Research Article Optimization of Vibration Reduction Ability of … · 2019. 7. 31. · ladder tracks. e idea for ladder track was originally from the baulk road system and was then

Research ArticleOptimization of Vibration Reduction Ability ofLadder Tracks by FEM Coupled with ACO

Hao Jin1 Weining Liu2 and Shunhua Zhou1

1Key Laboratory of Road and Traffic Engineering of Ministry of Education Tongji University Shanghai 201804 China2School of Civil Engineering Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Hao Jin zhujijinhaogmailcom

Received 28 March 2015 Revised 25 May 2015 Accepted 10 June 2015

Academic Editor Georges Kouroussis

Copyright copy 2015 Hao Jin et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Ladder track which has drawn increased attention in scientific communities is an effective method for reducing vibrations fromunderground railways In order to optimize the vibration reduction ability of ladder track a newmethod that is the finite elementmethod (FEM) coupled with ant colony optimization (ACO) has been proposed in this paper We describe how to build the FEMmodel verified by the vibration tests in the Track Vibration Abatement and Control Laboratory and how to couple the FEM withACO The density and elasticity modulus of the sleeper pad are optimized using this method After optimization the vibrationacceleration level of the supporting platform in the 1ndash200Hz range was reduced from 1028 dB to 944 dBThe optimized density ofthe sleeper pad is 620 kgm3 and the optimized elasticity modulus of the sleeper pad is 625 times 106Nm2

1 Introduction

Vibrations generated by underground railways are one of themost serious engineering problems of such systems Wavesinduced by the dynamic interaction between the train wheelsand the rails propagate from the surrounding soils to thefoundations of nearby buildings [1] resulting in structuralvibrations and reradiated noise One effective method forreducing vibrations from underground railways is to useladder tracks

The idea for ladder track was originally from the baulkroad system and was then applied in the Leeds and SelbyRailway in 1830 From the middle of the 20th centurysystematic research on ladder track was started in JapanRussia and France In the last 10 years the vibration reduc-tion performance of ladder track by the Railway TechnicalResearch Institute of Japan has attracted great attention fromAsian researchers especially in China

In the early 1990s Wakui et al [2] reported its new devel-opment in Japan Oyado et al [3] analyzed running perfor-mance and dynamic settlement test results of a ballasted lad-der track Initially the ladder track was usually used as a bal-lasted track Hosking andMilinazzo [4] built a simple mathe-matical model to study ladder track responses under steadily

moving loads by employing the periodic discrete elastic sup-port of the combined floating rails This model was extendedto include the support mass and viscous damping [5] HuiandNg [6]measured the vibration velocity level at the stationusing the ladder track The results showed that the laddertrack has better mitigation properties above 35Hz comparedwith ballast trackThe first bending resonance of ladder trackis 315Hz under a moving train load In the Beijing subwaysystem Xia et al [7ndash9] and Inoue et al [10] compared thedynamic response of an elevated bridge having ordinary non-ballasted slab track with a bridge having ladder track Theo-retical analysis and experimental study proved that the laddertrack has good vibration reduction characteristics Jin et alperformed a modal analysis of the ladder track with differentbearing forms by a numerical method [11] and a laboratorytest [12]The results showed that the first natural frequency ofladder track occurs at 33ndash36Hz To solve the problem of railcorrugation the dynamic properties of the ladder track usedin the Beijing subway were optimized by Yan et al [13 14]

The present contribution aims to optimize vibrationreduction ability of ladder track by FEM coupled withACO This paper is organized as follows Section 2 describesa vibration test of ladder track performed in the TrackVibration Abatement and Control Laboratory In Section 3

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 484827 6 pageshttpdxdoiorg1011552015484827

2 Shock and Vibration

Table 1 Properties of the ladder track

Part Density (kgm3) Elasticity modulus (Nm2) Poissonrsquos ratioRail 785 times 103 214 times 1011 03Longitudinal sleeper 2 times 103 5 times 1010 0167Supporting platform 26 times 103 36 times 1010 0167Connecting beam 785 times 103 214 times 1010 03

Lab 1

Lab 2

Miscellaneous fill

Sandy silt

Sandy clay

Sand

Boulder

Sand

6m

4m

4m

4m

Figure 1 Section plan of the laboratory

a description is given of an FEM model that was built usingthe commercial software LS-DYNA and verified based on thetested ladder trackThen the FEMmodel coupled with ACOis introduced in Section 4 In Section 5 the optimizationof the vibration reduction performance of ladder track isexplained Conclusions are given in Section 6

2 Vibration Testing in the Laboratory

The Track Vibration Abatement and Control Laboratoryof Beijing Jiaotong University is a two-story undergroundstructure for researching track vibration and is the only suchfacility in Asia The buried depth of Lab 1 is 6m and theburied depth of Lab 2 is 14m Figure 1 shows the groundconditions around the laboratory

One unit of ladder track was constructed in Lab 2(Figure 2) The cross section of Lab 2 is in the shape of ahorseshoe The height is 4m and the width is 4m

The test track used 60 kgm rail which was 615m inlength Ten WJ-2 fasteners were employed to fix each railin place The size of the longitudinal sleeper was 615m times046m times 0185m The size of the connecting beam whichwas designed to connect the two longitudinal sleepers was0975mtimes 006mtimes 006mTherewere five sleeper pads undereach longitudinal sleeper The size of the sleeper pad was046m times 025m times 003mThe size of the supporting platformwas 086m times 04m times 028m Ten supporting platforms wereused for the test ladder track Figure 3 shows the plan of thetest ladder track Figure 4 illustrates the cross section of thetest ladder track

Connecting beam

Rail

Sleeper pad

Longitudinal sleeper

Fastener

Supporting platform

Figure 2 Ladder track located in Lab 2

As the vibration source an automatic falling weightmachine shown in Figure 5 was designed and was employedto provide impulse to the rail By changing the number ofmass blocks and the drop height different impulse forcescould be obtained The material of the hammer head couldalso be changed to aluminum rubber nylon or steel To avoidinfluencing the sleeper by themass of the setup a scaffold wasinstalled to support the automatic falling weight machine

For this test fivemass blocks 73 kg in total were installedThe aluminum hammer head was used and the drop heightwas 10 cm A force sensor was installed in the hammer headThe impulse site is the middle of one rail (see Figure 3) Thesampling frequency of the force signal was 128 kHzThe timehistory of the average impulse force with a peak value of55 kN is shown in Figure 6The vibration acceleration sensorwas fixed on the middle supporting platform to measurethe vertical vibration as shown in Figure 3 The samplingfrequency of the acceleration signal was 1600Hz

3 FEM Model Building and Verification

31 Building the FEM Model The commercial software LS-DYNA was employed to build the FEM model of the testladder track The geometry of the longitudinal sleepersthe connecting beams and the supporting platforms aredescribed in Section 2 Considering the calculation time ofthe LS-DYNA software the cross section of the rail wassimplified as demonstrated in Figure 7

The properties of the rails the longitudinal sleepersthe supporting platforms and the connecting beams arepresented in Table 1

Shock and Vibration 3

575 5000 575

2625 625 625Rail

Screw spikesSleeper pad

Supportingplatform

Impluse

Accelerometer

Longitudinalsleeper

Figure 3 Plan of the test ladder track (unit mm)

185

460

Connectingbeam

Rail

Supportingplatform

Figure 4 Cross section of the test ladder track (unit mm)

DropheightMass

blocks

Hammerhead

Scaffold

Figure 5 Automatic falling weight machine

Springs were used to simulate the fasteners and thesleeper pads The vertical stiffness of the fastener was60MNm The vertical stiffness of the sleeper pad was18055MNm Figure 8 shows the FEM model established

000 001 002 003 004 0050

10

20

30

40

50

60

Forc

e (kN

)

Time (s)

Figure 6 Time history of the average impulse force

by LS-DYNA The bottom of all supporting platforms wasconstrained in all directions

32 FEM Model Verification The impulse force shown inFigure 6 which was obtained from laboratory testing was


120

30

30

120

30

60

Figure 7 Simplified cross section of the rail (unit mm)

Impulse

Accelerometer

Figure 8 FEMmodel established by LS-DYNA

used in the FEM model Then the vibration accelerationof the middle supporting platform was calculated Figure 9shows the calculated result and the test result From Figure 9we see that the calculated and the test results are almost thesameTherefore the FEMmodel is accurate for the followingcalculation in Section 4

4 FEM Coupled with ACO

41 Ant Colony Algorithm With the development of com-puter technology swarm intelligence optimization algo-rithms including ant colony optimization (ACO) andparticleswarm optimization (PSO) have attracted increased atten-tion ACO is one of the most successful swarm intelligenceoptimization algorithms It was proposed by Colorni et al[15] to solve the traveling salesman problem in 1991 Itwas named the ant system (AS) inspired by the foragingbehavior of the Argentine ants [16ndash18] In recent years ACOhas been used to successfully solve many combinatorialoptimization problems [19 20] and is being extended toobtain the solutions of continuous problems [21] There aremany different ACOs based on the AS In this paper ChenrsquosACO [22] was employed to solve the continuous functionHere is a function of one variable describing Chenrsquos ACO119891(119909) is the original objective function and 119909 is the

original design variable whose minimum (maximum) valueis a (b) Let 119891(119909) be 119891(1199091015840) by simple mathematical transformin which 1199091015840 = (119909 minus 119886)(119887 minus 119886) 1199091015840 isin (0 1)

0 25 50 75 100 125 150 175 200000

002

004

006

008

010

012

Test result

Calculatedresult

Frequency (Hz)

Acce

lera

tion

(ms

2 )

Figure 9 Time history of the vibration acceleration of the middlesupporting platform

90 8

0

0 91 8

0 91 8

0 91 8

0

The first place(nest)

The last place(food source)

1

120591kiminus(T(jkminus1)T(jk))

k minus 1

k

middot middot middot




Figure 10 Decimal digit string

Therefore the optimization process for function 119891(1199091015840) issimplified to an artificial ant that makes a selection from tendecimal numbers whenever it takes a step except for the firstplace and the last place (see Figure 10)

Each artificial ant goes from the first floor (the nest)toward the last floor (the food source) 119879(119895 119896 minus 1) is thedecimal number when ant 119895 is at floor (119896 minus 1) Ant 119895 selectsthe decimal number of the next floor according to

119879 (119895 119896) =

max 120591119896119894minus(119879(119895119896minus1)119879(119895119896))

119902 lt 1198760

randperm 119902 ge 1198760

(1)

in which 119902 is a real random variable uniformly distributed inthe internal array [0 1]119876

0is a tunable parameter controlling

the influence of the pheromone randperm is a numberrandomly selected from (0 1 9) and 120591119896

119894minus(119879(119895119896minus1)119879(119895119896))is

the pheromone intensity laid on the path between the number119879(119895 119896 minus 1) to 119879(119895 119896)

When an ant finishes one step that is an ant arrives atfloor 119896 from floor (119896 minus 1) the strength of the pheromone120591119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))laid on the path between the number


Start

Parameter initialization

ACO process

Stop conditions

Optimized results

End

No

Yes

LS-DYNAcalculation

Calculationresults

Ls-Prepostanalysis

In = 0

In = In + 1

k document

Figure 11 Program flow of FEM coupled with ACO

119879(119895 119896minus1) and the number 119879(119895 119896) by ant 119895 should be updatedas follows

120591119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))larr997888 (1minus 120588) 120591

119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))+120572 (2)

where 120572 is the modified coefficient of the pheromone inten-sity and 120588 is the local evaporation factor of the pheromone

After all the ants have arrived at the last place the bestsolution for a given interior can be obtained Through allinteriors the best solution of the function can be obtained

According to the function tests Chenrsquos ACO parametersare 120572 = 120588 = 03 1198760 = 055 The interior number In is 10 andthe ant number An is 10

42 FEMCoupled with ACO The calculation code for ChenrsquosACO was written in Matlab The FEMmodel was carried outthrough the DOS functions in Matlab The detailed programflow is demonstrated in Figure 11

5 Optimization

51 Optimization Objective Vibrations induced by the inter-action between the wheels and the rails are transferred fromthe rails to the invert and then propagate to the foundationsof nearby buildings resulting in structure vibrations andreradiated noise Therefore the vibration of the supportingplatform reflects the structure vibration To reduce thestructure vibration the platform vibration should first be

0 25 50 75 100 125 150 175 2000

2

4

6

8

10

12

Frequency (Hz)

NonoptimizationOptimization

Vibr

atio

n ac

cele

ratio

n of

the m

iddl

e sup

port

ing

plat

form

(times10

minus4

ms

2 )

Figure 12 Vibration acceleration comparison between nonopti-mization and optimization

reduced Consequently platform vibration acceleration wasset as the optimization objective The objective function was

min119881119886119871119898= 20times log

radic(1119873) times sum119873119894=1 1198862

119894-rms

1198860

(3)

where 119881119886119871119898

is the vibration acceleration level of the sup-porting platform 119873 is the tested number ranging from1Hz to 200Hz 1198862

119894-rms is the effective value of the vibrationacceleration at the frequency point and 1198860 = 1times 10

minus6 ms2 isthe reference value of the vibration acceleration

52 Optimization Variables In engineering the density andthe elasticity modulus of the sleeper pad are always modifiedfor the optimizing reduction in vibrations Consequentlythe density of the sleeper pad and the elasticity modulus ofthe sleeper pad were set as the optimization variables Inpractical applications the density of the sleeper pad rangesfrom 500 kgm3 to 1500 kgm3 The elasticity modulus of thesleeper pad varies from 26 times 106Nm2 to 78 times 106Nm2

53 Optimization Results The optimization results wereobtained by the program presented in Section 4 Theoptimized density of the sleeper pad is 620 kgm3 andthe optimized elasticity modulus of the sleeper pad is625 times 106Nm2 Before optimization the vibration acceler-ation level of the middle supporting platform ranging from1Hz to 200Hzwas 1208 dBAfter optimization the vibrationacceleration level of the middle supporting platform was944 dBThevibration acceleration level decreased by 264 dB

Figure 12 shows the frequency spectrum of the vibra-tion acceleration of the middle supporting platform Beforeoptimization the maximum vibration acceleration was107 times 10minus4ms2 After optimization the maximum vibration


acceleration was 399 times 10minus4ms2 From Figure 12 the vibra-tion accelerationwas reduced across the frequency range afteroptimization

6 Conclusion

To optimize the vibration reduction ability of ladder tracka new method that is the finite element method coupledwith ant colony optimization was proposed We introducedhow to build the FEM model and how to couple the FEMwith ACO The density of the sleeper pad and the elasticitymodulus of the sleeper pad were optimized using thismethod After optimization the vibration acceleration levelof themiddle supporting platformwas reduced from 1028 dBto 944 dB The optimized density of the sleeper pad was620 kgm3 The optimized elasticity modulus of the sleeperpad was 625 times 106Nm2

Conflict of Interests

The authors declare that there is no conflict of interests withregard to this study and the publication of this paper

References

[1] G Kouroussis D Connolly and O Verlinden ldquoRailway-induced ground vibrationsmdasha review of vehicle effectsrdquo Inter-national Journal of Rail Transportation vol 2 no 2 pp 69ndash1102014

[2] H Wakui N Matsumoto and H Inoue ldquoLadder sleeper andnew track structures developmentrdquo Quarterly Report of RTRIvol 37 no 3 pp 110ndash111 1996

[3] M Oyado N Matsumoto and H Wakui ldquoRunning perfor-mance on ballasted ladder trackrdquo RTRI Report vol 10 no 9pp 51ndash56 1996

[4] R J Hosking and F Milinazzo ldquoFloating ladder track responseto a steadily moving loadrdquoMathematical Methods in the AppliedSciences vol 30 no 14 pp 1823ndash1841 2007

[5] R J Hosking and F Milinazzo ldquoModelling the floating laddertrack response to a moving load by an infinite bernoulli-eulerbeam on periodic flexible supportsrdquo East Asian Journal onApplied Mathematics vol 2 no 4 pp 285ndash308 2012

[6] C K Hui and C F Ng ldquoThe effects of floating slab bendingresonances on the vibration isolation of rail viaductrdquo AppliedAcoustics vol 70 no 6 pp 830ndash844 2009

[7] H Xia Y Deng Y Zou G de Roeck and G DegrandeldquoDynamic analysis of rail transit elevated bridge with laddertrackrdquo Frontiers of Architecture and Civil Engineering in Chinavol 3 no 1 pp 2ndash8 2009

[8] H Xia Y Deng C Xia G De Roeck L Qi and LSun ldquoDynamic analysis of coupled train-ladder track-elevatedbridge systemrdquo Structural Engineering and Mechanics vol 47no 5 pp 661ndash678 2013

[9] H Xia J G Chen C Y Xia H Inoue Y Zenda and LQi ldquoAn experimental study of train-induced structural andenvironmental vibrations of a rail transit elevated bridge withladder tracksrdquo Proceedings of the Institution of MechanicalEngineers Part F Journal of Rail and Rapid Transit vol 224 no3 pp 115ndash124 2010

[10] H Inoue Y Zenda L Qi and C Y Xia ldquoDynamic experimentof an urban elevated bridge with ladder track under movingtrainsrdquo in Proceedings of the 4th International Symposiumon Environment VibrationsmdashPrediction Monitoring Mitigationand Evaluation 2009

[11] H Jin W Liu and Y Fan ldquoModal analysis of dampingperformances of the ladder track with different bearing stylesrdquoin Proceedings of the 2nd International Conference on RailwayEngineering 2012

[12] H JinW-N Liu andW-BWang ldquoAnalysis ofmodal test of theladder trackrdquo EngineeringMechanics vol 30 no 3 pp 459ndash4632013

[13] Z Yan V Markine A Gu and Q Liang ldquoOptimisation of thedynamic properties of ladder track to minimise the chance ofrail corrugationrdquo Proceedings of the Institution of MechanicalEngineers Part F Journal of Rail and Rapid Transit vol 228 no3 pp 285ndash297 2014

[14] Z Q Yan V Markine A J Gu and Q H Liang ldquoOptimizationof the dynamic properties of the ladder track system to controlrail vibration using the multipoint approximation methodrdquoJournal of Vibration and Control vol 20 no 13 pp 1967ndash19842014

[15] A ColorniMDorigo andVManiezzo ldquoDistributed optimiza-tion by ant coloniesrdquo in Proceedings of ECAL91mdashEuropean Con-ference on Artificial Life pp 134ndash142 MIT Press CambridgeMass USA 1992

[16] J-L Deneubourg S Aron S Goss and J M Pasteels ldquoThe self-organizing exploratory pattern of the argentine antrdquo Journal ofInsect Behavior vol 3 no 2 pp 159ndash168 1990

[17] S Goss S Aron J L Deneubourg and J M Pasteels ldquoSelf-organized shortcuts in the Argentine antrdquoNaturwissenschaftenvol 76 no 12 pp 579ndash581 1989

[18] S E V V Key and T C Baker ldquoObservations on the traildeposition and recruitment behaviors of the argentine antIridomyrmex humilis (Hymenoptera Formicidae)rdquo Annals ofthe Entomological Society of America vol 79 no 2 pp 283ndash2881986

[19] C Blum ldquoAnt colony optimization introduction and recenttrendsrdquo Physics of Life Reviews vol 2 no 4 pp 353ndash373 2005

[20] B C Mohan and R Baskaran ldquoA survey ant colony opti-mization based recent research and implementation on severalengineering domainrdquo Expert Systems with Applications vol 39no 4 pp 4618ndash4627 2012

[21] F A C Viana G I Kotinda D A Rade and V SteffenJr ldquoTuning dynamic vibration absorbers by using ant colonyoptimizationrdquo Computers and Structures vol 86 no 13-14 pp1539ndash1549 2008

[22] Y Chen ldquoAnt colony system for continuous function opti-mizationrdquo Journal of Sichuan University (Engineering ScienceEdition) vol 36 no 6 pp 117ndash120 2004

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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



Table 1 Properties of the ladder track

Part Density (kgm3) Elasticity modulus (Nm2) Poissonrsquos ratioRail 785 times 103 214 times 1011 03Longitudinal sleeper 2 times 103 5 times 1010 0167Supporting platform 26 times 103 36 times 1010 0167Connecting beam 785 times 103 214 times 1010 03

Lab 1

Lab 2

Miscellaneous fill

Sandy silt

Sandy clay

Sand

Boulder

Sand

6m

4m

4m

4m

Figure 1 Section plan of the laboratory

a description is given of an FEM model that was built usingthe commercial software LS-DYNA and verified based on thetested ladder trackThen the FEMmodel coupled with ACOis introduced in Section 4 In Section 5 the optimizationof the vibration reduction performance of ladder track isexplained Conclusions are given in Section 6

2 Vibration Testing in the Laboratory

The Track Vibration Abatement and Control Laboratoryof Beijing Jiaotong University is a two-story undergroundstructure for researching track vibration and is the only suchfacility in Asia The buried depth of Lab 1 is 6m and theburied depth of Lab 2 is 14m Figure 1 shows the groundconditions around the laboratory

One unit of ladder track was constructed in Lab 2(Figure 2) The cross section of Lab 2 is in the shape of ahorseshoe The height is 4m and the width is 4m

The test track used 60 kgm rail which was 615m inlength Ten WJ-2 fasteners were employed to fix each railin place The size of the longitudinal sleeper was 615m times046m times 0185m The size of the connecting beam whichwas designed to connect the two longitudinal sleepers was0975mtimes 006mtimes 006mTherewere five sleeper pads undereach longitudinal sleeper The size of the sleeper pad was046m times 025m times 003mThe size of the supporting platformwas 086m times 04m times 028m Ten supporting platforms wereused for the test ladder track Figure 3 shows the plan of thetest ladder track Figure 4 illustrates the cross section of thetest ladder track

Connecting beam

Rail

Sleeper pad

Longitudinal sleeper

Fastener

Supporting platform

Figure 2 Ladder track located in Lab 2

As the vibration source an automatic falling weightmachine shown in Figure 5 was designed and was employedto provide impulse to the rail By changing the number ofmass blocks and the drop height different impulse forcescould be obtained The material of the hammer head couldalso be changed to aluminum rubber nylon or steel To avoidinfluencing the sleeper by themass of the setup a scaffold wasinstalled to support the automatic falling weight machine

For this test fivemass blocks 73 kg in total were installedThe aluminum hammer head was used and the drop heightwas 10 cm A force sensor was installed in the hammer headThe impulse site is the middle of one rail (see Figure 3) Thesampling frequency of the force signal was 128 kHzThe timehistory of the average impulse force with a peak value of55 kN is shown in Figure 6The vibration acceleration sensorwas fixed on the middle supporting platform to measurethe vertical vibration as shown in Figure 3 The samplingfrequency of the acceleration signal was 1600Hz

3 FEM Model Building and Verification

31 Building the FEM Model The commercial software LS-DYNA was employed to build the FEM model of the testladder track The geometry of the longitudinal sleepersthe connecting beams and the supporting platforms aredescribed in Section 2 Considering the calculation time ofthe LS-DYNA software the cross section of the rail wassimplified as demonstrated in Figure 7

The properties of the rails the longitudinal sleepersthe supporting platforms and the connecting beams arepresented in Table 1


575 5000 575

2625 625 625Rail


Supportingplatform

Impluse

Accelerometer

Longitudinalsleeper


185

460

Connectingbeam

Rail

Supportingplatform


DropheightMass

blocks

Hammerhead

Scaffold



000 001 002 003 004 0050

10

20

30

40

50

60

Forc

e (kN

)

Time (s)





120

30

30

120

30

60


Impulse

Accelerometer






0 25 50 75 100 125 150 175 200000

002

004

006

008

010

012

Test result

Calculatedresult

Frequency (Hz)

Acce

lera

tion

(ms

2 )


90 8

0

0 91 8

0 91 8

0 91 8

0



1


k minus 1

k








119879 (119895 119896) =

max 120591119896119894minus(119879(119895119896minus1)119879(119895119896))

119902 lt 1198760

randperm 119902 ge 1198760

(1)




119894minus(119879(119895119896minus1)119879(119895119896))is





Start


ACO process

Stop conditions

Optimized results

End

No

Yes

LS-DYNAcalculation

Calculationresults

Ls-Prepostanalysis

In = 0

In = In + 1

k document



120591119896minus1


119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))+120572 (2)





5 Optimization


0 25 50 75 100 125 150 175 2000

2

4

6

8

10

12

Frequency (Hz)


Vibr

atio

n ac

cele

ratio

n of

the m

iddl

e sup

port

ing

plat

form

(times10

minus4

ms

2 )



min119881119886119871119898= 20times log

radic(1119873) times sum119873119894=1 1198862

119894-rms

1198860

(3)

where 119881119886119871119898









6 Conclusion




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










575 5000 575

2625 625 625Rail


Supportingplatform

Impluse

Accelerometer

Longitudinalsleeper


185

460

Connectingbeam

Rail

Supportingplatform


DropheightMass

blocks

Hammerhead

Scaffold



000 001 002 003 004 0050

10

20

30

40

50

60

Forc

e (kN

)

Time (s)





120

30

30

120

30

60


Impulse

Accelerometer






0 25 50 75 100 125 150 175 200000

002

004

006

008

010

012

Test result

Calculatedresult

Frequency (Hz)

Acce

lera

tion

(ms

2 )


90 8

0

0 91 8

0 91 8

0 91 8

0



1


k minus 1

k








119879 (119895 119896) =

max 120591119896119894minus(119879(119895119896minus1)119879(119895119896))

119902 lt 1198760

randperm 119902 ge 1198760

(1)




119894minus(119879(119895119896minus1)119879(119895119896))is





Start


ACO process

Stop conditions

Optimized results

End

No

Yes

LS-DYNAcalculation

Calculationresults

Ls-Prepostanalysis

In = 0

In = In + 1

k document



120591119896minus1


119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))+120572 (2)





5 Optimization


0 25 50 75 100 125 150 175 2000

2

4

6

8

10

12

Frequency (Hz)


Vibr

atio

n ac

cele

ratio

n of

the m

iddl

e sup

port

ing

plat

form

(times10

minus4

ms

2 )



min119881119886119871119898= 20times log

radic(1119873) times sum119873119894=1 1198862

119894-rms

1198860

(3)

where 119881119886119871119898









6 Conclusion




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120

30

30

120

30

60


Impulse

Accelerometer






0 25 50 75 100 125 150 175 200000

002

004

006

008

010

012

Test result

Calculatedresult

Frequency (Hz)

Acce

lera

tion

(ms

2 )


90 8

0

0 91 8

0 91 8

0 91 8

0



1


k minus 1

k








119879 (119895 119896) =

max 120591119896119894minus(119879(119895119896minus1)119879(119895119896))

119902 lt 1198760

randperm 119902 ge 1198760

(1)




119894minus(119879(119895119896minus1)119879(119895119896))is





Start


ACO process

Stop conditions

Optimized results

End

No

Yes

LS-DYNAcalculation

Calculationresults

Ls-Prepostanalysis

In = 0

In = In + 1

k document



120591119896minus1


119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))+120572 (2)





5 Optimization


0 25 50 75 100 125 150 175 2000

2

4

6

8

10

12

Frequency (Hz)


Vibr

atio

n ac

cele

ratio

n of

the m

iddl

e sup

port

ing

plat

form

(times10

minus4

ms

2 )



min119881119886119871119898= 20times log

radic(1119873) times sum119873119894=1 1198862

119894-rms

1198860

(3)

where 119881119886119871119898









6 Conclusion




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start


ACO process

Stop conditions

Optimized results

End

No

Yes

LS-DYNAcalculation

Calculationresults

Ls-Prepostanalysis

In = 0

In = In + 1

k document



120591119896minus1


119896minus1

119894minus(119879(119895119896minus1)119879(119895119896))+120572 (2)





5 Optimization


0 25 50 75 100 125 150 175 2000

2

4

6

8

10

12

Frequency (Hz)


Vibr

atio

n ac

cele

ratio

n of

the m

iddl

e sup

port

ing

plat

form

(times10

minus4

ms

2 )



min119881119886119871119898= 20times log

radic(1119873) times sum119873119894=1 1198862

119894-rms

1198860

(3)

where 119881119886119871119898









6 Conclusion




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











6 Conclusion




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Optimization of Vibration Reduction Ability of … · 2019. 7. 31. · ladder tracks. e idea for ladder track was originally from the baulk road system and was then