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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMECH.2019.2954910, IEEE/ASMETransactions on Mechatronics

High-static–low-dynamic Stiffness Isolator withTunable Electromagnetic Mechanism

Yi Sun#, Member, IEEE, Jinglei Zhao#, Min Wang, Yu Sun, Fellow, IEEE, Huayan Pu∗, Jun Luo, Yan Peng,Shaorong Xie, and Yi Yang

Abstract—A high-static–low-dynamic stiffness (HSLDS)vibration isolator based on a tunable nesting-type electro-magnetic negative stiffness (NS) mechanism is presented.The stiffness characteristics of the HSLDS system canbe tuned by regulating the current in the coil. When thecurrent is zero, the HSLDS system may degenerate into apassive isolator. The distinctive features of this proposedisolation system are demonstrated from two aspects: (1)in contrast to passive isolators, the proposed isolator canfurther widen the bandwidth of vibration isolation and im-prove the isolation performance near the natural frequencyof the passive system; (2) compared with certain otherelectromagnetic isolation systems, the proposed systemhas a more compact structure, heavier load capacity, andhigher NS-generating efficiency. The proposed electromag-netic NS mechanism consists of four permanent magnetsand four coil windings. Analytical models of the electro-magnetic force and the displacement transmissibility areestablished. To select an appropriate structural parameterfor the prototype, the effects of geometric parameters ontransmissibility are discussed from a theoretical viewpoint.The vibration isolation performance of the proposed isola-tor system is verified, and a tuning strategy is investigatedthrough experiments.

Index Terms—High-static–low-dynamic stiffness, Elec-tromagnetic negative stiffness, Vibration isolation

I. INTRODUCTION

MECHANICAL vibration is a naturally occurring phe-nomenon that exists in many aspects of the industry.

Therefore, vibration isolation equipment is critical to industrialsystems [1–3] and numerous vibration control [4–7] technolo-gies have been investigated in detail. Generally, for passivevibration isolators, which usually consist of linear springsand viscous dampers, there is a trade-off between the loadcapacity and the vibration attenuation performance. To a linearsystem, vibration isolation occurs in the frequency zone thatis greater than

√2 times the natural frequency of the system.

Thus, in order to improve the isolation performance from theperspective of broadening the isolation range and improving

Y. Sun, J. Zhao, M. Wang, H. Pu, J. Luo, Y. Peng, S. Xie and Y.Yang are with the School of Mechatronics Engineering and Automation,Shanghai University, Shanghai, China.

Y. Sun is with Department of Mechanical and Industrial Engineering,University of Toronto, Toronto, M5S 3G8, Canada.

#These authors contributed equally. This work was supported bythe National Natural Science Foundation of China under Grants51575329,61773254,61625304 and 61873157; in part by ShanghaiRising-Star Program under Grants 17QA1401500; in part by Scienceand Technology Commission of Shanghai under Grants 16441909400and 17DZ1205000.

∗Corresponding author: H. Pu (email: phygood [email protected]).

the transmissibility characteristic near the resonance zone,one of the most direct approaches is to lower the naturalfrequency, namely, to reduce the equivalent/overall stiffness ofthe isolator. However, for passive systems, the stiffness cannotbe reduced infinitely because large static deformation may becaused. Therefore, a novel vibration isolator, which is referredto as a high-static–low-dynamic stiffness (HSLDS) isolator [8–10], is investigated by introducing negative stiffness (NS) [11–16].

Several methods are employed to achieve NS. A com-mon method is to connect a vertical spring with twohorizontal/oblique springs [17], in which the oblique springsprovide NS once the isolated mass deviates from the equilib-rium position. Other methods include utilizing the magneticforce between permanent magnets [18–20], utilizing bracketsand hinges to construct an NS corrector [21], or employingfour oblique buckled Euler beams to provide NS [22].

However, even though oblique springs and buckled beamscan realize the HSLDS, the structure is relatively large becauseof their layouts. This may restrict the application range ifthe system installation space available is limited. In addition,for traditional mechanical (e.g., oblique springs and buckledbeams) and magnetic (e.g., tile magnets) HSLDS systems, itis difficult to adjust the characteristics with respect to externalexcitation once the structural dimensions are fixed, whichmay weaken the adaptability for different vibration sources.Compared with mechanical or magnetic variable stiffnesssystems, electromagnetic devices have two advantages: first,the non-contact characteristic of the electromagnetic force cannot only lead to a more compact mechanical structure, but alsoa longer fatigue life; second, the electromagnetic NS can bevaried by tuning the current in coil windings, which makes itpossible to optimize the system online in order to prevent adegradation in the attenuation performance.

Therefore, electromagnet-based isolators with smaller sizeand can be tuned online have attracted the attention of severalresearchers. Ledezma et al. [10, 23] devised an electromag-netic shock isolator. Zhou et al. [24, 25] proposed an HSLDSelectromagnetic isolator. Both these creative works use obliquecomponents (nylon wire/steel beam) to provide positive s-tiffness (PS), which restricts their structural compactness inthe axial plane. In addition, as static deformation is inevitablemaking it difficult to adjust the equilibrium positions for nylonwires or steel beams, these systems are suitable for horizontalmounting, which degrades their load capacity. Moreover, theirseparated sandwich-type structure also expands their effectivevolume (the volume of the part that generates NS). If the



Isolated

mass

Coil

windings

Base

xm

Permanent

magnets

(a)

(b)

xb

bm

bw

awam

ag

Winding

Magnet

(c)

Vibration control unit

(Econ VT 9008)

Shaker

(TMS Model 2100E11)

HSLDS

isolator

Data acquisition system

(LMS SCADAS XS)

Accelerometer X2

(PCB 393B31)

Analyzing system

(LMS Test.Lab)

Shaking plate

Power amplifier

(TIRA BAA 1000)

(d)

Spring Frame

Fig. 1. Experimental setup of the proposed isolator: (a) HSLDS system; (b) electromagnetic mechanism, where the green and red arrow representthe magnetization direction and the polarity of current, respectively; (c) coil winding (CW) and permanent magnet (PM); (d) experimental setup.

payload carried per unit effective volume is regarded as anindex of efficiency, smaller effective volumes and heavierpayloads are preferable from the perspective of engineering.

Thus, inspired by the pioneering studies of Zhou andLedezma, this work aims to develop a tunable HSLDS isolatorby utilizing a novel electromagnetic NS mechanism, whichhas a more compact design, heavier load capacity, and higherefficiency of isolation. Instead of the separated sandwich-type mechanism, we proposed a novel electromagnetic NSmechanism by nesting permanent magnets (PMs) within coilwindings (CWs). This nesting-type layout makes the structuremore compact and facilitates the integration of more PMs orCWs within a limited space to increase NS. PS is provided bytwo parallel mechanical springs, through which the equilibri-um position can be easily controlled by adjusting the preloadof the springs, regardless of vertical or horizontal mounting.Therefore, a large load capacity can be realized. Consequently,the efficiency is improved as isolation of a heavier load canbe realized through a smaller effective volume. In addition,a systematic tuning strategy is developed to achieve a highervibration attenuation performance than those of passive sys-tems or pure HSLDS systems. The generality of this systemwarrants its direct use in guiding the design and parameterselections of other HSLDS systems.

II. HSLDS SYSTEM DESCRIPTION

To construct an electromagnetic HSLDS isolation systemwith a compact design and high isolation efficiency, weproposed a nesting-type electromagnetic mechanism, whichis composed of four ring PMs and four CWs (Fig. 1a).The axial thickness of the PMs and the CWs are equalsince the interaction force/stiffness will be the largest in thisconfiguration according to literatures [9, 26]. All the PMsare axially magnetized and the magnetization directions ofthe adjacent PMs, as well as the directions of the current inadjacent CWs, are opposite. Two shaft collars are utilized to

remain the PMs in contact with adjacent ones, and to fastenthese four PMs at a specific position on the shaft. The CWs arestuck to the inner wall of the frame, and there exists a clearancebetween the PMs and the CWs to ensure non-interference ofmovement between them. It is noteworthy that the clearance isan important parameter that may influence the magnetic fluxdensity, hence the magnitude of the electromagnetic interactionforce/stiffness. Thus, it will be discussed in detail and selectedin the later section. Once it is determined, it remains a fixedvalue during the operation because there is no movement inradial direction for the PMs. Fig. 1a also shows the equilibriumposition of the isolator, at which the equivalent stiffness is thelowest. Thus, in order to achieve the maximum isolation effect,the center plane of the PMs should coincide with that of theCWs axially.

An apparent feature of this mechanism is that the PMsare nested into the CWs (Fig. 1b-c), which is beneficial forreducing the dimensions of the overall structure. Furthermore,owing to the nesting-type layout and the use of mechanicalsprings, the effective volume is small, and the load capacityis significant. Consequently, the load carried by per uniteffective volume increases. To further maximize the isolationperformance, on the basis of the nesting-type layout, weproposed a design procedure to derive the optimum structuralparameters (listed in Table I) in the following section. Themain objectives are to: (1) decrease the natural frequency tobroaden the frequency range that isolation occurs; (2) lowerthe peak transmissibility to decrease the influence of the basevibration on the payload.

Materials for the prototype include aluminum and acrylicplexiglass. The CWs are fixed to the base of the isolator, andthe PMs are connected to the isolated mass through a shaft.Sliding bearings are equipped to decrease the friction betweenthe base and the shaft and to ensure that the shaft can onlymove vertically. Fig. 1d shows a schematic of the experimen-tal setup. The prototype is mounted on a shaking platform



Air gap

Half cross

section

Fig. 2. Calculated distribution of the magnetic flux line and the magneticflux density using FEM software Comsol. The current is 0.9 A, and theother parameters have listed in Table. I.

L

cRcr

mrmR

11

2 1 1

m mzc m c m

z m

N nnL z l l l l

N N

J

mNzN

rN

Stiffness

Tester

ShaftPermanent

Magnet

Wire

WindingsElectrode

Shell

Base

Force

Sensor

(a)(b)

ga

wb

mb

x

L

cRcr

mrmR

J

mN

zN

rNga

wb

mb

x

Fig. 3. Schematic of a ring PM and a CW with multi-layers of current-carrying coils. • and × indicate the polarities of current.

attached to the stinger of a TMS Model 2100E11 shaker. Theexternal excitation signal for the shaker is controlled with anEcon VT 9008 vibration control system and a TIRA BAA1000 power amplifier. Two PCB 393B31 accelerometers areused to measure the acceleration signals of the shaking plateand the isolated mass. Acceleration data are collected andprocessed using an LMS SCADAS XS device and LMS TestLab software, respectively.

III. STATIC ANALYSIS

A. Theory of HSLDS

Owing to the axial symmetry of the proposed HSLDSisolator, only the axial electromagnetic force would be appliedon the PMs. When the CWs are not energized or the PMs arein their equilibrium locus, the force exerted on the PMs iszero. In this case, the stiffness of the entire system equals thestiffness of the mechanical springs. However, when the CWsare current-carrying, the steady state will be broken by therelative motion between the PMs and the CWs. Specifically,a repulsive electromagnetic force will be generated by thecoupling of the magnetic fields created by the CWs and PMs,as shown in Fig. 2. If the electromagnetic force exerted onthe PMs is opposite to the restoring force of springs, it willcounteract the restoring force. Consequently, both the resultantforce exerted on the PMs and the equivalent stiffness of theisolator decrease.

Increasing

current

Increasing

current (a)

(b)

mm

Fig. 4. Fitting results: (a) fitted curves (dotted lines) and calculated forcecurves (solid lines) with different current. The arrow means the currentincreases from 0.2 A to 1.0 A in a step of 0.2 A; (b) fitting error.

B. Force modeling

Although various analytical methods have been reportedin previous studies to calculate the electromagnetic field orforce [27, 28], they are mainly focused on configurations suchas PM–PM, CW–CW, and cylindrical PM–CW. Therefore, astrategy that solves the configuration of a ring PM–CW isproposed in this study. The filament method [29] is adoptedto calculate the interaction force between two coaxial coils (orfilaments). According to the Amperian current model, a ringPM consists of two equivalent surface currents with identicalcurrent magnitudes but opposite directions [30], as shown inFig. 3. The detailed expression of the axial force and stiffnessfor a one-magnet–one-winding configuration is provided in theappendix. Here, the total axial interaction force f∗ for a four-magnet–four-winding configuration can be calculated using

f∗ =

4∑i=1

4∑j=1

FCiMj (1)

where FCiMj( i, j = 1,2,3,4) denotes the electromagnetic

force between any PM–CW pairs. In order to more convenient-ly solve stiffness and dynamic equation, one common practiceis to employ a cubic polynomial to express the electromagneticforce, which is given as

f∗ = p1x+ p3x3 (2)

where p1 and p3 are fitting parameters computed by theCurve Fitting Toolbox in MATLAB. The embedded Matlabfunction ‘fit’ is called, the fitting type is set to be ‘poly3’,all the rest arguments remain default. Then, four coefficients,which represent the coefficients of the cubic polynomial, areobtained. The coefficients for quadratic term and the constantterm are neglected because they are very small, specifically, inorder of magnitude of 10−11 and 10−15, respectively. In otherwords, only the linear term and the cubic term is left in thefinal expression. The fitting results and the error are illustratedin Fig. 4. By observing Fig. 4a we can see that both thecalculated and the fitted results are in good agreement. And wecan conclude that the cubic polynomial is reasonably accurateto denotes the electromagnetic force because the fitting erroris less than 9 %, as shown in Fig. 4b.



TABLE ISTRUCTURAL PARAMETERS AND VARIABLES OF THE SYSTEM

Structural ParametersParameter Value unit Definitionrc, Rc 15.8, 23.5 mm Inner / outer radius of the CW.rm, Rm 5, 15 mm Inner / outer radius of the PM.Nm 50 - Number of turns axially of the PM.Nz , Nr 18, 16 - Number of turns axially / radially of the

CW.am, aw 10, 7.7 mm Radial thickness of the PM / CW.bm, bw 10, 10 mm Axial thickness of the PM / CW.ag 0.8 mm Clearance.Br 1.35 T Magnetization of the PM.Da - mm Axial clearance between adjacent CWs.m 3.519 kg Mass of the payload.c 0.017 Ns/mm Equivalent damping of the system.ξ 0.044 Equivalent damping ratio of the system.ks 5.4 N/mm Stiffness of the mechanical spring.

Variablesf, f∗ - N Total / electromagnetic forcep1, p3 - - Fitting parameters of the NS.k1, k3 N/mm Linear / cubic stiffness of the systemI1 - A Excited current in CWs.I2 - A Equivalent current of the PM.Xb - mm Excitation amplitude of the base.θ - rad Phase of the response.xb, xm - mm Displacement of the base / mass.xb, xm - - Dimensionless displacement of the base

/ mass.x - mm Relative displacement.ωb - rad/s Excitation frequency of the base.ωn, ωh - rad/s Natural frequency of the passive system

(without NS) / HSLDS system (withNS).

Tn, Th - - Peak transmissibility of the passive sys-tem (without NS) / HSLDS system (withNS).

X - - Dimensionless amplitude of the mass.α, γ - - Dimensionless linear / cubic stiffness.β - - Dimensionless excitation frequency.τ - - Dimensionless time.Ra, Rr, Rg - - Axial thickness ratio, radial thickness

ratio and clearance ratio.k2 - - Modulus.K,E - - Complete first / second elliptic integrals.r1, r2 - mm Radius of filaments.µ0 4πe-7 H/m Permeability of vacuum.L - mm Distance between two filaments.

IV. DYNAMIC ANALYSIS

The dynamic characteristics of the HSLDS isolator will beinvestigated in this section. All the symbols used here are listedand explained in Table I, and hence, they will not be explainedin detail below.

A. Motion equation

The sum of the spring force and the electromagnetic forceis

f = (2ks − p1)x− p3x3 (3)

Thus, the motion equation of the isolator under an externaldisplacement excitation xb = Xbcosωbt at the base is

mx+ cx+ k1x+ k3x3 = −mxb (4)

where the dots denote the derivatives with respect to time t,k1 = 2ks - p1 is the linear stiffness; k3 = -p3 is the cubic

nonlinear stiffness. Thus, the motion equation can be furthernon-dimensionalized as

x′′ + 2ξx′ + αx+ γx3 = β2 cosβτ (5)

where the primes denote the derivatives with respect to dimen-sionless time τ , and

ξ =c

2mωn, α =

k12ks

, γ =k3X

2b

2ks, x =

x

Xb, β =

ωb

ωn, ωn =

√2ksm

The harmonic balance (HB) method [16, 19, 20], which isusually applied to obtain the periodic solution approximately,is adopted to solve the above nonlinear differential equations.The solution to the equation indicates the steady-state responseof the mass under a given excitation of the base. According tothe HB method, assuming that the high order terms (greaterthan the first order) in the solution have little influence on thesteady-state response and hence can be neglected. Then, wecan derive the first order periodic solution of (5) by assumingthat it has a form of x = Xcos(βτ+θ). Substituting it into (5),neglecting the terms containing 3(βτ + θ), and after simplereduction, the following amplitude-frequency response can beobtained {

−β2X + αX + 34γX3 = β2 cos θ

−2ξXβ = β2 sin θ(6)

The above equation can be further simplified as[(α− β2) X +

3

4γX3

]2+(−2ξXβ

)2= β4 (7)

B. Displacement transmissibility

The amplitude X can be calculated numerically through (7).Because the dimensionless absolute displacement of the baseis xb = cosβτ , the dimensionless absolute displacement ofthe mass xm, which equals to the sum of xb and x, can beexpressed as

xm = xb + x = cosβτ + X cos (βτ + θ)

=(1 + X cos θ

)cosβτ − X sin θ sinβτ

(8)

The displacement amplitude of the mass can be derived by(8). Thus, the transmissibility T can be calculated by the ratioof the displacement amplitude of the mass to that of the base,which can be expressed as

T =

√(1 + X cos θ

)2+(X sin θ

)2/1 (9)

Substituting (6) into (9), the transmissibility T can bederived as

T =

√1 + X2 +

2X

β2

[(α− β2) X +

3

4γX3

](10)



A B

Q

Tra

nsm

issi

bil

ity (

dB

)

Fig. 5. Simulated transmissibility curves with various currents: (a) Xb =0.5 mm; (b) Xb = 1.0 mm.

C. Nonlinear characteristics

The HSLDS system behaves as a nonlinear system owing tothe existence of cubic nonlinearity p3 [9, 11, 12]. Two sets ofnumerical simulations with different excitation amplitudes Xb,namely 0.5 mm and 1.0 mm, are conducted to illustrate thenonlinearity of the proposed system. All the initial parametersfor simulations are listed in Table I. Fig. 5a shows that boththe resonance frequency ωh and the peak of transmissibilityTh decrease with the increase in current when Xb = 0.5 mm.This is explained by the fact that an increase in the current canimprove the NS effect, which will be proven experimentallyin Section VI-A. However, for the case of Xb = 1.0 mm, thecurve-bending and the jumping-down phenomena are observed(see Fig. 5b). This is because a high excitation amplitude maylead to a greater nonlinearity term γ (see (5)). The curve bendstoward the right side such that the resonance frequency ωh

moves to the high-frequency zone, and the isolation effectdiminishes. Notably, it is a hardening system because the curvebends to the right side.

V. SELECTION OF STRUCTURAL PARAMETERS

The fundamental principal for structural design is to findthe optimal structure dimensions that can generate the great-est electromagnetic NS under given conditions. Usually, forHSLDS systems, the greater the generated NS, the lower theequivalent stiffness of the isolator, and hence the lower thenatural frequency. In the meanwhile, the peak transmissibilitywould be lowered because the damping ratio ξ increaseswith the decrease in the equivalent stiffness of the isolator.Thus, generating the greatest NS can be achieved by attainingthe lowest natural frequency (ωh) or peak transmissibility(Th). Based on these considerations, in this section, ωh andTh are selected as indices to illustrate the influence of thegeometric parameters on the vibration isolation performance.To examine the effects more clearly, they are normalized asωh/ωn and Th/Tn, respectively. Once the stiffness of themechanical spring is fixed, the equivalent stiffness of thesystem is only determined by the electromagnetic stiffness. For

a given layout, the electromagnetic stiffness is entirely affectedby the current, geometric parameters, and residual flux density.Appropriate geometric parameters could improve the vibrationattenuation performance. Thus, three normalized variables areused to analyze the influences of geometric parameters onωh/ωn and Th/Tn: (1) the axial thickness ratio Ra = bw/bm,as shown in Fig. 1c; (2) the radial thickness ratio Rr = aw/am;(3) the clearance ratio Rg = ag/am.

Notably, changing the physical dimensions of the PM wouldbe highly impractical, whereas the geometric dimensions of theCW can be relatively easily altered. Hence, in the followinganalysis, the dimensions and characteristics of the PMs arefixed, namely, rm = 5 mm, Rm = 15 mm, am = 10 mm, bm= 10 mm, and Br = 1.35 T . Other constants for the simulationare Xb = 0.5 mm and I1 = 0.6 A.

A. Effect of geometric parameters

Radial thickness ratio Rr. The effect of Rr is shown inFig. 6a. With an increase in Rr, both the normalized peaktransmissibility Th/Tn and the resonance frequency ωh/ωn

decrease to some extent. However, when Rr > 0.7, this trendbecomes inconspicuous, which indicates that the increase inRr has a slight effect on the peak transmissibility and theresonance frequency. This is because, if Rr is relatively small,when the PM and current are given, a CW with a largerradial thickness can produce a larger NS. However, once thethickness exceeds a certain limit, it no longer has a significanteffect on the NS. With an increase in Rr, the nonlinearitybecomes much stronger and has sufficient strength to distortthe curve to the high-frequency band, which may weaken thevibration isolation performance of the system.Axial thickness ratio Ra. The transmissibility character-

istics of the proposed HSLDS isolator with various Ra valuesare presented in Fig. 6b. It can be observed that differentvalues of Ra result in different values of ωh/ωn and Th/Tn,namely different vibration isolation performances. The shapesof both curves are concave, which signifies that both the peaktransmissibility and the resonance frequency become relativelylarge when the value of Ra is either too large or too small.Especially, the resonance frequency becomes close to 1, whichindicates that the electromagnetic mechanism has almost noeffect on the stiffness of the system. This is because there isvirtually no NS produced within this size of CWs. Hence, Ra

is a key parameter for designing the system.Clearance ratio Rg . Fig. 6c shows that a decrease in the

clearance results in a decrease in the peak transmissibility andresonance frequency. The reason for this is that a decreasein the clearance between CWs and PMs can make the mag-netic induction lines passing through the clearance becomemuch denser, consequently, greater electromagnetic NS willbe generated. This is beneficial as greater NS will counteractmore stiffness of springs, such that the equivalent stiffness ofthe system becomes smaller and thus, the resonance frequencydecreases. On the contrary, when the ratio increases to a certainextent, the generated NS will be too weak and its effect on thestiffness of system will be neglected and hence, the resonancefrequency will be 1, namely, the same as that of the passive



(

a

)

(b

)

(a) (b) (c)

Fig. 6. Simulated resonance frequency and peak transmissibility with various: (a) radial thickness ratios Rr (bw = 10 mm, ag = 0.5 mm); (b) axialthickness ratios Ra (aw = 10 mm, ag = 0.5 mm); (c) clearance ratios Rg (aw = 10 mm, bw = 10 mm).

system (no current in CWs). Hence, it is better to choose aslight clearance for the design. However, the trade-off is thatslight clearance requires extreme accuracy of assembling andmanufacturing.

B. Selecting procedureJudicious selection of the geometric parameters should be

exploited in order to realize the design objectives mentionedin Section II, namely, decreasing the natural frequency andlowering the peak transmissibility. Hence, in this section, wewill explain how the geometric parameters listed in Table Iare obtained.

Based on the analysis in Section V-A, it appears reasonableto decrease the value of Rg . However, the clearance cannotbe always reduced because of the fabricating accuracy andassembling accuracy of CWs and PMs. Therefore, a value ofRg = 0.8 (namely ag = Rgam = 0.8 mm) is adopted, whichis almost the ultimate precision that can be achieved in labtests. Second, because an increase in the radial thickness ratioRr has a slight effect on the transmissibility characteristics ifRr > 0.7, considering saving copper wires in the CWs andreducing the overall size of the prototype, an Rr close to 0.7∼ 0.8 is economical. Here, Rr = 0.77 is selected, namely,aw = 0.77am = 7.7 mm. Thus, we can obtain rc = ag +Rm = 15.8 mm and Rc = rc + aw = 23.5 mm. Finally, forthe axial thickness Ra, the minimum resonance frequency andpeak transmissibility exist when Ra is 0.9 ∼ 1.1, and hence,Ra = 1 (namely bw = Rabm = 10 mm) is selected as thedesign parameter for the proposed prototype.

VI. EXPERIMENTAL RESULTS

A. Transmissibility resultsTo compute the transmissibility of the HSLDS system,

experiments for different currents were conducted. The whitenoise was chosen as the excitation signal. The attenuationperformance was examined for a payload of 3.519 kg. Theamplitude of the displacement of the base is 0.5 mm. Notably,the relative movement between the CWs and PMs will producean eddy current damping force. Technically, the damping fac-tors obtained under different relative movements and differentcurrent magnitudes are not the same, but the difference can beignored. Furthermore, in this study, the primary target of the

1.2 A

0.9 A

0.6 A0.3 A0.0 A

Tra

nsm

issi

bil

ity

/ dB

Fig. 7. Experimental results (colored solid) and analytical predictions(black dash-dotted) of transmissibility curves for different current values.

analytical model was to predict whether the NS characteristicswould influence the isolation performance, rather than specificdamping factors of the system. Thus, the damping coefficientof the system is treated as a constant.

Transmissibility curves measured experimentally (coloredsolid curves) are illustrated in Fig. 7 alongside the theoreticalones (black dash-dotted curves) computed using (9). Whenthe current increases, the proposed system exhibits consid-erably improved vibration isolation performance because theresonance frequency is reduced from 8.80 Hz to 5.66 Hz,and the corresponding zero-crossing point (the starting fre-quency of the isolation bandwidth) shifts from 13.0 Hz to7.8 Hz. Notably, 1.2 A is adopted as the upper limit toprevent overheating of the CWs. The experimental results areconsistent with the analytical ones in both the low- and high-frequency bands. The results also show that the HSLDS systemoutperforms the passive system in terms of the vibration atten-uation, e.g., the obtained transmissibilities are −7.3 dB@10Hz and −15.4 dB@15 Hz for the HSLDS system, whereasthey are 11.3 dB@10 Hz and −7.1 dB@15 Hz for thepassive system. However, the analytical model overpredictsthe resonance frequency and the peak transmissibility becausethere is an evident discrepancy between the tested resultand the theoretical one when the current equals 1.2 A. Thisdiscrepancy exists probably owing to the slight variation ofthe damping coefficient and the accuracy of the HB method.Therefore, the divergence between the theoretical predictionand experimental verification is deemed to be acceptable.



Excitation

signal

Calculating

frequency

> fqI1 = 1.2A I2 = -1.2Ayes no

(c)

(b)

Acc

eler

atio

n / g

Q

1.2 A0 A

-1.2 A

Frequency/ Hz

Tra

nsm

issi

bil

ity/ dB

(a)T

ran

smis

sib

ilit

y/

dB

1.2 A0 A

-1.2 A

Q

Acc

elera

tio

n /

g

(a)

(b)

Time/s1086420

0

0.05

0.10

0.1

0.2

-20

-10

0

10

20

30

100

101

Frequency/ Hz

Fig. 8. Experimental results: (a) transmissibility curves; (b) amplitude ofacceleration of mass with (blue)/without (red) tuning strategy when thebase is subjected to an external excitation with the frequency of 10 Hz(upper)/5 Hz (bottom).

B. Tuning capability

The experimental results indicate that the transmissibilitycan be tuned by regulating the current. Fig. 7 also illustratesthat, in the low-frequency band (cyan), a high-stiffness system(I1 = 0 A) has a better vibration attenuation performancethan a low-stiffness system (I1 = 1.2 A). However, the resultsare opposite in the high-frequency band (orange). This alsoindicates that: (1) it is preferable to increase the stiffnessof the system in the low-frequency band. By modifying thepolarity of the current, one can reverse the direction of theelectromagnetic force, and subsequently, NS turns into PS.Consequently, the equivalent stiffness increases because itequals the superposition of this PS and the stiffness of springs;(2) a tuning strategy to obtain the best attenuation effect atfull frequency band is obtained. To be specific, NS is offin the low-frequency band; instead, an electromagnetic PSis generated by reversing the polarity of the current, andhence the system exhibits a high stiffness behavior. In contrast,in the high-frequency band, NS is on, such that the systemexhibits a low stiffness behavior. Please note that we onlyfocus on harmonic base excitations because our main purposeis to obtain the optimal isolation effect for a wide range ofexcitation frequency through tuning the current, rather than torealize vibration isolation for any types of excitation, such asmulti-frequency excitation signals.

Based on these considerations, an ON - OFF tuning strategyis explored to verify the online tuning capability of theproposed HSLDS system. As shown in Fig. 8a, point Q isthe point of intersection of two transmissibility curves whenthe currents equal 1.2 A and -1.2 A (the minus sign refers to areversed current), and the corresponding frequency of Q is fQ= 6.8 Hz. Because payload affects the natural frequency ofthe isolator, frequency fQ should be recalculated for differentpayloads. When the isolation system is subjected to a sinu-soidal base excitation, it will gather the excitation signal andcompute the main frequency. If the main frequency is lower

Position of the

payload

Second maxima?

Velocity of the

payload

Differenciate

Strategy I Strategy II

No Yes

Position of the

payload

whether reaching the

maximum value for the

second time?

Velocity of the

payload

Differenciate

No Yes

k - kaux k + kaux

Shock input

uū ≥ 0 0uu

No

Yes

ùūu

Start

Collect sinusoidal

data

Calculate the main

frequency

Lowpass filter

whether the frequency

is larger than fQ?

Current = 1.2 A

(NS is applied)Current = -1.2 A

(PS is applied)

Yes No

Fig. 9. Flow chart of the proposed stiffness regulation strategy.

than fQ (cyan), the current will be set to -1.2 A; otherwise, itwill be set to 1.2 A when the excitation frequency is greaterthan fQ (orange). The detailed procedure of this strategy isillustrated in Fig. 9. Specifically, collecting the sinusoidal datais completed by NI DAQ card PXIe 4497; a lowpass filter witha cut-off frequency 100 Hz is adopted to recreate the collecteddata; then, the main frequency component of the collected datais computed through the ‘Power Spectrum’ function and the‘Peak Search’ function provided by the Sound & VibrationToolkit of LabVIEW. Finally, the corresponding current is fedinto the CWs according to the calculated main frequency.

To verify the proposed tuning strategy, two sets of experi-ments were carried out. Specifically, 5 Hz (< fQ) and 10 Hz(> fQ) were adopted as the excitation frequencies. The resultsare illustrated in Fig. 8b, where the acceleration responses ofthe isolated payload of the passive system (I1 = 0 A) andthe system with tuning strategy are illustrated in red and blue,respectively. Fig. 8b shows that the response of the systemwith tuning (blue) is smaller than the response of the passivesystem (red). Specifically, the root mean square (RMS) ofthe acceleration amplitude is reduced by 16.3% (for 5 Hz)and 79.8% (for 10 Hz). Thus, with the ON - OFF strategy,the system outperforms both the HSLDS system in the low-frequency band and the passive system in the high-frequencyband. In other words, this strategy is effective for a wide rangeof external excitation frequencies.

Transient effect is inevitable during current switching,which can result in displacement overshoot or sudden changein the static position of the payload. For the proposed isolator,electromagnetic stiffness becomes positive when the overshootexceeds a certain point (details in Section VII), which can helplimit the overshoot and prevent instability. Furthermore, Sincesudden change in the static position are highly dependent uponthe equivalent stiffness, and the lowest equivalent stiffness(at current I = 1.2 A) is still higher than quasi-zero, suddenchanges in the static position are within a tolerable range.

Table II presents comparisons between the results obtainedfrom the proposed design and the previous studies, which alsofocused on the vibration/shock isolation with electromagneticdevices. Even though the proposed isolator has a more com-pact size, such as a smaller volume (the radial thickness and



TABLE IICOMPARISON WITH RESULTS OF PREVIOUS STUDIES

Type Proposed system Zhou [24] Ledezma [8, 10]Layout Horizontal/Vertical Horizontal Horizontal

Range of current 0 ∼ 1.2 A 0 ∼ 1.2 A 0 A, 2 ARadial thickness 7.7 mm 10.3 mm *Axial thickness 40 mm 88 mm *Turns of coil 1152 7130 *

Payload 3.519 kg 0.170 kg 0.075 kgρ 9254 kg/m3 614 kg/m3 -

Performance -7.3 dB@10 Hz -6.0 dB@10 Hz 15 dB@10 Hz-15.4 dB@15Hz

* These values were not provided in Ref. [8, 10].

axial thickness are 7.7 mm and 10×4 mm, respectively) andfewer turns of coils (1152 < 7130), it can bear a heavier load(3.519 > 0.170 > 0.075 kg), which makes it much easier tosatisfy engineering requirements. For a more straightforwarddemonstration of the degree of compactness and load capacity,a so-called volume loading rate ρ is defined. ρ has thesame dimension as density, and it is defined as load carriedper unit effective volume (in this case, the effective volumerefers to the volume of the part that generates the tunable NS,e.g., volume of CWs). As shown in Table II, the proposedprototype has a considerably large ρ, which indicates that thevibration isolation for a heavy load can be realized by a smallstructure. The reason is that, on the surface, the load capacitydepends only upon the mechanical springs. Springs with largestiffness (positive) can carry a heavier load. However, inorder to achieve the same isolation effect, the system withgreater PS should introduce greater NS to neutralize its PSaccordingly. This indicates that the proposed system is capableof generating a larger NS with such a compact structure. Thus,ρ of the proposed design is greater.

In addition, as a power supply is required to energize theCWs, the power consumption is another key criterion thatshould be considered when evaluating the system. Fig. 10shows the power consumption at each normalized resonancefrequency ωh/ωn (See V-A). As ωh/ωn shifts to the lower-frequency zone, the consumed power increases. It is no longera linear relationship because an increase in the power has amuch smaller effect upon the reduction of ωh/ωn. However,the proposed system consumes the least power for the sameωh/ωn, even though its load is the heaviest. The reason is thatthe resistance of the proposed isolator is lower than that of theother systems. Moreover, the proposed system can generategreater NS with a small current. Thus, the proposed systemshows a relatively high efficiency in realizing a similarly scaledvibration attenuation because it requires less power, especiallyat ωh/ωn < 0.75.

VII. DISCUSSION

The above sections focused on realizing vibration attenu-ation from the perspective of tuning the magnitude of thestiffness. However, as the HSLDS system behaves as a nonlin-ear system, we can also realize vibration attenuation from thestandpoint of tuning the nonlinearity. In Section IV-C, weaknonlinearity is favorable for the hardening system because of

Power

increases

ωh/ωn

Fig. 10. Consumed power of electromagnetic mechanisms measuredusing experiments.

the curve-bending phenomenon induced by the strong nonlin-earity of NS. The more the system approximates to a linearsystem, the smaller the γ will be. Thus, from the perspective ofthe vibration attenuation, a smaller γ is appropriate. Inspiredby the Helmholtz coil [31], we can obtain a linear systemby producing an approximate uniform magnetic field. For ourproposed system, this can be achieved by enlarging the axialclearance (denoted by Da) between adjacent windings. Anexample is shown in Fig. 11.

We obtain two force–displacement curves (as illustrated inFig. 11a) with the same α but different γ by precisely tuningI1 and Da. When I1 = 1.55 A and Da = 10 mm (the red curvein Fig. 11a), the force–displacement curve is an approximatestraight line, which indicates that the system is close to alinear system. This is because, if the produced magnetic field isuniform, the nonlinearity of NS will be eliminated. Therefore,the effect of the nonlinearity term γ can be neglected as itis too small. When I1 = 1.2 A and Da = 0 mm (the bluecurve in Fig. 11a), γ cannot be neglected and hence, theforce–displacement curve is nonlinear. The simulation resultsof transmissibilities also reveal the advantage of small γ (thered curve in Fig. 11b) because it shows that the resonancefrequency shifts to the left slightly for a smaller γ.

In addition, mechanical stability is also important to HSLDSisolators, especially when deformation is too large. For theproposed system, the electromagnetic stiffness within about ±5.5 mm is negative (see Fig. 12b). This range is determinedby the dimensions of the electromagnetic mechanism, andoptimal isolation performance can be achieved within thisrange because the equivalent stiffness is reduced. Beyondthis range, the electromagnetic stiffness becomes positive.Therefore, even if the deformation is too large, it is notpossible for the equivalent stiffness to become negative and thepositive electromagnetic stiffness can ensure the mechanicalstability of the proposed system.

VIII. CONCLUSION

This paper proposed an HSLDS isolator with a tunableNS. The NS is provided by a nesting-type electromagneticmechanism that consists of four coaxial CWs and four ringPMs. The NS is combined in parallel with the PS producedby mechanical springs. The equivalent stiffness of the isolatoris expressed as the superposition of the PS and the NS. Bytuning the magnitude of the current, the equivalent stiffness



α = 0.77, γ = 0.29×10-3

α = 0.77, γ = 0.02×10-3

(b)(a)

βDisplacement/mm

Forc

e/N

-15

-10

-5

0

5

10

15

0

2

4

6

8

10

12

Tra

nsm

issi

bil

ity

-5 50 0.6 1.11.00.90.80.7

Fig. 11. Simulated results: (a) force–displacement curve; (b) transmis-sibility under two different conditions. (bm = 10 mm, bw = 10 mm, Br =1.35 T , Nz = 18, Xb = 5 mm, ag = 0.5 mm, rc = 15.8 mm, Rc = 23.5mm, rm = 5 mm and Rm = 15 mm).

A B

Tra

nsm

issi

bil

ity

(d

B)

Deformation / m

Sti

ffnes

s /

N/m

Fo

rce

/ N

Eelectromagnet

Passive isolator

HSLDS isolator

N/m

(a)

(b)

(a)

(b)

N/m

-10 -5 0 5 10

mm

Fig. 12. Simulated (a) electromagnetic force and (b) stiffness when I =1.2 A.

can be adjusted dynamically. The calculation of the interactionforce/stiffness is achievable using the Amperian current mod-el. The motion equation and transmissibility characteristicsof the isolator were set up and analyzed in detail. Boththe numerical simulation analysis and experimental resultsshow that the isolator can realize better performance thanpassive system. Compared with previous studies, the proposedisolator has three outstanding advantages, i.e., a more compactstructure, heavier load capacity, and higher efficiency.

APPENDIX

The axial force between two coaxial filaments is given by

Fa (r1, r2, L) = µ0I1I2L

√k2

4r1r2

[K −

12k

2 − 1

k2 − 1E

](A.1)

where K and E are the complete first and second ellipticintegrals with modulus k2, respectively, and

k2 =4r1r2

(r1 + r2)2+ L2

(A.2)

Four steps are used to calculate the interaction force exertedbetween CWs and ring PMs. First, each turn of the CW isconsidered as a separate coil (the filament) with current I1.Second, the ring PM is considered as two cylindrical magnetswhose radii equal Rm and rm. Third, the arrangement of“turns” used to model the cylindrical PM is related to anequivalent surface current density; specifically, the equivalentcurrent in each filament is I2 = Brbm/(Nmµ0), and thenumber of “turns” Nm should be sufficiently large to ensurethat the calculation result converges to a stable value. Finally,the total force between a CW and a ring PM can be expressedas a superposition of every pair of filaments

FCM = F1 + F2 (A.3)

where

F1 = −Nm∑

nm=1

Nr∑nr=1

Nz∑nz=1

Fa (r (nr) , rm, L (nm, nz)) (A.4)

F2 =

Nm∑nm=1

Nr∑nr=1

Nz∑nz=1

Fa (r (nr) , Rm, L (nm, nz)) (A.5)

r = rc +nr − 1

Nr − 1(Rc − rc) (A.6)

L = x− 1

2(bc + bm) +

nz − 1

Nz − 1bc +

Nm − nmNm − 1

bm (A.7)

The sign of the force is determined by the directions ofthe (equivalent) current. If the direction of the applied forceexerted on the PM is identical to the positive direction of the xaxis, the force is positive, and vice versa. NS can be obtainedby differentiating FCM with respect to the relative displace-ment x, namely, −∂F /∂x. The minus sign is introduced inthe expression because the restoring force produced by theNS system is opposite to the electromagnetic force.

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Yi Sun received his BEng degrees in Mechanical Engineering and in Computer Science and Technology in 2003, and MEng degree in Mechatronic Engineering in 2006, all from Huazhong Univerisity of Science and Technology (Wuhan, China). In 2013, he received his Dr Eng degree in Robotics from Ritsumeikan University (Kyoto, Japan). From 2013 to 2016 he worked as a senior researcher at Ritsumeikan University. In July 2016, granted by the Program of Young Eastern Scholar of Shanghai, he joined Shanghai University as an Assistant Professor in School of Mechatronic Engineering and Automation. His research interests include robotics and vibration controlling.

Kai Meng received his B.Eng. degree in Mechanical Engineering from Henan University of Technology (Zhengzhou, China) in 2005. He received his M.Sc. in Mechanical Engineering from Sichuan University of Science & Engineering (Zigong, China) in 2009. He worked as a Teaching Assistant at Henan University of Engineering (Zhengzhou, China) from 2009 to 2014, and was appointed as a Lecturer in 2014. Since 2015, he has been a Ph. D Candidates at Shanghai University (Shanghai, China). His research interests include modelling and design of negative-stiffness-based vibration isolation devices.

Rongqing Xie received his BEng degrees in 2016 from School of Mechatronic Engineering and Automation, Shanghai University (China), and then continued to study for MEng degree in Mechanical Electronic Engineering in Shanghai University. His research interests include vibration and noise reduction, and machine design.

Yi Sun received his B.Eng degrees in Mechan-ical Engineering in 2003, and M.Eng degreein Mechatronic Engineering in 2006, all fromHuazhong University of Science and Technology(Wuhan, China). In 2013, he received his Dr.Engdegree in Robotics from Ritsumeikan University(Kyoto, Japan). From 2013 to 2016 he workedas a senior researcher at Ritsumeikan Univer-sity. In July 2016, granted by the Program ofYoung Eastern Scholar of Shanghai, he joinedShanghai University as an Assistant Professor.

His research interests include robotics and vibration controlling.

Jinglei Zhao received both B.Eng. degree andM.Eng degree in Mechanical Engineering fromShanghai University (Shanghai, China) in 2012and 2015. He has been a doctoral candidateat Shanghai University (Shanghai, China) since2017. His research interests include modeling ofnonlinear vibration isolation systems.



Min Wang received his B.Eng and M.Eng de-gree in Mechatronic Engineering in 2012, allfrom Wuhan University of Technology (Wuhan,China) in School of Mechanical and ElectronicEngineering. In 2018, he received his Dr.Engdegree in Vibration Isolation and Active Controlfrom Huazhong University of Science and Tech-nology (Wuhan, China). He is now working as alecturer in Shanghai University, and his researchinterests include vibration isolation and vibrationcontrolling.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

8 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING

[34] Y.-F. Lin and W.-B. Jian, “The impact of nanocontact on nanowirebased nanoelectronics,” Nano Lett., vol. 8, no. 10, pp. 3146–3150, Oct.2008.

[35] A. Asthana, T. Shokuhfar, Q. Gao, P. Heiden, C. Friedrich, and R.S. Yassar, “A study on the modulation of the electrical transport bymechanical straining of individual titanium dioxide nanotube,” Appl.Phys. Lett., vol. 97, no. 7, p. 072107, Aug. 2010.

[36] A. Cagliani, R. Wierzbicki, L. Occhipinti, D. H. Petersen, K. N.Dyvelkov, Ö. S. Sukas, B. G. Herstrøm, T. Booth, and P. Bøggild,“Manipulation and in situ transmission electron microscope char-acterization of sub-100 nm nanostructures using a microfabricatednanogripper,” J. Micromech. Microeng., vol. 20, no. 3, p. 035009,Mar. 2010.

Xutao Ye received the B.Eng. degree in electrical en-gineering from the Hong Kong University of Scienceand Technology, Hong Kong, China, in 2010, and theM.A.Sc. degree in mechanical engineering from theUniversity of Toronto, Toronto, ON, Canada, in 2012.His research interests include robotics and

automation.

Yong Zhang received the B.S. and M.S. degreesin mechatronics engineering from Harbin Instituteof Technology, Harbin, China, in 2005 and 2007,respectively, and the Ph.D. degree in electricaland computer engineering from the University ofToronto, Toronto, ON, Canada, in 2011.He is currently a Postdoctoral Fellow in the School

of Aerospace Engineering, Georgia Institute of Tech-nology, Atlanta, GA, USA. His research interests in-clude the design and fabrication of MEMS devices,micro/nanomanipulation under optical and electron

microscopy, and three-dimensional micro/nanomanufacturing.

Changhai Ru (M’07) received the Ph.D. degree inmechatronics engineering from Harbin Institute ofTechnology, Harbin, China, in 2005.He was a Postdoctoral Fellow in the Department of

Mechanical and Industrial Engineering, Universityof Toronto, Toronto, ON, Canada. He is currently aProfessor with the College of Automation, HarbinEngineering University, China. His research interestsinclude micro/nanomanipulation, nanopositioningtechnologies, and solid-state actuators’ driving andcontrol methods.

Jun Luo received the B.S. degree in mechanicalengineering from Henan Polytechnic University,Jiaozuo, China, in 1994, the M.S. degree in mechan-ical engineering from Henan Polytechnic University,Jiaozuo, China, in 1997, and the Ph.D. degree fromthe Research Institute of Robotics, Shanghai JiaoTong University, Shanghai, China, in 2000.He is a Professor with the School of Mechatronic

Engineering and Automation, Shanghai University,Shanghai, China. He is the Head of Precision Me-chanical Engineering Department, Shanghai Univer-

sity, and the Vice Director of Shanghai Municipal Key Laboratory of Robotics.His research areas include robot sensing, sensory feedback, mechatronics, man-machine interfaces, and special robotics.

Shaorong Xie received the B.S. and M.S. degreesin mechanical engineering from Tianjin PolytechnicUniversity, Tianjin, China, in 1995 and 1998,respectively, and the Ph.D. degree in mechanical en-gineering from the Institute of Intelligent Machinesat Tianjin University and the Institute of Roboticsand Automatic Information System, Nankai Univer-sity, Nankai, China, in 2001.She is a Professor with the School of Mechatronic

Engineering and Automation, Shanghai University,Shanghai, China. Her research areas include ad-

vanced robotics technologies, bionic control mechanisms of eye movements,and image monitoring systems.

Yu Sun (S’01–M’03–SM’07) received the B.S. de-gree in electrical engineering from Dalian Universityof Technology, Dalian, China, in 1996, the M.S.degree from the Institute of Automation, ChineseAcademy of Sciences, Beijing, China, in 1999, andthe M.S. degree in electrical engineering and thePh.D. degree in mechanical engineering from theUniversity of Minnesota, Minneapolis, MN, USA,in 2001 and 2003, respectively.He is a Professor with the Department of Me-

chanical and Industrial Engineering and is jointlyappointed with the Institute of Biomaterials and Biomedical Engineering andthe Department of Electrical and Computer Engineering, University of Toronto,Toronto, ON, Canada. He is the Canada Research Chair in Micro and NanoEngineering Systems. His research areas include the design and fabrication ofM/NEMS devices, micronanorobotic manipulation, and the manipulation andcharacterization of cells, biomolecules, and nanomaterials.

Yu Sun received the B.S. degree in electrical en-gineering from Dalian University of Technology,Dalian, China, in 1996, the M.S. degree fromthe Institute of Automation, Chinese Academyof Sciences, Beijing, China, in 1999, and theM.S. degree in electrical engineering and thePh.D. degree in mechanical engineering fromthe University of Minnesota, Minneapolis, MN,USA, in 2001 and 2003, respectively. He is aProfessor with the Department of Mechanicaland Industrial Engineering and is jointly appoint-

ed with the Institute of Biomaterials and Biomedical Engineering andthe Department of Electrical and Computer Engineering, University ofToronto, Toronto, ON, Canada. He is the Canada Research Chair inMicro and Nano Engineering Systems. His research areas include thedesign and fabrication of M/NEMS devices, micronanorobotic manipu-lation, and the manipulation and characterization of cells, biomolecules,and nanomaterials.

JOURNAL OF IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 14, NO. 8, AUGUST 2017 10




Yi Sun Yi Sun received his BEng degrees in Me-chanical Engineering and in Computer Science andTechnology in 2003, and MEng degree in Mecha-tronic Engineering in 2006, all from Huazhong Uni-versity of Science and Technology (Wuhan, China).In 2013, he received his Dr Eng degree in Roboticsfrom Ritsumeikan University (Kyoto, Japan). From2013 to 2016 he worked as a senior researcher atRitsumeikan University. In July 2016, granted by theProgram of Young Eastern Scholar of Shanghai, hejoined Shanghai University (Shanghai, China) as an

Assistant Professor in School of Mechatronic Engineering and Automation.His research interests include robotics and vibration controlling.




Kai Meng Kai Meng received his B.Eng. degreein Mechanical Engineering from Henan Univer-sity of Technology (Zhengzhou, China) in 2005.He received his M.Sc. in Mechanical Engineeringfrom Sichuan University of Science & Engineering(Zigong, China) in 2009. He worked as a Teach-ing Assistant at Henan University of Engineering(Zhengzhou, China) from 2009 to 2014, and wasappointed as a Lecturer in 2014. Since 2015, hehas been a Ph. D Candidate at Shanghai University(Shanghai, China). His research interests include

modelling and design of negative-stiffness-based vibration isolation devices.

Shujin Yuan received his BEng degree in Mechanical Engineering and Automation from Shanghai University (Shanghai, China) in 2016, and then continued to study for MEng degree in Mechatronic Engineering at Shanghai University. His research interests include Vibration and noise control, and nonlinear systems

Jinglei Zhao received both B.Eng. degree and M.Eng degree in Mechanical Engineering from Shanghai University (Shanghai, China) in 2012 and 2015. He has been working toward the Ph.D degree since 2017 at Shanghai University (Shanghai, China). His research interests include modeling, control, and simulation of nonlinear vibration isolation systems.

Shujin Yuan Shujin Yuan received his BEng degreein Mechanical Engineering and Automation fromShanghai University (Shanghai, China) in 2016,and then continued to study for MEng degree inMechatronic Engineering at Shanghai University.His research interests include Vibration and noisecontrol, and nonlinear systems.




Rongqing Xie Rongqing Xie received his BEng de-grees in 2016 from School of Mechatronic Engineer-ing and Automation, Shanghai University (Shanghai,China), and then continued to study for MEng degreein Mechanical Electronic Engineering in ShanghaiUniversity. His research interests include vibrationand noise reduction, and machine design.



Jinglei Zhao Jinglei Zhao received both B.Eng.degree and M.Eng degree in Mechanical Engineer-ing from Shanghai University (Shanghai, China) in2012 and 2015. He has been a doctoral candidateat Shanghai University since 2017. His researchinterests include modeling, control, and simulationof nonlinear vibration isolation systems.

Jun Luo Jun Luo received the B.S. and M.S. degreesin mechanical engineering from Henan PolytechnicUniversity (Jiaozuo, China) in 1994 and 1997, re-spectively, and the Ph.D. degree from the ResearchInstitute of Robotics, Shanghai Jiao Tong University(Shanghai, China) in 2000. He is a Professor in theSchool of Mechatronics Engineering and Automa-tion, Shanghai University (Shanghai, China). He isthe Head of the Precision Mechanical EngineeringDepartment at Shanghai University and Vice Di-rector of the Shanghai Municipal Key Laboratory

of Robotics. His research areas include robot sensing, sensory feedback,mechatronics, manCmachine interfaces, and special robotics.

Yan Peng Yan Peng received the Ph.D. degreein pattern recognition and intelligent systems fromShenyang Institute of Automation, Chinese Acade-my of Sciences (Shenyang, China) in 2009. Sheis currently a Professor with Shanghai University(Shanghai, China) where she is the Executive Deanof the Research Institute of USV Engineering. Hercurrent research interests include modeling and con-trol of unmanned surface vehicles, field robotics, andlocomotion systems.

Shaorong Xie Shaorong Xie received the B. Eng.and M. Eng. degrees in mechanical engineeringfrom Tianjin Polytechnic University (Tianjin, China)in 1995 and 1998, respectively, and the Dr. Eng.degree in mechanical engineering from the Instituteof Intelligent Machines at Tianjin University andthe Institute of Robotics and Automatic InformationSystem, Nankai University (Tianjin, China) in 2001.She is a Professor with the School of MechatronicEngineering and Automation, Shanghai University(Shanghai, China). Her research areas include ad-


Huayan Pu Huayan Pu received the M.Sc.and Ph.D. degrees in mechatronics engineeringfromHuazhong University of Science and Technolo-gy (Wuhan, China) in 2007 and 2011, respectively.Currently, she is a Professor at Shanghai University(Shanghai, China). Her current research interestsinclude vibration controlling and robotics. Dr. Puwas awarded the best paper in biomimetics at the2013 IEEE International Conference on Roboticsand Biomimetics. She was also nominated as thebest conference paper finalist at the 2012 IEEE

International Conference on Robotics and Biomimetics.

Yang Yang Yang Yang received his PhD degree in2015 from Ritsumeikan University (Kyoto, Japan).From 2015 to 2016, he was a postdoctoral researcherat Department of Mechanical and Aerospace En-gineering, Tokyo Institute of Technology (Toky-o, Japan). In July 2016, granted by the Programof Young Eastern Scholar of Shanghai, he joinedShanghai University (Shanghai, China) as an Assis-tant Professor in School of Mechatronic Engineeringand Automation. His research interests include softrobots, mobile robots, and terramechanics.

Huayan Pu received the M.Sc. and Ph.D.degrees in mechatronics engineering fromHuazhong University of Science and Technology(Wuhan, China) in 2007 and 2011, respective-ly. Currently, she is a Professor at ShanghaiUniversity (Shanghai, China). Her current re-search interests include vibration controlling androbotics. Dr. Pu was awarded the best paperin biomimetics at the 2013 IEEE InternationalConference on Robotics and Biomimetics. Shewas also nominated as the best conference pa-

per finalist at the 2012 IEEE International Conference on Robotics andBiomimetics.






























Jun Luo received the B.S. and M.S. degrees inmechanical engineering from Henan PolytechnicUniversity (Jiaozuo, China) in 1994 and 1997,respectively, and the Ph.D. degree from theResearch Institute of Robotics, Shanghai JiaoTong University (Shanghai, China) in 2000. Heis a Professor in the School of MechatronicsEngineering and Automation, Shanghai Univer-sity (Shanghai, China). He is the Head of thePrecision Mechanical Engineering Departmentat Shanghai University and Vice Director of the

Shanghai Municipal Key Laboratory of Robotics. His research areasinclude robot sensing, sensory feedback, mechatronics, man-machineinterfaces, and special robotics.






























Yan Peng received the Ph.D. degree in pat-tern recognition and intelligent systems fromShenyang Institute of Automation, Chinese A-cademy of Sciences (Shenyang, China) in 2009.She is currently a Professor with Shanghai U-niversity (Shanghai, China) where she is theExecutive Dean of the Research Institute of USVEngineering. Her current research interests in-clude modeling and control of unmanned surfacevehicles, field robotics, and locomotion systems.






























Shaorong Xie received the B. Eng. and M. Eng.degrees in mechanical engineering from TianjinPolytechnic University (Tianjin, China) in 1995and 1998, respectively, and the Dr. Eng. degreein mechanical engineering from the Institute ofIntelligent Machines at Tianjin University andthe Institute of Robotics and Automatic Informa-tion System, Nankai University (Tianjin, China)in 2001. She is a Professor with the Schoolof Mechatronic Engineering and Automation,Shanghai University (Shanghai, China). Her re-

search areas include advanced robotics technologies, bionic controlmechanisms of eye movements, and image monitoring systems.

Yi Yang received his Doctoral degree in Me-chanical Engineering from Beihang Universi-ty (Beijing, China) in 2012. He has beenan associate professor at Shanghai Universi-ty(Shanghai, China) since 2016. His researchinterests include designing, modeling and syn-thesizing of mechanical systems.

high-static-low-dynamic stiffness isolator with tunable ...amnl.mie.utoronto.ca/data/j178.pdf ·...

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