng andHaynes [58] designed a 6-DOF Stewart platform to reducevibrations in space structures, as shown in figure 21(b). At theresonant frequency of 62.4Hz, the adaptive filter controllerachieved a 30dB vibration attenuation. Nakamuraet al [56]implemented 8 air-magnetostrictive hybrid actuators to con-struct a micro-vibration isolation table, as shown infigure 20(a), where 4 of them are aligned vertically and therest 4 are oriented horizontally. The performance of the iso-lation table has been experimentally validated to isolate floorvibrations for a focused ion beam (FIB) imagemachine [59, 60].

Patterned magnetostrictive actuators can also providelarge actuation power for civil engineering applications.Fujitaet al [61] replaced the existing current-active vibrationabsorbers by 32magnetostrictive actuators to activelyattenuate seismic vibrations in a three-story building. A 15%modal damping ratio was achieved up to the 3rd mode of thestructure.

Most of the existing studies utilized Terfenol-D-basedactuators, which exhibit low tensile strength and requirespecial protection mechanisms. Flexible magnetostrictive

Figure 20. (a) Physical assembly and (b) schematic of magnetos-trictive-air hybrid actuator [56].

Figure 21. (a) 3-DOF vibration isolation table [57] and (b) 6-DOFStewart platform [58].

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actuators have been developed by embedding magnetos-trictive particles into resins. Murtyet al [62] created a lami-nated composite beam that contains a Terfenol-D particleembedded layer. Zhou and Zhou [63] later implemented anegative velocity feedback controller together with an ana-lytical nonlinear constitutive model to mitigate the compositebeam vibrations. Due to the large actuation force enabled bythe Terfenol-D composite layer, this numerical studydemonstrated a maximum effective damping factor ofabout 0.09.

Limited by the volume fraction of Terfenol-D particles,the magneto-mechanical coupling in magnetostrictive com-posites is dramatically weaker than that in the monolithicmagnetostrictive materials. Taking advantage of mechani-cally-robust Galfenol, Shuet al [64] fabricated aunimorph composite beam by bonding a Galfenol layer on anonmagnetic substrate, as shown in figure 22. A finite-dimensional sliding-mode controller was developed to accu-rately control the tip deflection to 400Hz. The bendingmotion can effectively amplify the deformation of the mag-netostrictive layer, but the super glue utilized to bond theunimorph degrades the reliability [64]. To improve themechanical strength and corrosion resistance of theunimorph composites, Scheidler and Dapino [65] utilizedultrasonic additive manufacturing to encapsulate magnetos-trictive Galfenol within aluminum structures, as shown infigure 23. Magnetostrictive materials have low inherentstructural damping and will induce instability when an erroroccurs in feedback control. Bhattacharyaet al [66] andBandopadhyaet al [67] combined the magnetostrictivecomposite actuator with passive damping materials (e.g.,poly-ethylene glycol, Fe-Cr-Al alloys) to achieve distributedcontrol of vibrations.

Besides direct force compensation, the actuation forcecan be generated indirectly via driving inertia masses at highfrequencies. As shown in figure 24, Chen and Brennan [68]

mounted three magnetostrictive actuators with tip inertiamasses on a gear body. The inertia force successfully dampedout the gear angular vibrations by 7.5dB at the tooth meshingfrequency around 250Hz. However, this configurationinduced mass imbalance. The inertia actuator cannot attenuatelow frequency vibrations, since the inertia force is relativelysmall at low frequencies.

Figure 22. (a) Schematic and (b) physical assembly of amagnetostrictive unimorph actuator.

Figure 23. (a) Magnetostrictive composites with embedded Galfenolinside Al 3003 base structure using ultrasonic additive manufactur-ing (UAM); (b) unimorph actuator based on UAM-ed magnetos-trictive composites [65].

Figure 24. Three magnetostrictive actuator driven inertia massesmounted on a gear body [68].

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Braghinet al [69] numerically studied the four flexuremechanisms presented in figure 25, where the small elonga-tion of the magnetostrictive material and the resulting smallinertia force are significantly amplified. Experimental resultsshows that the flexure mechanism is able to achieve a largeinertia force down to 167Hz. As shown in figure 26,Mayet al [70] enclosed a magnetostrictive actuator inside aflexure cage, which was mounted on the fuselage of a tur-boprop aircraft. It can attenuate the vibration tones generatedby the propeller at the fundamental blade passage frequencyand its harmonics. The anti-resonance of the actuator providean vibration attenuation of 12dB. Aurilioet al [71] laterdesigned a multi-input-multi-output feedback controller forthe actuator and attained 15–50 dB vibration attenuationbetween 40 and 200Hz. Cavalloet al [72] connected a fiberBragg grating sensor in parallel to the magnetostrictiveactuator to create a low-level control loop that compensatesthe nonlinear behavior of the magnetostrictive actuator.Within a frequency range between 150 and 400Hz, anaverage 14.4dB vibration reduction was obtained experi-mentally from an actual aircraft fuselage skin shown infigure 26(b).

In addition to the Joule magnetostriction that generates aforce or a displacement counteracting the external dis-turbances, the Delta-E effect of magnetostrictive materialsprovides another actively vibration control strategy by tuningsystem stiffness. Scheidleret al [73] developed a variable

spring, as shown in figure 27, whose stiffness can be activelycontrolled by tuning the current through the electromagnet. Apeak-to-peak sinusoidal Young’s modulus variation of21.9GPa was achieved up to 500Hz. The maximum peak-to-peak Young’s modulus for a square wave switch was12.3GPa. A numerical simulation of this device demon-strated an effective loss factor of 0.13 [40].

4.2. Passive control

The damping capacity of magnetostrictive materials is usuallydescribed by the loss factor η in previous studies [15, 74]. Thevalue of η is calculated from strain versus stress curves as

tan , 9TSh f= ( ) ( )

where fTS is the phase lag between the strain and stress.Bozorth [75] demonstrates two energy dissipation mechan-isms in ferromagnetic materials: magnetic hysteresis and eddycurrents.

Following Bozorth’s theory, the magnetic hysteresis isconstant up to the characteristic frequency of the magneticsystem (f > 1MHz) [76]. The magnetic hysteresis of poly-crystalline Galfenol (at 18.4% Ga) was characterized byRestorffet al [29], which is not significant enough for passivedamping. Hathawayet al [76] observed a loss factor of 0.29from the hysteretic strain versus stress loops of Terfenol-D.

Figure 25. Flexure mechanisms for low frequency inertia forcegeneration.

Figure 26. (a) Schematic of a magnetostrictive flexure actuator and(b) a magnetostrictive flexure actuator mounted on a fuselage skinpanel of a Boeing 717 [72]. Figure 27. (a) Computer-Aided Design (CAD) drawing and (b)

physical assembly of magnetostrictive variable spring [73].

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Smart Mater. Struct. 27 (2018) 113001 Topical Review

The damping effect of Terfenol-D relies on material compo-sition, crystal structure, and fabrication method.Hathawayet al [76] qualitatively showed the trend of lossfactor with respect to material anisotropy using an analyticalmodel. Teteret al [77] experimentally investigated thedamping capacity of Terfenol-D with respect to differentmicro structures. The loss factors of polycrystalline Terfenol-D (Tb Dy Fe0.3 0.7 2) and eutectic Terfenol-D (Tb Dy Fe0.6 0.4 1.4)samples fabricated by free-standing zone melt (FSZM)method were characterized under no magnetic field. Theeutectic sample exhibits a stress-independent loss factor ofabout 0.04; the loss factor of polycrystalline Terfenol-Dvaries with respect to stress amplitude and reaches a max-imum value of 0.28 at 4.1MPa. Wun-Fogleet al [78]experimentally investigated the damping capacity of FSZM-fabricated Terfenol-D (Tb Dy Fex 1 x 1.92- ) as a function of theterbium content x. A maximum loss factor of 0.22 wasobserved for x=0.45 under 23.9kA/m bias field. Hoet al[79] measured the damping capacity of Terfenol-D(Tb Dy Fex 1 x 1.92- ) fabricated by arc-melt method for x variesfrom 0.35 to 1.0. A maximum loss factor of 0.15 wasachieved at x=0.5 under a magnetic field of 23.9kA/m.The optimal x is similar to the monolithic FSZM samples, butthe loss factor is much smaller.

To resolve the brittleness of monolithic Terfenol-D,Sandlundet al [80] embedded Terfenol-D particles intoinsulating binders and created flexible magnetostrictive par-ticulate composites (MPC). Hoet al [79] experimentallycompared the loss factors of MPC that are made of Terfenol-D particles fabricated by FSZM and arc-melt. Unlike theresults from the monolithic samples, MPC based on arc-meltTerfenol-D particles exhibit a higher loss factor than that ofthe FSZM-fabricated MPC. The arc-melt MPC is able toprovide a maximum loss factor of 0.09 while maintaining ahigh Young’s modulus of about 10GPa. Pulliamet al [81]later applied a thin layer of MPC on top of a turbomachineryfan blade and achieved a 35% increment in structuraldamping.

The other energy dissipation mechanism associated withmagnetostrictive materials is the stress-induced eddy currents.Deng [27] and Scheidler and Dapino [28] have developedanalytical constitutive models describing the eddy current lossin magnetostrictive materials. Scheidleret al [82] experi-mentally characterized the eddy current loss up to 1kHz bycomparing the strain versus stress curves measured from asolid and a laminated Galfenol sample (Φ6.35 mm).Denget al [83] later conducted a parametric study for a solid-state damper where the active component is a 6mm diameterand 10mm long Galfenol rod. The proposed damper wasvalidated experimentally by Denget al [84], which demon-strated a maximum loss factor of 0.05 at 1kHz.

The stress-induced eddy current loss depends on thedevice’s geometry. To create significant damping for arbitrarygeometries, recent studies have incorporated a shunted circuitwith the magnetostrictive materials, as shown in figure 28.Due to the Villari effect, mechanical stress induces magneti-zation variation inside magnetostrictive materials and gen-erates electrical energy in the coil. The vibration energy is

eventually dissipated on the electrical shunt as joule heat.Davinoet al [85] measured the damping capacity of a shuntedGalfenol damper via impact testing. However, the biasmagnetic field in this device was applied via an electromagnetrequiring external power supply. Denget al [84] experi-mentally characterized the loss factor available from thisshunted damper which was biased by permanent magnets. At750Hz, the maximum loss factors from a Galfenol-basedshunted damper are 0.06 and 1.34 for resistive shunt andcapacitive shunt, respectively. Asnaniet al [15] measured theloss factor of a Terfenol-D damper and achieved a maximumloss factor of 0.25 at 300Hz for resistive shunts. Fenn andGerver [86] developed a Terfenol-D-based shunted damperwhich simultaneous operates as a velocity sensor. A max-imum loss factor of 0.22 and a velocity sensitivity of 180V/(m/s) were measured. Figure 29 compares the loss factor andYoung’s modulus of magnetostrictive materials and otherindustrial passive damping materials. Magnetostrictive

Figure 28. (a) Schematic and (b) physical assembly of magnetos-trictive unimorph [84]. (CL: capacitive shunt; RL: resistive shunt; LL:inductive shunt).

Figure 29. Loss factor versus Young’s modulus map. PMMA:polymethylmethacrylate; Terfenol-D: Tb Dy Fe ;0.3 0.7 2 Galfenol:100á ñ-oriented polycrystalline Fe Ga ;81.6 18.4 Piezoelectric: NoliacNCE51F, soft-doped polycrystalline PZT.

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Smart Mater. Struct. 27 (2018) 113001 Topical Review

materials are ideal candidates for structural damping appli-cations when high stiffness is desirable.

Magnetostrictive materials are usually appropriate forsmall vibration amplitude and high frequencies. Hybriddamping materials based on magnetostrictive materials havebeen developed to lift these limitations. Kerriganet al [87]fabricated a NiTi/Ni/Terfenol-D laminated composite. TheNiTi film dissipates vibration energy for low frequency andlarge strain amplitudes; the Terfenol-D film manufactured bysputter deposition targets the high frequency vibrations.Overall, the hybrid damper is feasible for a wide strain rangefrom 0.05% to 1%. A maximum loss factor of 0.21 isachieved at 0.27% strain.

4.3. Semi-active control

Semi-active vibration control that requires minimum controleffort or energy consumption has been investigated in recentapplications. The first type of semi-active control is to inte-grate traditional magnetostrictive actuators with passivemechanisms. Ohmataet al [88] developed a smart joint,shown in figure 30, whose hinge friction increases as themagnetostrictive rod elongates. Figure 31 shows anothersemi-active mechanism that mitigates higher harmonics fol-lowing individual blade control [89]. The semi-active systemis able to tilt the edge flap by±5° while taking less than 1%of the gross vehicle weight and using only 0.7% of cruisepower.

Section 4.1 presented several actuators that can activelygenerate time-varying inertia forces to compensate externaldisturbance. However, the real-time actuation requires com-plicated controllers and distributed sensors. Semi-activevibration absorbers that utilize DC driving currents have beendeveloped in the literature to reduce the control complexity.Flatauet al [90] designed a Terfenol-D-based vibrationabsorber whose resonant frequency was tuned by applyingdifferent DC currents through the solenoid. The anti-reso-nance introduced by the vibration absorber shifted from1375Hz to 2010Hz by applying a current of 2A.Braghinet al [91] configured a similar device and developed

a lumped parameter model to describe the current-inducedresonance tuning.

Other semi-active vibration control mechanisms can bedeveloped by modifying the aforementioned active and pas-sive control strategies. As shown in figure 27, the stiffness ofmagnetostrictive materials can be actively controlled byapplying a suitable current to the solenoid. Recent studiesdemonstrated that the stiffness can also be tuned by attachingvarious electrical impedances to the coil. Semi-active smartmounts based on Terfenol-D and Galfenol have been devel-oped for the main rotor gearbox of helicopters, as shown infigure 32. Scheidler and Asnani [92] derived a lumped para-meter model and conducted parametric studies for the pro-posed tunable mount based on linearized constitutive models.The Terfenol-D mount and Galfenol mount were experi-mentally characterized in [93] and [84], respectively. Table 2summarizes the relative stiffness variation under variouselectrical impedances.

Figure 30. Active hinge that incorporates the magnetostrictiveactuator with lever mechanisms [88].

Figure 31. (a) Arrangement of magnetostrictive actuators and trailingedge flaps for the UH-60A helicopter blades; (b) Top and aft view ofthe magnetostrictive actuator linked to flap [89].

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Section 4.2 demonstrated typical passive magnetos-trictive dampers by attaching shunt circuits to magnetos-trictive materials. Recent studies have shown that the shuntdamper can be tuned by changing the impedance of theelectrical shunt. Yooet al [94] first evaluated the impedance-dependent loss factor of a Galfenol-based unimorph, asshown in figure 33. Deng [93] and Denget al [84] latercharacterized the damping capacity of Terfenol-D and Gal-fenol, respectively, by applying axial mechanical load to themounts presented in figure 32. The loss factors under varioustypes of electrical impedance are summarized in table 3.Compared with similar shunted dampers based on piezo-electric materials [15], magnetostrictive materials are able toprovide a higher loss factor. Due to the mechanical robust-ness, high stiffness, and large damping capacity of Galfenol,Denget al [74] recently developed a ring-shaped damperwhich can be mounted inside gear body and dissipate gearmeshing vibrations before they propagate and induce struc-ture-borne noise. The semi-active vibration control devicesmentioned above can also be self-sustained, since part of theelectrical energy on the shunted circuit can be scavenged[95, 96]. Theoretical results show that larger stiffness varia-tion are available when negative inductive loads isattached [92].

5. Conclusion

The magneto-mechanical coupling in magnetostrictive mate-rials forms the basis for several responses including Joulemagnetostriction, Villari effect, magnetic hysteresis, andDelta-E effect. Each of these effects have been shown toprove useful in the design of active, passive, or semi-activevibration control approaches. Many magnetic materialsexhibit magnetostrictive behavior, but this article focuses on

Figure 32. (a) Installation locations of the smart mount in a helicopter main gear box; (b) Terfenol-D-based and (c) Galfenol-based smartmounts.

Table 2. Relative stiffness K K K Kmax min max= -¯ ( ) measured fromsolid Terfenol-D (f 7 mm×10 mm), solid and laminatedFe Ga81.6 18.4 Galfenol (f 6 mm×10 mm) under various types ofelectrical shunts. A 750Hz and 280N amplitude was applied to theTerfenol-D sample and a 750Hz and 73.51N amplitude sinusoidalforce was applied to the Galfenol samples.

Material Resistive Capacitive Inductive

Terfenol-D 19.5% 24.6% NASolid Galfenol 6.7% 17.9% 6.7%Laminated Galfenol 11.0% 60.9% 10.9%

Figure 33. (a) Schematic and (b) physical assembly of tunableshunted dampers [94].

Table 3. Loss factor η range measured from solid Terfenol-D (Φ7 mm× 10 mm), solid and laminated Fe Ga81.6 18.4 Galfenol(Φ6 mm× 10 mm) under various types of electrical shunts. A750Hz and 280N amplitude was applied to the Terfenol-D sampleand a 750Hz and 73.51N amplitude sinusoidal force was applied tothe Galfenol samples.

Material Resistive Capacitive Inductive

Terfenol-D 0.11−0.21 0.21−0.37 NASolid Galfenol 0.01−0.05 0.03−0.22 0.01−0.03Laminated Galfenol 0.01−0.06 0.01−1.34 0−0.01

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two widely-used magnetostrictive materials: Terfenol-D andGalfenol.

Due to the Joule magnetostriction, magnetostrictivematerials are able to provide a large actuation stress (MPalevel) or moderate strain (0.16%) that can actively counteractexternal disturbances. Compared to conventional electro-magnetic motors, magnetostrictive actuators exhibit a largestiffness and a broad frequency bandwidth. Certain magne-tostrictive materials, such as Galfenol or Alfenol, aremechanically-robust and can withstand complex loadings.The magnetostrictive actuators are activated by magnetic fieldand thus are suitable for wireless or non-contact cases.Monolithic magnetostrictive materials typically have a highelectrical conductivity. Hence, the frequency bandwidth ofthe magnetostrictive actuators is mainly limited by the eddycurrents. Lamination or particle embedded composites arecommon solutions to mitigate the eddy currents. Anotherlimitation of magnetostrictive actuators is their relativelysmall deformation. To extend the applications of magnetos-trictive actuators to large deformation cases, existing studieseither fabricate composites (e.g., magnetostrictive unimorph)that converts small elongation to large bending motion orconstruct hybrid actuators that incorporate lever mechanisms,flexural mechanisms, hydraulic cylinder, or pneumatic sys-tems to amplify the deformation. Magnetostrictive actuatorsthat are installed in the load path can efficiently counteractvibration sources although a disadvantage of this approach isthe added complexity. Control force can be applied indirectlythrough inertia masses. The indirect mechanisms have beendeveloped and experimentally validated to attenuate vibra-tions on aircraft fuselage and gear bodies. However, theinertia mass introduces additional weight that is undesirablefor mobility applications. Adding inertia mass on gear pairsalso induces rotating unbalance that can be detrimental tosystem reliability. Future studies should further explore thepotential applications of mechanically-robust magnetos-trictive materials, which can simultaneously operate asstructural materials and actuators. The discovery of Delta-Eeffect in magnetostrictive materials has recently led to activevibration control via stiffness or resonance tuning. TheYoung’s modulus level of magnetostrictive materials is muchhigher than that of other smart materials, for instance shapememory alloys and MR rubber [97]. Magnetically-variablesprings have been developed and tested in the laboratory, butthe effectiveness of these devices in practice is still underinvestigation. The nonlinearities of magnetostrictive materi-als, including hysteresis, anisotropy, and saturation, are one ofthe main challenges in magnetostrictive active vibrationcontrol, especially for multi-DOF vibration control systems(e.g., Stewart platforms). Advanced control algorithms arenecessary to compensate for the material nonlinearities.Details of the control algorithms, which are not the scope ofthis article, can be found in the literature [98–100].

Passive dampers that consume no external power andrequire no controllers is another convenient option forvibration control. Magnetostrictive dampers can dissipatemechanical energy via magnetic hysteresis, magneto-mechanical coupling, and eddy currents. Compared with

traditional passive damping materials, magnetostrictivematerials is able to provide comparable loss factors whilemaintaining a high Young’s modulus in GPa. As passivedamping materials, magnetostrictive materials can be directlyapplied in the load path without increasing system com-pliance. Previous studies have investigated the damping effectdue to the magnetic hysteresis loss alone. Terfenol-D exhibitsa relatively large hysteresis but brittleness. To facilitate thebonding between fragile Terfenol-D and structural materials,flexible MPC have been developed. The hysteresis loss ofTerfenol-D depends on material composition, crystal struc-ture, and fabrication method. The FSZM fabrication and arc-melt fabrication are preferable for monolithic- and MPC-based dampers, respectively. Shunted magnetostrictive dam-pers that take advantage of all three energy dissipationmechanisms have recently been developed. A typical shuntedmagnetostrictive damper consists of a magnetostrictive ele-ment, coil, permanent magnet array, and electrical shunts.Even though Terfenol-D exhibits much higher magnetichysteresis, Galfenol-based shunted dampers are able to pro-vide larger loss factors due to its relatively higher saturationflux. The damping effect depends on finely-tuned bias con-ditions (e.g., pre-stress and permanent magnet strength) andthe impedance of electrical shunts. The loss factor on theshunted magnetostrictive damper is maximized when themagnetostrictive element operates in the center of its burstregion and an electrical resonance is created on a capacitiveshunt circuit. In existing studies, the optimal capacitive load isselected manually and thus is sensitive to system uncertaintiesand environmental variations. Future studies should investi-gate resonance tracking techniques that can automaticallyensure operation at electrical resonance. Eddy currents in theshunted magnetostrictive dampers induce additional Jouleheating loss but also reduce magneto-mechanical coupling.Overall, eddy currents are detrimental to shunted magnetos-trictive dampers and need to be avoided through lamination.However, eddy currents inside electrically-conductive mag-netostrictive materials can facilitate compact and coil-lessdamper designs for tight locations and harsh environmentswhere shunt circuits are infeasible. The mechanically-inducededdy currents and the resulting structural loss factor can becontinuously tuned by adjusting the system bias conditions.Future studies should further investigate the possibility ofimplementing magnetostrictive materials as structural andtunable-damping materials at the same time.

Passive vibration control can be de-tuned when the sys-tem dynamics varies over time. Active vibration control isadaptive but requires complicate sensor arrangement, com-plex controller design, and large power sources. The uniquematerial properties of magnetostrictive materials allow forsemi-active control strategies where the drawbacks of passiveand active control methods can be resolved. Most semi-activevibration control strategies based on magnetostrictive mate-rials simply utilize the magnetostrictive actuator as a switch totrigger a larger control mechanism. Recent studies have dis-covered advanced semi-active control methods by using theaforementioned shunted magnetostrictive devices. Both theloss factor and the stiffness of the shunted magnetostrictive

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device can be continuously adjusted via tuning the electricalimpedance in the shunt circuit. Future studies can incorporatenegative electrical shunt circuits with existing devices andfurther improve tunability. The tuning of shunt impedancecan be self-sustainable, since part of the mechanical vibrationenergy can be scavenged from the shunt circuit.

Acknowledgments

We wish to acknowledge the member organizations of theSmart Vehicle Concepts Center, a Phase III National ScienceFoundation Industry-University Cooperative Research Center(www.SmartVehicleCenter.org) established under NSF GrantIIP-1738723.

ORCID iDs

Zhangxian Deng https://orcid.org/0000-0003-1084-1738Marcelo J Dapino https://orcid.org/0000-0003-4888-1903

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