Vibration Reduction Of High Speed Railway Bridges

Presented by

Roy Roshan Chandy

M1 Machine Design

Roll 1104

Guided by

Dr. A. Samson

College of Engineering

Trivandrum

Contents

• Introduction• Load Tests Of Bridges• Static Tests• Dynamic Tests• Mathematical Model• Vibration Reduction• Bridges With Elastic Bearings• Use Of Size Adjusted Vehicles• Bridge Model• Train Model• Conclusion• References

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IntroductionHigh Speed railway lines are affected by

numerous technical problems.About 35% length of the total length of

High Speed Railway line is made of bridges

Periodic wheel loads of train cause severe vibration on these bridges

Resonance may cause fatigue and impact related damage, scattering of ballasts, increase of bridge maintenance costs, compromise on safety and comfort of passengers

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Load Tests Of Bridges

► An important procedure to check the quality of structure

►Compare the theoretical assumption & actual behavior of a bridge

►Types of Tests:►STATIC TESTS

►DYNAMIC TESTS►LONG TERM TESTS

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STATIC TESTS

۩ Testing Institute decides the۩ Load۩ Distribution of the Load۩ Measured Points۩ Experimental method & necessary datas

۩ Recording made during tests۩ Temperature of ambient air & parts of

structure۩ Maximum vertical deflection۩ Strain, stresses, deformations۩ Development of cracks

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STATIC TESTS

۩ Heavy vehicles are used for loading such as Locomotives, Rail wagons, Rail crane

۩ Efficiency factor kstatic= UN/UV

Where UN= effect of test load

UV= effect of standard load

0.5≤ kstatic≤1.0

۩ From experience minimum loading time is 30 min for concrete bridges & 15 min for steel bridges

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DYNAMIC TESTS♦ Carried out on bridges of large spans,

unusual structural systems or new materials♦ It gives

Natural frequencyForms of free & forced vibrationDeflection- or stress time historiesDamping characteristicsObserved dynamic impact factor

♦ Before testing leveling of rails in front of, on and beyond the bridge is necessary

♦ Measurements are made of :♦ Strain or stress time history♦ Horizontal transverse response at midspan♦ Horizontal longitudinal movements of the

bearings♦ Temperature

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DYNAMIC TESTS

♦ For dynamic tests kdyn ≤1♦ kdyn = Udyn/U where

Udyn= response to test load

U = response to standard load

d = standard dynamic impact factor

♦ Measured dynamic impact factor, obs Smax/Sm , where

♦ Smax= Max. dynamic response due to the load at the measured point

♦ Sm= Max. static response due to the same load at the same point

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Mathematical ModelThe train is modelled as a sequence

of moving loads of constant intervals.The rail was modelled as an infinite

beam on an simple supports

P1P2Pk

xvt

l

dk

Movement of loads with velocity v on a beam of span l

Equation Of Motion Of Bridge

Where

U(x,t) is vertical deflection of bridge deck

m(x) is mass

c(x) is the damping

EI(x) is the flexural rigidity

Where

Pkdenotes kth wheel load

d k is the distance between the 1st and kth wheel

is the constant speed of train

is the delta function

• Using Mode superposition method

Mi , i , Ki, Qi(t) & i denote the generalised modal mass, damping ratio, stiffness, force and natural frequency respectively

i (x) is the ith mode shape of bridge deck deflection

qi(t) is the generalised modal coordinate

• Deflection u(x,t) calculated as

•Acceleration Ü(x,t) calculated as

• Moment M(x,t) calculated as

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Force transmitted by a train comprises of constant load component & alternating components

Intensity of constant component determined by weight carried by axle

Intensity of alternating components determined by:

Type of train

Maintenance of train track system

Presence or absence of shock absorbers

At low speeds effect due to alternating component predominates leading to resonance amplification

Vibration ReductionIt can be achieved

by METHOD DISADVANTAGEVarying the span length Span length constrained by other factors

thus making its field application limited

Viscous Damper Reduces successfully vibration locally but fails to decrease vibration globally in flexural & torsional modes

Shifting Resonance frequency of the bridge by adding concrete material in PSC Box Girder

7-10% reduction in vertical acceleration . But costly procedure to retrofit multiple bridges

Use of Multiple tuned Mass Dampers 61.5% reduction in vertical acceleration in a 30m box girder bridge. But installation & maintenance costs very

expensive

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Bridges With Elastic Bearings

• Elastic bearings are used as devices at the supports of bridge girders to isolate the earthquake forces transmitted from the ground

• Disadvantage: Prevent the vehicle induced vibrations from dissipation to the supports and then to the ground

• May lead to – Resonance (Build up of free vibration response )

or– Cancellation (waves associated with free

vibration cancel out each other) phenomenon at certain critical traveling speed of train

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Bridges With Elastic Bearings٭ From analytical studies & field

measurements, we come to know that٭ Elastically supported beam has lower

frequency of vibration compared to simply supported beam

٭ Hence easily excited٭ Cancellation speed close to that of

simply supported beam٭ Cancellation more decisive than

resonance٭ Much larger peak response at resonance

compared to simply supported

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Use Of Size Adjusted Vehicles

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Use Of Size Adjusted Vehicles

Instead of altering the of railway bridges, which may be costly , site specific & tailored for each bridgeVibration reduction is possible by

altering the train system itselfIntroduction of size adjusted vehicles

lead to out of phase loadingThus suppress resonance & reduce

vibration

Bridge Model

• The bridge is a PSC Box girder bridge• It has two continuous spans of 40 m• Damping ratio is taken as 2.4%• First fundamental frequency is taken

as 4.27Hz.

Section properties of Bridge model

21PSC box girder section

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Bridge model

Mode shapes of the bridge model with two continuous span

Train Model

• The assumed model has a total of 20 vehicles composed OF 2 power cars (PC), 2 motorized trailers (MT), and 16 passenger trailers (T ).

• The individual vehicle length is 18.7 m except PCs 18.6 m and MTs of 21.8 m

• total length of train model arrangement is 387.9 m.

• The axle load at each wheel is about 17 tons, • the typical axle distance between two

adjacent wheels is 15.7 m

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Train model

Bridge and train model

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1/4 point 1/3 point 1/2 point 2/3point 3/4point

Location of inserted size adjusted vehicles

Configuration of size adjusted vehicle

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ᴥ The critical speed Vcr, causing Resonance

Vcr (m/s) = w.Seff

Where w = resonance frequency of the bridge (4.27 Hz)

Seff = effective periodic wheel loading interval (18.7 m)

Vcr = 288 km/hr

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CONCLUSION

The bridges resonant vibration can be reduced always by using size adjusted vehicles regardless of train speed & resonance frequency of the bridge

Thereby the proposed scheme can reduce subsequently the repair and maintenance costs associated with vibration induced damage.

The safety and the comfort of the passengers are also not compromised

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REFERENCES→ J-R Shin, Yun-Kyu An, Hoon Sohn,Chung-Ban Yun ,Vibration Reduction

Of High-speed Railway Bridges By Adding Size Adjusted Vehicles, Engineering Structures,2010, 2839-2849

→Fryba. L, Pirner.M, Load Tests And Modal Analysis Of Bridges, Engineering Structures,2001, 102-109

→Garinei.A, Risitano. G, Vibration Of Railway Bridges For High Speed Trains Under Moving Loads Varying In Time, Engineering Structures,2008, 724-732

→Yang Y.B, Lin C.L , Mechanisn Of Resonanace And Cancellation for Train Induced Vibration On Bridges With Elastic Bearings, Journal Of Sound Vibration,2004, 345-360

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