study on the stiffness correction method of novel antivibration...

Research ArticleStudy on the Stiffness CorrectionMethod of Novel Antivibration Bearing forUrban Rail Transit Viaduct

Weiping Xie12 Youfu Du2 Liangming Sun12 Agostino Marioni3 and Xu Liang23

1Hubei Key Laboratory of Roadway Bridge amp Structure Engineering Wuhan University of TechnologyWuhan 430070 China2School of Civil Engineering and Architecture Wuhan University of Technology Wuhan 430070 China3Wuhan Hirun Engineering Equipment Co Ltd Wuhan 430084 China

Correspondence should be addressed to Liangming Sun sunliangming126com

Received 30 April 2017 Revised 20 July 2017 Accepted 29 August 2017 Published 18 October 2017

Academic Editor Lutz Auersch

Copyright copy 2017 Weiping Xie et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel antivibration bearing is developed to reduce the train-induced vibrations for urban rail transit viaduct It adopts fourhigh-damping thick rubber blocks stacking slantingly to reduce the vibration and provide large lateral stiffness But the existingstiffness calculationmethod of laminated rubber bearing aimed at horizontal seismic isolation is unsuitable for thick rubber bearingdesigned for vertical vibration reduction First the stiffness correctionmethod has been proposed based on the characteristics of thenovel bearing Second to validate the design method mechanical property tests are performed on a specimen of the novel bearingwith design frequency at 8Hz and with 3500 kN bearing capacity Third damping effects of the novel bearing are investigatedthrough impulse vibration tests on scaled models Results show that the mechanical property of the novel bearing can satisfy theengineering demand and the proposedmethod for calculating the stiffness agreeswell with the test resultsTheoverall insertion lossof the novel bearing is 1349 dB which is 532 dB larger than that of steel bearing showing that the novel bearing is very promisingto be used in the field to mitigate train-induced vibrations

1 Introduction

Using viaduct as its main structure rail transit connectsthe main cities or economic regions It plays a vital role inthe public transportation Train-induced bridge vibrationswill propagate to the subsoil via the bearings piers andfoundations and then spread to the surroundings causingthe vibration of surrounding ground the secondary vibrationof adjacent buildings and its associated structural noiseSince most elevated rail lines close to or even run across thedensely populated areas and high-tech industrial parks incities the vibration will not only affect the structural safetyof the adjacent ancient buildings and peoplersquos normal life butalso may have a serious impact on the normal use of thatvibration-sensitive high precision instruments in the nearbyhospitals schools and research institutions [1] Mitigatingat the vibration source and along the vibration propagation

path are two major ways to circumvent such train-inducedvibrations problem [2] At the vibration source the train-bridge system shall be treated sophisticatedly with focus onthe vibration mitigation Elastic track structure [3] tunedmass dampers [4] and fluid viscous dampers [5] are commoncountermeasurements applied in the field But the designis sophisticated and costly The other way is to control thevibration along propagation path Open or in-filled trenches[6 7] barriers of piles [8ndash10] and wave impedance blocks[11 12] are found to be adopted to mitigate vibrations Butthe construction is difficult and site conditions are restrictedTherefore economical and effective countermeasures arebeing urgently sought

The bridge bearing which connects the superstructureand piers is on the route of the train-induced vibration prop-agation and plays a key role as the target of vibration controlBut most existing bridge bearings are renowned for their

HindawiShock and VibrationVolume 2017 Article ID 1402301 15 pageshttpsdoiorg10115520171402301

2 Shock and Vibration

antiseismic function such as laminated rubber bearings [13]SMA-based rubber bearings [14] and fiber-reinforced rubberbearings [15] Those bearings have deficient performance ofvertical vibrationmitigation because of the high compressionstiffness Considering the dominant direction of the train-induced vibration is vertical retrofits have to be done on theexisting rubber bearings

To mitigate the train-induced vibrations elastic bear-ing pad (EBP) with the assorted shear key (SK) as thesupported system of the bridge has been applied to about5 km of Taiwan high speed railway [16] Later this kindof antivibration bearing was also adopted by the YichangYangtze River Railway Bridge in Yichang-Wanzhou Railwayand the Minjiang River Railway Bridge in Fuzhou-XiamenRailway to reduce the train-induced vibrations [17] Sun etal [18] testified the damping effect of EBP and pot rubberbearing when trains are running on the Yichang YangtzeRiver Railway Bridge Tests result showed that the overallinsertion loss between the upper and lower plates for EBP andpot rubber bearingwas 1340 dB and 965 dB respectively andEBP could reducemore vertical train-induced vibrations thanpot rubber bearing in most frequency components

Li et al [19 20] analyzed the effect of elastic bearings ontrain-induced vibrations by simulating the elastic bearingsas spring-damper elements The results showed that thestiffness of elastic bearings had marginally influenced wheelunloading rate and the vertical acceleration of the vehiclebecause the elastic bearings could absorb the vibrations inthe medium and high frequency bands and amplify theirown vibration of natural frequency band Besides mostresearches [21ndash25] about the elastic bearings were simulatedas spring elements to explore the impact of the dynamicresponses of vehicle-bridge interaction system For exampleKawatani et al [21] analyzed dynamic responses of vehicle-bridge interaction system of certain highway bridge withsteel bearings compared to that with elastic bearings basedon numerical simulation method The results showed thatelastic bearings could effectively reduce the high frequencyvibration Through the theoretical analysis Yang et al [2324] studied the impact on dynamic responses of vehicle-bridge interaction system exerted by elastic bearings undermoving train loads The results indicated that the elasticbearings could prevent the transmission or dissipation ofvehicle-induced forces from the superstructure to the groundcausing the huge amount of train-induced vibrations energyaccumulated and amplified on the bridge during its passage

The above works indicated that elastic bearing withcertain flexibility in vertical direction can reduce the train-induced vertical vibrations transferred to the substructureCurrently only EBP has been preliminarily applied to miti-gate train-induced vibrations but it must assort SK to resistlateral load because of its small horizontal stiffnessThereforebased on the attenuationmechanismof antivibration bearinga novel antivibration bearing with four high-damping thickrubber blocks stacking slantingly is proposed to mitigatevertical vibrations in this paper Compared with EBP thenovel bearing can mitigate the train-induced vertical vibra-tions more effectively and provide a large lateral stiffnessto limit the lateral displacement caused by train braking

or turning at a high speed The straight forward design ofsuch rubber bearing with lowmanufacturing costs makes thedevice promising to be used in the field

Yabana and Matsuda [26] and He et al [27] conductedmechanical property tests on thick rubber bearing Resultsshowed that large compression deformation of thick rubberbearing would be produced under design pressure and thecalculation method of compression stiffness of laminatedrubber bearing aimed at horizontal seismic isolation was notsuitable for thick rubber bearingTherefore the calculation ofstiffness of the novel bearing with thick rubber blocks mustbe corrected Considering the novel antivibration bearingis modeled linearly in the train-bridge interaction systemthe stiffness correction method based on multiple iterationswith design compression displacement has been proposed Tovalidate the design method of the novel bearing mechanicalproperty tests are performed on a specimen Finally dampingeffects of the novel bearing are investigated through impulsevibration tests on scaled models

2 Design of Novel Antivibration Bearing

21 Antivibration Mechanism Rail transit viaduct withantivibration bearing can be treated as mass-spring-dampersystem It can mitigate the sensitivity of the substructureto the train-induced vibrations over the superstructure byinserting a simple harmonic oscillator with lower naturalfrequency [16] It can be described as antivibration systemwith single degree of freedom as shown in Figure 1

The mass block represents the bridge superstructureAssume that the mass block and foundation are rigid andthe elastic spring has damping characteristic 119898 is the massof the block in the antivibration system 119896 is spring stiffness119888 is viscous damping coefficient 119865(119905) is external force and119909(119905) is vertical vibration displacement of the mass blockWhen motivated by the external harmonic excitation 119865(119905) =1198650 sin(120579119905) the motion equation of the mass block is

119898 (119905) + 119888 (119905) + 119896119909 (119905) = 1198650sin (120579119905) (1)

Based on the theory of structural dynamics [28] thetransmissibility coefficient of the antivibration system is

119879 =radic1 + (2120585120573)2

radic(1 minus 1205732)2 + (2120585120573)2 (2)

where 120573 = 120579120596 is the frequency ratio 120579 is the circularfrequency of the external harmonic excitation120596 is the naturalcircular frequency of the system and 120585 is the damping ratio

The variation curve of transmissibility coefficient 119879 withthe frequency ratio120573 for discrete values of the damping ratio 120585is shown in Figure 2 It is indicated that all curves of differentdamping ratios pass through the same point when frequencyratio120573 = 212 Clearly because of this feature the effectivenessof vibration reduction system will be enhanced by increasingthe dampingwhen120573 lt 212 Similarly the effectivenesswill bedecreased by increasing the dampingwhen120573 gt 212 Since thetransmissibility coefficients for 120573 gt 212 are generally much

Shock and Vibration 3

F(t)

x(t)

c

m

k

Figure 1 Antivibration system with single degree of freedom

0 1 2 30

1

2

3

Tran

smiss

ibili

ty co

effici

ent T

Frequency ratio 212

= 0 = 15 = 14 = 13

= 12 = 1 = 2

Figure 2 Transmissibility coefficient

lower than those for 120573 lt 212 it is more efficient to applycountermeasurements at the region with high frequencyratio However this is not always practical because the systemmust operate below 120573 = 212 in many cases for some intervalsof time and in many other cases it may even operate nearthe resonant condition 120573 = 1 Consequently the principleof vibration mitigation is to increase the frequency ratioas much as possible by decreasing natural frequency of thevibration system meanwhile to provide proper damping forthe bearing to avoid the resonance

22 Design Method The novel antivibration bearing isdesigned for urban rail transit viaduct with simply supportedbox girder The main type of train used in Chinese urbanrail transit is Type-B metro vehicle and its distance betweenbogies in the same carriage (119871119888) or adjacent carriages (119871119887)is 126m or 19m while between the axles (119871119886) it is 22mConsidering the normal operating speed as 60 kmh therange of variation of the train excitation frequencies is from

088Hz to 758Hz Therefore it is appropriate to controlthe vertical natural frequency of the bridge around 8ndash10Hzby proper designing the compression stiffness of the novelbearing which can efficiently avert from the train excitationfrequencies and the noise frequency of the upper structure(10ndash100Hz) Generally the antivibration bearing is modeledlinearly in the train-bridge interaction system thus its naturalfrequency119891 (Hz) can be calculated based on the deflection119863(m) of bridge structure under static load if the damping isignored (3) And from the load-deformation curve obtainedthrough the mechanical property test the compression stiff-ness of the bearing can be estimated

119891 = radic1198922120587radic119863 asymp 1

2radic119863 (3)

where 119892 is the gravitational accelerationFrom (3) the natural frequency of the antivibration

bearing can be decreased with the increase of the deflectionof the bridge but the deflection should not exceed 3-4mm orit would impact the serviceability and safety of running trainHence the appropriate natural frequency of the novel bearingshould be set around 8ndash10Hz But in some cases the verticalnatural frequency of the bridge with the novel bearingmay belower than 8Hz but generally greater than 4Hz (dependingon the bridge type mass and span length) It overlaps withthe axis frequency but is far greater than the bogie frequencyActually the axle frequency 119891119886 (V119871119886) exerts less influenceon the vibration response of train-bridge interaction systembecause the wavelength is short and the energy input fromthe track is small The resonance response mainly dependson bogie frequency 119891119887 (V119871119887) or 119891119888 (V119871119888) Considering themaximum speed as 80 kmh the resonance frequency is lessthan 176Hz Thus only little effects would be conductedon the vibration response of train-bridge interaction systemwhen the natural frequency of the bridge is lower than 8Hz

The structure diagrams of novel antivibration bearing areshown in Figure 3where two rubber blocks are120572 inclined sideby side on the left and another two are laid symmetricallyon the right The value range of 120572 is 20∘ndash70∘ The lateraldirection of the novel bearing is fixed and the longitudinaldirection is moveable To satisfy the different engineeringdemand the novel bearing can be designed in differentfrequency and bearing capacity by changing the parametersof rubber block The compression stiffness of the novelbearing can ensure the vertical capacity of urban rail transitviaduct and reduce the bridge deflection under dynamic loadCertain horizontal stiffness in lateral direction can limit thelateral displacement caused by extra horizontal load whentrain is braking or turning at a high speed ensuring thesafety and stability of running trains And smaller horizontalstiffness in longitudinal direction can ensure the longitudinaldisplacement of the bridge caused by thermal effect of girderThe application of novel antivibration bearing can increasethe frequency ratio 120573 by decreasing the circular naturalfrequency 120596 of the bridge and thus the frequency ratio 120573can be adjusted to the damping range to meet the expecteddamping effect


(1)

(2)

(3)(4)

(5)

(6)(7)(8)

(9)(10)

(a)

(2)

(3)

(6)

Lateral (fixed direction)

Long

itudi

nal (

mov

able

dire

ctio

n)

(b)

Figure 3The structure diagram of novel antivibration bearing (a) front view and (b) relative location arrangement diagram of rubber blocksNotes (1) Upper plate (2) high-damping thick rubber block (3) lower plate (4) anchor stud (5) connection plate (6)sim(9) bolt (10) nut

23 Stiffness Correction Method

231 Stiffness Calculation for Single Rubber Block The effec-tive size of rubber block that constitutes the novel bearing is119886 times 119886 Based on Chinese national standard GB206882-2006[29] the shape coefficient of the rubber block is

1198781 =1198864119905119903

1198782 =119886119899119905119903

(4)

where 119905119903 is the thickness of single layer rubber and 119899 isnumber of rubber layers

Horizontal equivalent stiffness is

119870ℎ =119866119860119899119905119903 (5)

where 119866 is the shear modulus of rubber and 119860 is effectiveloaded area of rubber block

Compression stiffness is

119870119881 =119864119888119860119899119905119903

(6)

where 119864119888 is the compression elasticity modulus of rubber andthe empirical equation 119864119888 = 3119866(1 + 211987821) is adopted in thispaper [30]

232 Stiffness Calculation for Novel Antivibration BearingBased on the composition and separation of mechanics thecompression stiffness of the novel bearing can be calculatedthrough the mechanical calculation model

119870119873 = (119870119881cos2120572 + 119870ℎsin2120572) times 4 (7)

Horizontal equivalent stiffness in longitudinal directionis

119870ℎ1 = 4119870ℎ (8)

Horizontal equivalent stiffness in lateral direction is

119870ℎ2 = (119870119881sin2120572 + 119870ℎcos2120572) times 4 (9)

where 120572 is vertical inclination angle of rubber block

233 Stiffness Correction The stiffness calculation equationsof rubber bearings are all based on design pressure 1198750 inthe test methods of elastomeric seismic-protection isolators[31] Different from the laminated rubber bearing aimed athorizontal seismic isolation the thick rubber bearing hasthick single layer rubber and thus the restraining effect fromthe internal steel plate to the rubber layer is weaker Weakerrestraintswould cause smaller compression stiffness and largecompression deformation would be expected under designpressure 1198750Therefore for the thick rubber bearing the effectof large compression deformation on the shape coefficientcannot be ignored in the stiffness calculation Since the novelbearing is composed of thick rubber blocks its stiffnesscalculation method must be corrected

Four thick rubber blocks of the novel bearing will havecompression deformation and shear deformation simultane-ously under design pressure 1198750 as shown in Figure 4 Thecompression deformation of each rubber block is 119889 cos120572and the shear deformation is 119889 sin120572 when compressiondisplacement of the novel bearing is 119889 The deformationof single layer rubber is shown in Figure 5 where 119889V =119889 cos120572119899 and 119889ℎ = 119889 sin120572119899 The shape coefficient 1198781will increase with the decrease of 119905119903 caused by compressiondeformation and the effective loaded area 119860 will decrease byshear deformation


d

d ＭＣＨ

d ＝ＩＭ

Figure 4 Deformation of the novel bearing under compressionload

d

tr minus d

dℎdℎ a minus dℎ

Figure 5 Deformation of single layer rubber

Therefore the horizontal equivalent stiffness of singlerubber block is corrected as

1198701015840ℎ =119866119860

119899 (119905119903 minus 119889V) (10)

Shape coefficient 1198781 will turn into

11987810158401 =119886

4 (119905119903 minus 119889V) (11)

Compressive elasticity modulus 119864119888 will turn into

1198641015840119888 = 3119866 (1 + 2119878101584021 ) (12)

Compression area of single layer rubber will turn into

1198601015840 = 119886 times (119886 minus 119889ℎ) (13)

And compression stiffness is corrected as

1198701015840119881 =11986410158401198881198601015840

119899 (119905119903 minus 119889V) (14)

Putting the corrected horizontal equivalent stiffness andcompression stiffness of single rubber block into calculationequations (7)ndash(9) the corrected stiffness of the novel bearingcan be calculated

Therefore to carry out stiffness correction of the novelbearing the compression displacement 119889 under design pres-sure 1198750 must be confirmed at first Considering the novelantivibration bearing is modeled linearly in the train-bridgeinteraction system 1198891 can be obtained through dividing thedesign pressure 1198750 by the original compression stiffness 119870119881

Table 1 Design parameters of the specimen of the novel bearing

Rubber blockRubber hardness 60Shear modulus 119866 (MPa) 08Effective size 119886 times 119886 (mm) 300 times 300Overall thickness (mm) 995Primary shape factor 1198781 455Secondary shape factor 1198782 606Specimen of the novel bearingFrequency (Hz) 8Vibration damping ratio 120585 10Vertical capacity (kN) 3500Lateral capacity (kN) 700Lateral displacement (mm) plusmn0Longitudinal displacement (mm) plusmn50

Figure 6 Test specimen of novel antivibration bearing

and 1198701198811 can be obtained based on 1198891 1198892 = 11987501198701198811 andthen the value of 119889 will tend toward stability after multipleiterations and it will be utilized to correct the stiffness of thenovel bearing Besides the displacement 119889 can be confirmedthrough compression test

3 Mechanical Property ofNovel Antivibration Bearing

31 Specimen and Testing Apparatus To validate the designmethod mechanical property tests are performed on aspecimen of the novel bearing with design natural frequencyat 8Hz andwith 3500 kNbearing capacityThe design param-eters of the specimen are shown in Table 1 The inclinationangle 120572 of rubber block is 45∘

The specimen and testing equipment are fixed mechan-ically through an external fixing plate to avoid the relativesliding between the specimen and test platform as shownin Figure 6 The mechanical property tests are performedthrough 75000 kN multipurpose testing machine as shownin Figure 7 The machine can conduct dynamic control inboth vertical and horizontal direction simultaneously Per-formance parameters of this testing machine are as followsvertical dynamic load 75000 kN horizontal dynamic load


Table 2 Mechanical property test program of novel antivibration bearing

Test types Loading direction Amplitude LoadingfrequencyHz

Loadingwaveform

VerticalloadskN

Cycle-index

Compression property Vertical 3500 3

Shear property Longitudinal plusmn50mm 0005 2600 3Lateral plusmn700 kN 02 2600 3

Shearing strain correlation Longitudinal25mm 05 Sine 2600 350mm 05 Sine 2600 375mm 05 Sine 2600 3

Loading frequency correlation Longitudinal

50mm 0001 Ramp 2600 150mm 0005 Ramp 2600 150mm 001 Ramp 2600 350mm 01 Sine 2600 350mm 05 Sine 2600 350mm 10 Sine 2600 350mm 20 Sine 2600 3

Loading times correlation Longitudinal 50mm 05 Sine 2600 50Ultimate shear property Longitudinal plusmn75mm 3500

Figure 7 Multifunctional testing machine

6000 kN maximum vertical displacement 120mm max-imum horizontal displacement plusmn600mm and maximumhorizontal peak velocity 1000mms

32 Testing Program The mechanical property tests arestrictly performed according to GBT 206881-2007 [31]Three-cyclic loading of 0-119875max-0 will be conducted in verticaldirection during the compressive property test among which119875max is maximum design pressure 3500 kN Displacementloading in longitudinal direction and horizontal load loadingin lateral direction are adopted in shear property test Shearproperty correlation tests include the correlation of shearingstrain loading frequency and loading time which mainlystudy horizontal mechanical property under varying hori-zontal deformation After the correlation tests the ultimateshear property tests are performed in longitudinal positivedirection and negative direction respectively to measure theultimate shear displacement ability of the test specimenunderthe maximum design pressure The detailed testing programis shown in Table 2

33 Definition of Mechanical Property Index The calculationequation of compression stiffness is

119870119873 =1198752 minus 11987511198842 minus 1198841

(15)

where1198751 is 0711987501198752 is 1311987501198750 is the design pressure 2600 kNin normal train operation and 1198841 and 1198842 are compressiondisplacement corresponding to the third cycle of compressionloads 1198751 and 1198752 respectively

The equation of horizontal equivalent stiffness is

119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)

where 1198761 is the maximum shear force 1198762 is the minimumshear force 1198831 is maximum displacement and 1198832 is mini-mum displacement

The equation of horizontal equivalent damping ratio is

ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)

where Δ119882 is envelop area of the third cycle of the hystereticloops

34 Results and Discussion

341 Compression Property and Shear Property Compressiveload-displacement curve under three-cyclic loading is shownin Figure 8 Based on (15) compression stiffness 119870119873 of thespecimen is 4798 kNmm which can ensure the verticalcapacity of urban rail transit viaduct

Horizontal load-displacement curves of the specimenunder three-cyclic loading are shown in Figure 9 The hori-zontal load shown in the figure comprises the actual shearing


Table 3 Comparison among the theoretical stiffness and measured stiffness

Stiffness Measured Standard calculated Error Corrected value Error119870119873 (kNmm) 4798 3720 225 4719 17119870ℎ1 (kNmm) 731 580 207 632 157119870ℎ2 (kNmm) 8614 3720 568 4719 452

Table 4 Test results of119870ℎ1 in different shear strain

Shear strain 1198761 (kN) 1198762 (kN) 1198831 (mm) 1198832 (mm) 119870ℎ1 (kNmm) Normalization50 1950lowast minus1929lowast 2459 minus2417 796 108100 3665lowast minus3596 4936 minus4913 737 100150 5050lowast minus5031lowast 737 minus736 684 093Notes The value with lowast is actual shear load which is equal to horizontal load minus the friction of machinery equipment the same in Tables 5 and 6

0 2 4 6 80

1000

2000

3000

4000

Compression displacement (mm)

Com

pres

sion

load

(kN

)

Figure 8 Compressive load-displacement curve under three-cyclicloading

load and the friction of machinery equipment itself Thenthe actual shearing load is equal to horizontal load minusthe friction of machinery equipment Based on (16) hori-zontal equivalent stiffness of the specimen in longitudinaldirection (119870ℎ1) and lateral direction (119870ℎ2) is 731 kNmmand 8614 kNmm respectively Thus the measured 119870ℎ1 issmaller which can ensure the horizontal displacement of thelongitudinal bridge caused by thermal effect of girder Basedon (17) the equivalent damping ratio ℎeq in longitudinaldirection is 96 showing the specimen possesses greatenergy-dissipating capacity Besides Figure 9(b) indicatesthat the lateral displacement of the specimen is less than 1mmwhen the horizontal load reaches the design lateral bearingcapacity 700 kN It shows that119870ℎ2 of the specimen is sufficientto resist the expected horizontal load in the lateral directionof bridge and to limit the lateral displacement caused by trainbraking or turning at a high speed

The theoretical stiffness of the specimen can be calculatedbased on the stiffness calculation method mentioned inSection 23 It should be noted that the design compressiondisplacement119889 required for stiffness correction is obtained bytrialThe deviation between 1198895 = 551mmand 1198894 = 552mm

is less than 1 Thus the iteration number should be set to5 and the final design compression displacement 119889 set to551mm Figure 8 shows that the measured compression dis-placement of the specimen is 583mmwhen the compressionload is 2600 kN The error between measured compressiondisplacement and design compression displacement is only55 It proves that the design compression displacementafter multiple iterations has high precision

Comparison among the theoretical stiffness and mea-sured stiffness of the specimen is shown inTable 3 It indicatesthat the error between corrected value and measured valueis smaller than that of standard calculated value whethercompression stiffness or horizontal equivalent stiffness 119870ℎ2of the specimen is much larger than theoretical value That isbecause the lateral deformation is less than 1mm (shearingstrain 120574 lt 2) in the test and the actual shear modulusis much larger than theoretical value (120574 = 100) when 120574is minimal Higher horizontal equivalent stiffness in lateraldirection means stronger lateral load resistance to meet theoperating requirements better Since the damping effect ofthe novel bearing depends mainly on compression stiffnessand the error between corrected compression stiffness andmeasured compression stiffness is only 17 the stiffness cor-rection method is much more consistent with real situation

342 Correlation of Shear Property in Longitudinal DirectionThe horizontal load-displacement curves of the specimenin different shear strain are shown in Figure 10 And thecorresponding test results of 119870ℎ1 are shown in Table 4 Itis indicated that 119870ℎ1 decreases with the increase of longi-tudinal displacement which agrees with characteristics ofthe hysteresis loop of high-damping rubber Based on theshearing strain 100 (50mm) the variation range of119870ℎ1 willbe 093ndash108

The horizontal load-displacement curves of the specimenin different loading frequency are shown in Figure 11 And thecorresponding test results of 119870ℎ1 are shown in Table 5 It isindicated that119870ℎ1 of the specimendecreaseswith the increaseof loading frequency Based on the loading frequency 05Hzthe variation range of119870ℎ1 will be 093ndash112

The loading time correlation test of the specimen requiresrepetitive loading for 50 times Considering the capacity of


minus60 minus40 minus20 0 20 40 60minus600

minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)

Figure 9 Horizontal load-displacement curves under three-cyclic loading (a) longitudinal and (b) lateral


minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)

minus80 minus60 minus40 minus20 0 20 40 60 80minus800

minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)

Figure 10 Curves of the shearing strain correlation test (a) 50 (b) 100 and (c) 150


0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

minus60 minus40 minus20minus800

minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)

Figure 11 Curves of loading frequency correlation test (a) 0001Hz and 0005Hz (b) 001Hz (c) 01 Hz (d) 05Hz (e) 10Hz and (f) 20Hz


Table 5 Test results of119870ℎ1 in different loading frequency

Frequency (Hz) 1198761 (kN) 1198762 (kN) 1198831 (mm) 1198832 (mm) 119870ℎ1 (kNmm) Normalization0001 3973lowast minus4144lowast 4914 minus5091 811 1120005 3983lowast minus4041lowast 4914 minus5093 807 112001 3852lowast minus4074lowast 4897 minus5074 796 11001 3676lowast minus3465lowast 4974 minus4930 721 10005 3579lowast minus3504lowast 4929 minus4900 721 10010 3337lowast minus3269lowast 4814 minus4827 685 09520 3233lowast minus3334lowast 4904 minus4924 668 093

Table 6 Test results of 119870ℎ1 in different loading times

Times 1198761 (kN) 1198762 (kN) 1198831 (mm) 1198832 (mm) 119870ℎ1 (kNmm) Normalization1 3524lowast minus3375lowast 4923 minus4917 701 1083 3227lowast minus3178lowast 4921 minus4917 651 1005 3125lowast minus3169lowast 4919 minus4917 639 09810 3061lowast minus3159lowast 4917 minus4917 632 09730 3109lowast minus3143lowast 4996 minus4937 629 09750 3072lowast minus3086lowast 5020 minus4913 620 095

Table 7 Similarity relation between model and prototype

Similarity factor Symbol Formula Value (modelprototype)Size 119878119897 119878119897 = 119897119872119897119875 0182Elastic modulus 119878119864 119878119864 = 119864119872119864119875 1000Acceleration 119878119886 119878119886 = 1198781198641198782119897 119878119898 1002Mass 119878119898 119878119898 = 119898119872119898119875 0033Time 119878119905 119878119905 = (119878119897119878119886)05 0426Frequency 119878119891 119878119891 = 1119878119905 2347Displacement 119878119906 119878119906 = 119878119897 0182Stress 119878120590 119878120590 = 119878119864 1000Strain 119878120576 119878120576 = 1 1000Force 119878119865 119878119865 = 1198781198641198782119897 0033

energy accumulator in testing machine the loading timecorrelation test will be conducted for three times with loadingcycles 1ndash15 16ndash32 and 33ndash50 successively The horizontalload-displacement curves of the specimen under differentloading time are shown in Figure 12 And the correspondingtest results of 119870ℎ1 are shown in Table 6 It is indicated that119870ℎ1 decreases with the increase of loading time Based onthe third loading time the variation range of 119870ℎ1 will be095ndash108

343 Ultimate Shear Property in Longitudinal Direction Inultimate shear property test of the specimen test picturewhen shear displacement is +75mm (150 shear strain) isshown in Figure 13 Test curves of ultimate shear propertyare described as Figure 14 Results show that the specimendoes not have any signs of damage when shear displacementreaches its ultimate value 75mm under the design bearingcapacity and the shear load monotonously increased withthe increase of displacement It proves that the ultimate

shear property of the specimen in longitudinal direction hassatisfactory performance

4 Damping Effects ofNovel Antivibration Bearing

41 Test Scheme Damping effects of the novel bearing areinvestigated through impulse vibration tests on scaled mod-els The scaled models of the novel bearing and steel bearingare shown in Figure 15 The similarity relation of length ratiobetween the model and prototype is set as 155 and theirsimilarity relation is shown in Table 7 It should be noted thatthe full-scaled specimen of the novel bearing is constitutedby four rubber blocks while scaled model is constituted bytwo rubber blocks That is to say one scaled model of thenovel bearing is equivalent to half of scaled bearing specimenaccording to the similarity relation of length ratio 155

42 Test Process The impulse vibration tests of scaledmodel are performed in Earthquake Engineering Center of


0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)

Figure 12 Curves of loading time correlation test (a) 1ndash15 (b) 16ndash32 and (c) 33ndash50

Figure 13 Test picture when shear displacement is +75mm

Guangzhou University Test scheme is shown in Figure 16There are four scaled bearings placed in each corner of thesquare ground and every two of them are placed by T-typerelations which is equivalent to two-scaled bearing speci-men Considering design bearing capacity is 2600 kN for the

normal train operation additional weight composed of theconcrete and steel slab is 1716 kN based on the similarityratio 0033 Dynamic loads are excited by an electromagneticvibrator which is placed at the center of slab Sweep frequencyis 5ndash230Hz This test applies four accelerometers to gathervertical acceleration responses as shown in Figure 16 whereaccelerometer 1 is located at the lower plate of the bearingaccelerometers 2 and 3 are located on the concrete slab andaccelerometer 4 is located on the vibrator

43 Results and Discussion Under the impulse vibration invertical direction the time histories and Fourier spectra ofnovel antivibration bearing and steel bearing at accelerom-eter 2 and accelerometer 1 are shown in Figure 17 It isindicated that the maximum acceleration responses of theupper and lower plates in the novel bearing are 011ms2 and00048ms2 withmain frequency components around 20Hzor 50ndash60Hz While in steel bearing the corresponding value


0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)

Figure 14 Test curves of ultimate shear property (a) 75mm and (b) minus75mm

(a) (b)

Figure 15 Scaled models (a) novel antivibration bearing and (b) steel bearing

Accelerometer 1

Accelerometer 2 Accelerometer 3

Accelerometer 4

Figure 16 Test scheme of impulse vibration test on scaled models

of upper and lower plates are 0073ms2 and 00021ms2 withmain frequency components around 20ndash30Hz or 65ndash75Hz

In accordance with the Chinese national standards GB1007-1988 [32] the vibration level is defined as follows

(1) Vibration acceleration level is

VAL = 20 lg 119886RMS1198860

(18)

where 1198860 = 10minus6ms2 is a reference vibration acceleration and119886RMS is the vibration acceleration RMS

(2) 119885 vibration level is as followsCorrected by119885-weighted factor of the whole-body vibra-

tion the vibration acceleration level is noted as VL119885 based onISO26311-1997 [33]

The dominant frequency of vertical ground vibrationinduced by the passage of trains is 10ndash100Hz and the domi-nant frequency of transverse vibration is 4ndash100Hz [34] Basedon GB 10071-1988 [32] only 1ndash80Hz of vertical vibrationneeds to be assessed Therefore 1ndash80Hz was adopted tomake assessment on the damping effect of the novel bearingThe 13 octave band analysis is performed to discuss thevertical 119885 vibration level in the range of 1ndash80Hz Resultsshow that the average VL119885 of upper and lower plates forthe steel bearing are 6767 dB and 5950 dB respectively and


0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)

Figure 17 Vertical acceleration time histories and Fourier spectra (a) novel antivibration bearing and (b) steel bearing

the whole insertion loss is 817 dB while the average VL119885 ofupper and lower plates for the novel bearing are 7029 dBand 5680 dB respectively and the whole insertion loss is1349 dB Therefore the overall insertion loss of the novelbearing is 532 dB larger than that of steel bearing

Comparison of the insertion loss for steel bearing andthe novel bearing in the frequency domain of 1ndash80Hz isshown in Figure 18 From the comparison both steel bearingand the novel bearing can cause the insertion loss in mostfrequency components which shows that both can reduce


11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)

13 octave band center frequency (Hz)Steel bearingNovel antivibration bearing

Figure 18 Comparison of the insertion loss for steel bearing andnovel antivibration bearing

certain vertical vibrationHowever the vibration responses ofthe novel bearing are amplified below 13 octave band centerfrequency 4HzThat is because the novel bearing as a flexiblesupport decreases the natural frequency of the structure Thevibration responses are mitigated in the medium and highfrequency bands and amplified in the low frequency bandsIn this sense the damping effects of the novel bearing is worsethan that of the steel bearing below the center frequency4Hz But above the center frequency 4Hz that contains themain dominant frequency of vertical vibration induced by thepassage of trains (10ndash80Hz) the novel bearing can reducemore vibrations than the steel bearing It can be concludedthat the novel bearing can effectively mitigate the train-induced vertical vibrations

5 Conclusion

For the bridge bearing the principle to mitigate verticalvibration is to increase the frequency ratio by appropriatelydecreasing natural frequency of the vibration system andalso provide proper damping to avoid the resonance In thispaper a novel antivibration bearing that adopts four high-damping thick rubber blocks stacking slantingly is proposedto reduce vertical vibrations and provide a large lateralstiffness simultaneously Considering the novel bearing ismodeled linearly in the train-bridge interaction system theassociated stiffness correction method is proposed based onmultiple iterations with design compression displacement

To validate the design method mechanical property testsare performed on a specimen of the bearing device withdesign natural frequency at 8Hz and with 3500 kN bearingcapacity Test results show that the measured 119870119873 of thespecimen is 4798 kNmm which can ensure the verticalcapacity of urban rail transit viaduct the measured 119870ℎ1 is731 kNmmwhich can ensure the horizontal displacement ofthe longitudinal bridge caused by thermal effect of girder the

measured119870ℎ2 is 8614 kNmm which can resist the expectedlateral load of bridgeThe equivalent damping ratioℎeq in lon-gitudinal direction is 96 showing the specimen possessesgreat energy-dissipating capacityThe tests also prove that thespecimen has stable performance in longitudinal directionTherefore the mechanical property of the novel bearing cansatisfy the engineering demandThe error between correctedvalue and measured value is smaller than that of standardcalculated value whether compression stiffness or horizontalequivalent stiffness So the test results agree well with theprediction of the proposed stiffness correction method

Damping effects of the novel bearing are investigatedthrough impulse vibration tests on scaledmodelsWhen elec-tromagnetic vibrator is operating on test model it shows thatvibration amplitudes of the novel bearing at the upper andlower plates are smaller than those of steel bearingThewholeinsertion loss of the novel bearing is 1349 dB which is 532 dBlarger than that of steel bearing in the range of 1ndash80Hz Thedamping effect of the novel bearing is worse than that ofthe steel bearing below the center frequency 4Hz becauseof the vibration amplification effect of flexure supportingstructure in the low frequency bands But above the centerfrequency 4Hz that contains themain dominant frequency ofvertical vibration induced by the passage of trains (10ndash80Hz)the novel bearing can reduce more vibrations than the steelbearing Therefore the novel bearing can effectively mitigatethe train-induced vertical vibrations and it will benefit thecircumvention of the vibration problem along the elevatedrail line

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51608410) Hubei Provincial NaturalScience Foundation of China (2016CFB272) Hubei KeyLaboratory of Roadway Bridge and Structure Engineering(Wuhan University of Technology) (DQJJ201505) and theFundamental Research Funds for the Central Universities(2016IVA028 and 2017-zy-062)

References

[1] S Yokoshima and A Tamura ldquoA study on factors constitutingannoyance due to Shinkansen railway vibrationrdquo Journal ofArchitecture Planning and Environmental Engineering vol 64no 526 pp 1ndash7 1999

[2] S Lakusic and M Ahac ldquoRail traffic noise and vibrationmitigation measures in urban areasrdquo Technical Gazette vol 19no 2 pp 427ndash435 2012

[3] G Lombaert G Degrande B Vanhauwere B Vandeborghtand S Francois ldquoThe control of ground-borne vibrations fromrailway traffic by means of continuous floating slabsrdquo Journal ofSound and Vibration vol 297 no 3-5 pp 946ndash961 2006


[4] J F Wang C C Lin and B L Chen ldquoVibration suppressionfor high-speed railway bridges using tuned mass dampersrdquoInternational Journal of Solids and Structures vol 40 no 2 pp465ndash491 2003

[5] M D Martınez-Rodrigo J Lavado and P Museros ldquoDynamicperformance of existing high-speed railway bridges underresonant conditions retrofitted with fluid viscous dampersrdquoEngineering Structures vol 32 no 3 pp 808ndash828 2010

[6] L Andersen and S R K Nielsen ldquoReduction of groundvibration by means of barriers or soil improvement along arailway trackrdquo Soil Dynamics and Earthquake Engineering vol25 no 7ndash10 pp 701ndash716 2005

[7] M Adam and O Von Estorff ldquoReduction of train-inducedbuilding vibrations by using open and filled trenchesrdquo Comput-ers and Structures vol 83 no 1 pp 11ndash24 2005

[8] J Aviles and F J Sanchez-Sesma ldquoFoundation isolation fromvibrations using piles as barriersrdquo Journal of EngineeringMechanics vol 114 no 11 pp 1854ndash1870 1988

[9] G Y Gao Z Y Li C Qiu and Z Q Yue ldquoThree-dimensionalanalysis of rows of piles as passive barriers for ground vibrationisolationrdquo Soil Dynamics and Earthquake Engineering vol 26no 11 pp 1015ndash1027 2006

[10] P-H Tsai Z-Y Feng and T-I Jen ldquoThree-dimensional anal-ysis of the screening effectiveness of hollow pile barriersfor foundation-induced vertical vibrationrdquo Computers andGeotechnics vol 35 no 3 pp 489ndash499 2008

[11] H Takemiya and A Fujiwara ldquoWave propagationimpedimentin a stratum and wave impeding block (WIB) measured for SSIresponse reductionrdquo Soil Dynamics and Earthquake Engineer-ing vol 13 no 1 pp 49ndash61 1994

[12] H Takemiya ldquoField vibration mitigation by honeycomb WIBfor pile foundations of a high-speed train viaductrdquo Soil Dynam-ics and Earthquake Engineering vol 24 no 1 pp 69ndash87 2004

[13] T H Kim Y J Kim and H M Shin ldquoSeismic perfor-mance assessment of reinforced concrete bridge piers supportedby laminated rubber bearingsrdquo Structural Engineering andMechanics vol 29 no 3 pp 259ndash278 2008

[14] A R Bhuiyan and M S Alam ldquoSeismic performance assess-ment of highway bridges equipped with superelastic shapememory alloy-based laminated rubber isolation bearingrdquo Engi-neering Structures vol 49 no 2 pp 396ndash407 2013

[15] H Zhang J Li and T Peng ldquoDevelopment and mechanicalperformance of a new kind of bridge seismic isolator for lowseismic regionsrdquo Shock and Vibration vol 20 no 4 pp 725ndash735 2013

[16] Marioni L Chen and J T Hu ldquoApplication of EBP onTaiwan high-speed railwayrdquo Earthquake Resistant Engineeringand Retrofitting vol 33 no 2 pp 63ndash66 2011

[17] X Y Hu and G Z Yu ldquoBrief discussion about bridge vibrationisolation bearing productsrdquo inProceedings of the fifthnationwiderubber products technical seminar Rubber cup in Donghai pp79ndash84 Ningbo China 2009

[18] L M Sun W P Xie and W He ldquoField measurement onvibration reduction effects of anti-vibration bearings for verticaltrain-induced vibrationsrdquo in Proceedings of the Fourteenth Inter-national Symposium on Structural Engineering FundamentalResearch in Structural Engineering Retrospective and Prospec-tive pp 982ndash988 Beijing China 2016

[19] Z J Zhang X Z Li X Zhang et al ldquoStudy on the vibrationisolation effects of elastic bearings on train-induced vibration ofrailway bridgerdquo Engineering Mechanics vol 32 no 4 pp 103ndash111 2015

[20] X Li Z Zhang and X Zhang ldquoUsing elastic bridge bearings toreduce train-induced ground vibrations An experimental andnumerical studyrdquo Soil Dynamics and Earthquake Engineeringvol 85 pp 78ndash90 2016

[21] M Kawatani Y Kobayashi and H Kawaki ldquoInfluence ofelastomeric bearings on traffic-induced vibration of highwaybridgesrdquo Transportation Research Record Journal of the Trans-portation Research Board vol 1696 pp 76ndash82 2000

[22] C-W Kim M Kawatani and W-S Hwang ldquoReduction oftraffic-induced vibration of two-girder steel bridge seated onelastomeric bearingsrdquo Engineering Structures vol 26 no 14 pp2185ndash2195 2004

[23] J-D Yau Y-S Wu and Y-B Yang ldquoImpact response of bridgeswith elastic bearings to moving loadsrdquo Journal of Sound andVibration vol 248 no 1 pp 9ndash30 2001

[24] Y B Yang C L Lin J D Yau and D W Chang ldquoMechanismof resonance and cancellation for train-induced vibrations onbridges with elastic bearingsrdquo Journal of Sound and Vibrationvol 269 no 1-2 pp 345ndash360 2004

[25] T Jiang C Y Ma and X Zhang ldquoDynamic analysis of train-bridge system with elastic supportsrdquo Chinese Quarterly ofMechanics vol 25 no 2 pp 256ndash263 2004

[26] S Yabana and AMatsuda ldquoMechanical properties of laminatedrubber bearings for three-dimensional seismic isolationrdquo inProceedings of the 12th World Conference on Earthquake Engi-neering 2000

[27] W F He W G Liu Y F Yang et al ldquoThe basic mechanicalproperties of thick rubber isolatorsrdquo Journal of PLA Universityof Science and Technology (Natural Science Edition) vol 12 no3 pp 258ndash263 2011

[28] R Clough and J Penzien Structural of Dynamics Computers ampStructures Inc USA 3rd edition 1995

[29] GB 206882-2006 Rubber Bearings-Part 2 Elastomeric seismic-protection isolators for bridges China Standards Press BeijingChina 2006

[30] EN 15129-2009 Anti-seismic devices 2009[31] GBT 206881-2007 Rubber Bearings-Part 1 Seismic-protection

isolators test methods China Standards Press Beijing China2006

[32] GB 10071-1988 Measurement Method of Environmental Vibra-tion of Urban Area National Environmental Protection AgencyChina 1988

[33] ISO 26311-1997 Mechanical Vibration and Shock Evaluationof Human Exposure to Whole-Body Vibration-Part 1 GeneralRequirements 1997

[34] X Z Li Q M Liu X Zhang et al ldquoGround vibration inducedby inter-city express trainrdquo Journal of Vibration and Shock vol33 no 16 pp 56ndash61 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



antiseismic function such as laminated rubber bearings [13]SMA-based rubber bearings [14] and fiber-reinforced rubberbearings [15] Those bearings have deficient performance ofvertical vibrationmitigation because of the high compressionstiffness Considering the dominant direction of the train-induced vibration is vertical retrofits have to be done on theexisting rubber bearings

To mitigate the train-induced vibrations elastic bear-ing pad (EBP) with the assorted shear key (SK) as thesupported system of the bridge has been applied to about5 km of Taiwan high speed railway [16] Later this kindof antivibration bearing was also adopted by the YichangYangtze River Railway Bridge in Yichang-Wanzhou Railwayand the Minjiang River Railway Bridge in Fuzhou-XiamenRailway to reduce the train-induced vibrations [17] Sun etal [18] testified the damping effect of EBP and pot rubberbearing when trains are running on the Yichang YangtzeRiver Railway Bridge Tests result showed that the overallinsertion loss between the upper and lower plates for EBP andpot rubber bearingwas 1340 dB and 965 dB respectively andEBP could reducemore vertical train-induced vibrations thanpot rubber bearing in most frequency components

Li et al [19 20] analyzed the effect of elastic bearings ontrain-induced vibrations by simulating the elastic bearingsas spring-damper elements The results showed that thestiffness of elastic bearings had marginally influenced wheelunloading rate and the vertical acceleration of the vehiclebecause the elastic bearings could absorb the vibrations inthe medium and high frequency bands and amplify theirown vibration of natural frequency band Besides mostresearches [21ndash25] about the elastic bearings were simulatedas spring elements to explore the impact of the dynamicresponses of vehicle-bridge interaction system For exampleKawatani et al [21] analyzed dynamic responses of vehicle-bridge interaction system of certain highway bridge withsteel bearings compared to that with elastic bearings basedon numerical simulation method The results showed thatelastic bearings could effectively reduce the high frequencyvibration Through the theoretical analysis Yang et al [2324] studied the impact on dynamic responses of vehicle-bridge interaction system exerted by elastic bearings undermoving train loads The results indicated that the elasticbearings could prevent the transmission or dissipation ofvehicle-induced forces from the superstructure to the groundcausing the huge amount of train-induced vibrations energyaccumulated and amplified on the bridge during its passage

The above works indicated that elastic bearing withcertain flexibility in vertical direction can reduce the train-induced vertical vibrations transferred to the substructureCurrently only EBP has been preliminarily applied to miti-gate train-induced vibrations but it must assort SK to resistlateral load because of its small horizontal stiffnessThereforebased on the attenuationmechanismof antivibration bearinga novel antivibration bearing with four high-damping thickrubber blocks stacking slantingly is proposed to mitigatevertical vibrations in this paper Compared with EBP thenovel bearing can mitigate the train-induced vertical vibra-tions more effectively and provide a large lateral stiffnessto limit the lateral displacement caused by train braking

or turning at a high speed The straight forward design ofsuch rubber bearing with lowmanufacturing costs makes thedevice promising to be used in the field

Yabana and Matsuda [26] and He et al [27] conductedmechanical property tests on thick rubber bearing Resultsshowed that large compression deformation of thick rubberbearing would be produced under design pressure and thecalculation method of compression stiffness of laminatedrubber bearing aimed at horizontal seismic isolation was notsuitable for thick rubber bearingTherefore the calculation ofstiffness of the novel bearing with thick rubber blocks mustbe corrected Considering the novel antivibration bearingis modeled linearly in the train-bridge interaction systemthe stiffness correction method based on multiple iterationswith design compression displacement has been proposed Tovalidate the design method of the novel bearing mechanicalproperty tests are performed on a specimen Finally dampingeffects of the novel bearing are investigated through impulsevibration tests on scaled models

2 Design of Novel Antivibration Bearing

21 Antivibration Mechanism Rail transit viaduct withantivibration bearing can be treated as mass-spring-dampersystem It can mitigate the sensitivity of the substructureto the train-induced vibrations over the superstructure byinserting a simple harmonic oscillator with lower naturalfrequency [16] It can be described as antivibration systemwith single degree of freedom as shown in Figure 1

The mass block represents the bridge superstructureAssume that the mass block and foundation are rigid andthe elastic spring has damping characteristic 119898 is the massof the block in the antivibration system 119896 is spring stiffness119888 is viscous damping coefficient 119865(119905) is external force and119909(119905) is vertical vibration displacement of the mass blockWhen motivated by the external harmonic excitation 119865(119905) =1198650 sin(120579119905) the motion equation of the mass block is

119898 (119905) + 119888 (119905) + 119896119909 (119905) = 1198650sin (120579119905) (1)

Based on the theory of structural dynamics [28] thetransmissibility coefficient of the antivibration system is

119879 =radic1 + (2120585120573)2

radic(1 minus 1205732)2 + (2120585120573)2 (2)

where 120573 = 120579120596 is the frequency ratio 120579 is the circularfrequency of the external harmonic excitation120596 is the naturalcircular frequency of the system and 120585 is the damping ratio

The variation curve of transmissibility coefficient 119879 withthe frequency ratio120573 for discrete values of the damping ratio 120585is shown in Figure 2 It is indicated that all curves of differentdamping ratios pass through the same point when frequencyratio120573 = 212 Clearly because of this feature the effectivenessof vibration reduction system will be enhanced by increasingthe dampingwhen120573 lt 212 Similarly the effectivenesswill bedecreased by increasing the dampingwhen120573 gt 212 Since thetransmissibility coefficients for 120573 gt 212 are generally much


F(t)

x(t)

c

m

k


0 1 2 30

1

2

3

Tran

smiss

ibili

ty co

effici

ent T

Frequency ratio 212

= 0 = 15 = 14 = 13

= 12 = 1 = 2






2radic119863 (3)





(1)

(2)

(3)(4)

(5)

(6)(7)(8)

(9)(10)

(a)

(2)

(3)

(6)


Long

itudi

nal (

mov

able

dire

ctio

n)

(b)




1198781 =1198864119905119903

1198782 =119886119899119905119903

(4)



119870ℎ =119866119860119899119905119903 (5)



119870119881 =119864119888119860119899119905119903

(6)



119870119873 = (119870119881cos2120572 + 119870ℎsin2120572) times 4 (7)


119870ℎ1 = 4119870ℎ (8)


119870ℎ2 = (119870119881sin2120572 + 119870ℎcos2120572) times 4 (9)





d

d ＭＣＨ

d ＝ＩＭ


d

tr minus d




1198701015840ℎ =119866119860

119899 (119905119903 minus 119889V) (10)


11987810158401 =119886

4 (119905119903 minus 119889V) (11)


1198641015840119888 = 3119866 (1 + 2119878101584021 ) (12)


1198601015840 = 119886 times (119886 minus 119889ℎ) (13)


1198701015840119881 =11986410158401198881198601015840

119899 (119905119903 minus 119889V) (14)













Loadingwaveform

VerticalloadskN

Cycle-index











119870119873 =1198752 minus 11987511198842 minus 1198841

(15)



119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)



ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)










0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










F(t)

x(t)

c

m

k


0 1 2 30

1

2

3

Tran

smiss

ibili

ty co

effici

ent T

Frequency ratio 212

= 0 = 15 = 14 = 13

= 12 = 1 = 2






2radic119863 (3)





(1)

(2)

(3)(4)

(5)

(6)(7)(8)

(9)(10)

(a)

(2)

(3)

(6)


Long

itudi

nal (

mov

able

dire

ctio

n)

(b)




1198781 =1198864119905119903

1198782 =119886119899119905119903

(4)



119870ℎ =119866119860119899119905119903 (5)



119870119881 =119864119888119860119899119905119903

(6)



119870119873 = (119870119881cos2120572 + 119870ℎsin2120572) times 4 (7)


119870ℎ1 = 4119870ℎ (8)


119870ℎ2 = (119870119881sin2120572 + 119870ℎcos2120572) times 4 (9)





d

d ＭＣＨ

d ＝ＩＭ


d

tr minus d




1198701015840ℎ =119866119860

119899 (119905119903 minus 119889V) (10)


11987810158401 =119886

4 (119905119903 minus 119889V) (11)


1198641015840119888 = 3119866 (1 + 2119878101584021 ) (12)


1198601015840 = 119886 times (119886 minus 119889ℎ) (13)


1198701015840119881 =11986410158401198881198601015840

119899 (119905119903 minus 119889V) (14)













Loadingwaveform

VerticalloadskN

Cycle-index











119870119873 =1198752 minus 11987511198842 minus 1198841

(15)



119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)



ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)










0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(1)

(2)

(3)(4)

(5)

(6)(7)(8)

(9)(10)

(a)

(2)

(3)

(6)


Long

itudi

nal (

mov

able

dire

ctio

n)

(b)




1198781 =1198864119905119903

1198782 =119886119899119905119903

(4)



119870ℎ =119866119860119899119905119903 (5)



119870119881 =119864119888119860119899119905119903

(6)



119870119873 = (119870119881cos2120572 + 119870ℎsin2120572) times 4 (7)


119870ℎ1 = 4119870ℎ (8)


119870ℎ2 = (119870119881sin2120572 + 119870ℎcos2120572) times 4 (9)





d

d ＭＣＨ

d ＝ＩＭ


d

tr minus d




1198701015840ℎ =119866119860

119899 (119905119903 minus 119889V) (10)


11987810158401 =119886

4 (119905119903 minus 119889V) (11)


1198641015840119888 = 3119866 (1 + 2119878101584021 ) (12)


1198601015840 = 119886 times (119886 minus 119889ℎ) (13)


1198701015840119881 =11986410158401198881198601015840

119899 (119905119903 minus 119889V) (14)













Loadingwaveform

VerticalloadskN

Cycle-index











119870119873 =1198752 minus 11987511198842 minus 1198841

(15)



119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)



ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)










0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










d

d ＭＣＨ

d ＝ＩＭ


d

tr minus d




1198701015840ℎ =119866119860

119899 (119905119903 minus 119889V) (10)


11987810158401 =119886

4 (119905119903 minus 119889V) (11)


1198641015840119888 = 3119866 (1 + 2119878101584021 ) (12)


1198601015840 = 119886 times (119886 minus 119889ℎ) (13)


1198701015840119881 =11986410158401198881198601015840

119899 (119905119903 minus 119889V) (14)













Loadingwaveform

VerticalloadskN

Cycle-index











119870119873 =1198752 minus 11987511198842 minus 1198841

(15)



119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)



ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)










0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Loadingwaveform

VerticalloadskN

Cycle-index











119870119873 =1198752 minus 11987511198842 minus 1198841

(15)



119870ℎ =1198761 minus 11987621198831 minus 1198832

(16)



ℎeq =2Δ119882

120587119870ℎ (1198831 minus 1198832)2 (17)










0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














0 2 4 6 80

1000

2000

3000

4000


Com

pres

sion

load

(kN

)











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(a)


minus800

minus400

0

400

800

1200

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

(b)



minus400

minus200

0

200

400

600

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

25ＧＧ (50)

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

50ＧＧ (100)

(b)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

75ＧＧ (150)

(c)



0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

0001 （Ｔ

0005 （Ｔ

(a)


minus600

minus400

minus200

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

001 （Ｔ

(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

01 （Ｔ

(c)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

05 （Ｔ

(d)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

10 （Ｔ

(e)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

20 （Ｔ

(f)
















0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

1ndash15 (a)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(kN

)


minus600

minus400

minus200

16ndash32(b)

0 20 40 60

0

200

400

600

800

Displacement (mm)

Hor

izon

tal l

oad

(mm

)


minus600

minus400

minus200

33ndash50(c)







0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 800

200

400

600

800

1000

Displacement (mm)

Hor

izon

tal l

oad

(kN

)

+75ＧＧ

(a)

0 20 40 60 800

200

400

600

800

1000

Displacemnet (mm)

Hor

izon

tal l

oad

(kN

)

minus75ＧＧ

(b)


(a) (b)


Accelerometer 1


Accelerometer 4





VAL = 20 lg 119886RMS1198860

(18)






0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)A

mpl

itude

(mＭ

2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

0 10 20 30 40 50 60 70 80 90 100

minus0006

minus0003

0000

0003

0006

Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 1(a)

0 10 20 30 40 50 60 70 80 90 100

minus004

minus002

000

002

004

Time (s)

Accelerometer 1

Acce

lera

tion

(mＭ

2)

0 10 20 30 40 50 60 70 80 90 10000000

00002

00004

00006

Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 1

00000

00008

00016

00024

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Am

plitu

de (m

Ｍ2H

z)

Accelerometer 2

minus012

minus006

000

006

012

0 10 20 30 40 50 60 70 80 90 100Time (s)

Acce

lera

tion

(mＭ

2)

Accelerometer 2

(b)





11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










11

25 16 2

25

315 4 5

63 8 10

125 16 20 25

315 40 50 63 80

minus10

0

10

20

30

40

Z v

ibra

tion

leve

l (dB

)




5 Conclusion







Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









study on the stiffness correction method of novel antivibration...

Documents