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Noise and Vibration Emissions of Railway Bridges
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 4 (2017) 3745–3753
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Noise and Vibration Emissions of Railway Bridges Anubhav Shivaaand Rajesh Purohita *, R. S. Ranaa and Dinesh Kumar Kolib Department of Mechanical Engeering, Maulana Azad National Institute of Technology, Bhopal-462003, India Department of Mechanical Engeering, SIRT, Bhopal, India.
Abstract
The goal of the paper is to address the problem of ground Bourne vibration and ways in which both humans and railway bridge structures respond to it. The methods of reducing the vibration and noise caused to railways bridges have been discussed. Transportation noise is one of the main components of environmental noise. It is estimated that around 1.7% of the total noise caused in the environment is due to the rail noise. Mainly the source of noise and vibration emissions of railway lines is due to the rough contact area of the wheel-rail, the time when a train is travelling on a bridge. Vibration is transmitted from the rail to the bridge via the track support structure. As of now, there is only little knowledge about the noise emission from railway bridges. The recent finding on the causes and reduction of these noise and vibration in bridges has been presented here. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:
1. Introduction The time when a train passes over a railway bridge, vibration generated by the combined wheel-rail roughness is transmitted from the rail to the bridge through the track support structure. As the tracks have properties like non-elasticity, so during the vibration displacement of particles is irreversible. This may be worsening and it also might lessenthe safety. Large amplitude of vibration of railway bridges may cause damages like ballast instability may change the geometry. That's whyit's important to regularly maintain the geometry and quality of component.
* Corresponding author. Tel.+09479953671. E-mail address:[email protected]
2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
3746
Rajesh Purohit et al / Materials Today: Proceedings 4 (2017) 3745–3753
This vibration energy disseminate via bridge resulting the whole bridge to radiate noise[1].The noise disseminated by this large structure normally constitutes a significant addition to the wheel-rail noise and other noise sources. There are also some different kinds of rail track structures used on bridges instead of plain track at-grade [2]. Measurements show that the overall noise level associated with a train travelling on a bridge may be up to 20dB greater than that for a train on plain track at-grade [3]. The source of noise and vibration emissions of railway lines is the rough contact are of the wheel rail. The roughness creates vibrations that are induced in the superstructure andpropagate through the soil to building in the neighborhoods. Moreover vibrations are also defined as perceptible low frequency oscillation between 1Hc and 80 Hz, whereas structure or grounds borne noise aremechanicalvibrations in an audible frequency range between 16 Hz and 20 kHz. These two kinds of emissions are disseminating though the air (railway track at ground level) and through the soil (railway tracks at ground level and underground). In adjacent structures these induced vibrations in the frequency range of around 8Hz to 20Hz, affect timber-ceiling structures or steel girder construction. As from the data the excitation frequencies of railway induced vibrations is almost between 40 to 80Hz. That may cause major acoustic phenomena that are called structure borne sound. As for the minimizing the vibration. Sufficient experiments have been performed and the results show these results more effective for the same by the applicationof Mass-Spring-Systems. The audible noise emission mainly from old steel bridge is a problem that has to be solved in future. 2. Structures 2.1 Railway bridge structures Nowadays in contemporary world bridges and viaducts are required in the railway in order to cross valleys, water (rivers, river estuaries and flood plains), roads and other railway lines. Here the term "viaduct" refers to a longer elevated structure,composed of many consecutive spans. The majority of modern bridges and viaducts can be divided into three groups like Concrete box-section, Concrete-steel composite and all steel shown here in Fig.1
(i) Concrete box section
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(ii) Concrete steel composite
(iii) All steel Fig.1 Modern Bridge Structures (i) Concrete box section,(ii) Concrete steel composite,(iii) All steel [5]
However in the past, masonry, iron and steel bridges were built for the railway. Masonry bridges are normally regarded as very low-noise elevated structures [6]. As they have required less attention with regard to noise. So in contemporary world these types of structures are not made as of their highcosting. As with different configurations Iron and Steel bridges have been building. And these all are only constructed through beams and these will be referred here as open bridge. The most common configurations of iron and steel bridges are Fig.2
(i)
Side-deck I-beam
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(ii) Under-deck I-beam
(iii) Side and under-deck I-beam Fig.2 Historical Design for Iron and Steel Railway Bridges:(i) Side-deck I-beam,(ii) Under-deck I-beam,(iii) Side and under-deck I-beam [6]
2.2.1. Railway Bridge tracks with Ballast layer Large numbers of railway tracks are ballasted. That means the rails are fastened to sleepers, which are supported by a layer of ballast. A cross-sectional view of a typical ballasted track arrangement on a railway bridge is shown Fig.3
Fig.3 Typical Ballast Track Arrangement on a Railway-Bridge [7]
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2.2.2Railway Bridge tracks without Ballast Layer In some of the conditions track structures do not include a ballast Layer or sleepers. So thesetypes of tracks are called as directly-fastened track. The only reason to use this type of track us that it requires less maintenance than ballasted track. The use of ballasted track is the major part of the running costs onrailway [8]. Though construction costs for directly-fastened track are greater than those for ballasted tracks. As bridges considered the use directly fastened track in preference to ballasted also brings the reduction in the total weight of the structure. And therefore it must support the bearing strength requirements. More and more use of directlyfastened track can lead tothe reduction in the overall depth of the bridge rail height. Modern rail fasteners on directly-fastened track are referred to as base plate-type rail, fasteners or base plates. A different base plate range is used. 3. Noise Reduction 3.1. Railway Bridge Noise All kind of bridges have the same noise characteristics. Among all the structures the lowest noise level are for concrete bridges with ballast track and can be compared with the at-grade track for given train speed [4]. And the highest noise level if for steel bridges with directly-fastened track. For bridges, ballast tracks the noise levels are lesser than those for the directly-fastened tracks. As the weight added on the bridge deck in case of ballast tracks, the vibration damping and sound absorption is more. In some of the report on noise generation due to different kind of bridges it was found that a concrete bridge produce noise mainly in the range up to about 500Hz, while steel bridges produce significant noise about 2kHz. 3.2. Noise control measures for Railway Bridges There are different approaches to reduce the noise for railway bridges [5]. Those are: i. ii. iii. iv. v. vi. vii.
Source reduction Vibration Isolation Vibration Damping Mass Addition Acoustic Isolation Acoustic Absorption Reduction of Radiating Area.
Here, Source reduction means improving the quality of the wheel and rail running surfaces. But as we talk there is very less and limited scope for such improvements [9].This vibration isolation principle and its application to Railway Bridges describe the use of this approach to achieve significant reductions in the noise radiated by the bridge/ Vibration Isolation using resilient base-plates found to be one of the most effective noise control measures for railway bridges. 3.3. Predictive models for bridge noise There have been many studies on the Railway bridge noise reduction. As the most effective model is Finite Element Model (FEM). The difficulty in using FEM is to predict bridge vibration and noise is the enormous number of modes expected in the frequency range of interest for bridge noise up to approximately 1500Hz. On another hand we have Statically Energy Analysis (SEA) method seems to address the difficulty of using the FE method for
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Railway bridges. The input power to each significant component of the structure or in SEA terms, each subsystem of the SEA network is equated to the power dissipated within it and the power flow to other subsystems (the coupling power). SEA has been widely used to predict the bridge noise and vibration [11]. 4. Vibration Reduction 4.1. Source of vibration in Railway bridges The vibration generated by the train as it crosses a bridge, the hammer blow caused due to the balance-weight which is attached to the driving wheels of a locomotive for the purpose of minimizing the inertia effect of its reciprocating parts. Due to the fact that the moving load is more or less suddenly applied. But oscillations of this character are very short-lived and relatively insignificant in magnitude. Vibrations also are caused by the rail-joints. 4.2. Natural frequencies This structure may be modeled as simply supported beam [12]. We know a beam has different modes of vibrations. The natural frequency of different modes of vibrations is given by equation, 𝒇𝒋 =
(i) First Bending Mode
𝒋𝟐
𝟐𝑳𝟐
𝑬𝑰
(1)
�µ
(ii) Second Bending Mode
Fig.3 First two Natural Modes of Vibration for a Simply Supported Beam: (i) First Bending Mode,(ii) Second Bending Mode [12]
4.3. Excitation at the Wheel-Rail Interface The component velocities at the contact point and the excitation force applied to the rail can be found the wheel-rail interaction calculation of each frequency [9].
𝒗𝒘,𝒐 = �
𝒗𝒓,𝒐 = �
𝒊𝝎𝒓𝒀𝒘
𝒀𝒓 +𝒀𝒘 +𝒀
𝑪
�
F=�
𝒊𝝎𝒓𝒀𝒓
𝒀𝒓 +𝒀𝒘 +𝒀𝑪
𝒊𝒘𝒓
𝒀𝒓 +𝒀𝒘 +𝒀𝑪
�
(2)
�
(4)
(3)
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Nowconsider, Vertical motion, which is expected to be adequate for the case for straight track. Though lateral excitation forces may be important for curved track. The wheel mobility is found from a two degree-offreedommodel for each wheel shown in Fig.4
Fig.4 Two degree freedom system for each wheel of train [10]
So the conclusion of this is that the rail mobility is found from a model of the rail as a beam continuously connected to another beam for the bridge by up to three continuous resilient layers end up to two continuous mass layers. This referred to as coupled beam model. 4.4. Vibration response of the bridge This vibration of the bridge is determined by the simplified SEA Scheme. As the equations state.
𝑷𝒃𝒓𝒊𝒅𝒈𝒆 = 𝑷𝒅𝒊𝒔𝒔𝒊𝒑𝒂𝒕𝒆𝒅 + 𝑷𝒓𝒂𝒅𝒊𝒂𝒕𝒊𝒐𝒏 ⩭ 𝑷𝒅𝒊𝒔𝒔𝒊𝒑𝒂𝒕𝒆𝒅
(5)
As it is assumed that the Radiated Power is small relative to dissipated power. [13].
Now, the power dissipated within each plate subsystem is related to its mean-square velocity as follows
𝑷𝒅𝒊𝒔𝒔,𝒊 = 𝟐𝝅𝒇𝒏𝒊 𝝆𝒊 𝒉𝒊 𝑨𝒊 < 𝒗𝒊 𝟐 >
(6)
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The equipartition of modal energy, ratio of mean-square velocities in two subsystems equals,
<𝒗𝒊 𝟐 >
<𝒗𝒋 𝟐 >
=
𝑹𝒆(𝒀𝒊 )
(7)
𝑹𝒆(𝒀𝒋 )
The situation when all the subsystems of the bridge have the same material properties and damping loss factor. The spatially averaged mean square velocity of subsystem j is obtained by equation [1],
< 𝒗𝒋 𝟐 >=
𝑷𝒃𝒓𝒊𝒅𝒈𝒆
(8)
𝑨 𝟐𝝅𝒇𝒏𝝆𝒉𝒋 𝟐 ∑ 𝒊 𝒉𝒊
On further solving, the power low between the two networks is then given by equations [14].
𝑷𝒆𝒅𝒈𝒆 = 𝑳𝒆𝒙 𝒗𝟏 𝟐 𝑹𝒆(𝒁′ )
(9)
4.5. Vibration control
4.5.1. Using fluid viscous dampers As fast trains induce more resonance situations in railway bridges, especially when structure is a simply supported beam type. The cause of resonance is when the time interval between the passages of repeated groups of loads over a particular section of the railway bridge comes out to be one of its natural periods. These resonant vibrations can be resolved by the use of Linear Fluid Viscous Dampers (FVD). These dampers have to be connected in the railway tracks. 4.5.2. Using Tuned Mass Dampers The use of Tuned Mass Dampers (TMDs) has maximally reduced the vertical bridge displacement by 21%, whereas the vertical acceleration remains virtually unchanged. Likewise the dampers are configured as in figure 5.
Fig.5 Retrofit configuration for a concrete girder bridge [15]
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The final installation consists of two main elements. The first element is an auxiliary, simply supported beam which is located underneath the main beam. The second element is a set of FVDs joining the vertical motion of certain sections of the main beam and the auxiliary one. Here our main focus is on the flexural vibrations of the main beam when the train of moving loads induces a resonance situation. So here we are analyzing a retrofit configuration as shown in fig.5.1. 5. Long span suspension bridges The long span bridge is playing a critical link in the transportation system and hence these are being under regular monitor for the purpose of both traffic and structural performance. The method of monitoring the structure using vibration measurements has been really attractive. By inversely solving the structural parameters that are obtained by the vibration response. The vibration can be used to examine the performance of structures. As the long span bridges are very flexible and dynamic properties are also very important as long span bridges can become unstable due to dynamic wind effects. 6. Conclusions When the simply supported beams are subjected to the moving loads, high resonant vibrations are produced. With the help of damping system proposed here, the resonant vibrations can be reduced. The damping system can also be applied to various situations when beams start vibrating at resonance due to different causes. The Finite Element Modeling (FEM) are used for only some lower range of frequencies. Since there are immense numbers of modes awaited in the frequency range of interest for bridge noise, therefore more difficulties arise using this model. One of the other methods to predict bridge noise and vibration is through Statistical Energy Analysis (SEA) method. This method is better sued for complex systems at high frequencies, where there are larger numbers of effective modes. Statistical Energy Analysis (SEA) method involves analogously lesser computational cost. Hence Statistical Energy Analysis (SEA) methodis widely used. Normal regular monitoring of Long Span Suspension Bridges are essential for better structural performance. References [1] M.H.A. and Thompson, D.J. Journal of Sound and Vibration, 1996, 193(1), 295-306. [2] Poisson and Margiocchi, Journal of sound and vibration, 2006, 51(3), 944-952. [3] Hardy, Noise from Railway Bridges, 1999, 213(3), 161-172. [4] L.G. Kurzweil, Prediction and Control of noise from railway bridges and tracked transit elevated structures, Journal of sound and vibration, 51, 418-438 [5] O.G. Bewes, Engineering Doctorate Thesis, University of Southampton, 2006, [6] Shield, Roberts and Vuillermoz, Noise on Docklands Light Railway, 1989, 26, 305-314 [7] Zhai, W.M., Wang and Lin J.H., Modeling and Experiment of Railway Ballast Vibrations, 2004, 270, 673-683. [8] Ban, Miyanmoto, Noise Control of High-Speed Railways, 1975, 43, 273-280 [9] A. Wang, O.G. Bewes, Cox, SJ Jones, Measurement and Modelingof Noise from the Arsta Bridge in Stockholm, 2007. [10] Fitzgerald B.M., Journal of sound and vibration, 193(1), 377-385. [11] Lyon, R.H. and Dejong, Theory and Application of Statistical Energy Analysis, 2nd Edition, 1995. [12] Fryba L, A rough assessment of railway bridges for high speed train engineering structures, 2000. [13] Cremer L., Heckl M.,Ungar E.E., Strucute-Borne Sound, Springer Verlag, 2nd Edition, 1998. [14] Beranek L.L, and Ver I.L., Noise nad Vibration Control Engineering, John Wiley and Sons, New Yord, 1992. [15] Kwon H.C., Kim M.C., Lee I.W., Vibration control of bridges under moving loads, Computers and Strucutres,1998, 66, 473-480.
ScienceDirect Materials Today: Proceedings 4 (2017) 3745–3753
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Noise and Vibration Emissions of Railway Bridges Anubhav Shivaaand Rajesh Purohita *, R. S. Ranaa and Dinesh Kumar Kolib Department of Mechanical Engeering, Maulana Azad National Institute of Technology, Bhopal-462003, India Department of Mechanical Engeering, SIRT, Bhopal, India.
Abstract
The goal of the paper is to address the problem of ground Bourne vibration and ways in which both humans and railway bridge structures respond to it. The methods of reducing the vibration and noise caused to railways bridges have been discussed. Transportation noise is one of the main components of environmental noise. It is estimated that around 1.7% of the total noise caused in the environment is due to the rail noise. Mainly the source of noise and vibration emissions of railway lines is due to the rough contact area of the wheel-rail, the time when a train is travelling on a bridge. Vibration is transmitted from the rail to the bridge via the track support structure. As of now, there is only little knowledge about the noise emission from railway bridges. The recent finding on the causes and reduction of these noise and vibration in bridges has been presented here. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:
1. Introduction The time when a train passes over a railway bridge, vibration generated by the combined wheel-rail roughness is transmitted from the rail to the bridge through the track support structure. As the tracks have properties like non-elasticity, so during the vibration displacement of particles is irreversible. This may be worsening and it also might lessenthe safety. Large amplitude of vibration of railway bridges may cause damages like ballast instability may change the geometry. That's whyit's important to regularly maintain the geometry and quality of component.
* Corresponding author. Tel.+09479953671. E-mail address:[email protected]
2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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Rajesh Purohit et al / Materials Today: Proceedings 4 (2017) 3745–3753
This vibration energy disseminate via bridge resulting the whole bridge to radiate noise[1].The noise disseminated by this large structure normally constitutes a significant addition to the wheel-rail noise and other noise sources. There are also some different kinds of rail track structures used on bridges instead of plain track at-grade [2]. Measurements show that the overall noise level associated with a train travelling on a bridge may be up to 20dB greater than that for a train on plain track at-grade [3]. The source of noise and vibration emissions of railway lines is the rough contact are of the wheel rail. The roughness creates vibrations that are induced in the superstructure andpropagate through the soil to building in the neighborhoods. Moreover vibrations are also defined as perceptible low frequency oscillation between 1Hc and 80 Hz, whereas structure or grounds borne noise aremechanicalvibrations in an audible frequency range between 16 Hz and 20 kHz. These two kinds of emissions are disseminating though the air (railway track at ground level) and through the soil (railway tracks at ground level and underground). In adjacent structures these induced vibrations in the frequency range of around 8Hz to 20Hz, affect timber-ceiling structures or steel girder construction. As from the data the excitation frequencies of railway induced vibrations is almost between 40 to 80Hz. That may cause major acoustic phenomena that are called structure borne sound. As for the minimizing the vibration. Sufficient experiments have been performed and the results show these results more effective for the same by the applicationof Mass-Spring-Systems. The audible noise emission mainly from old steel bridge is a problem that has to be solved in future. 2. Structures 2.1 Railway bridge structures Nowadays in contemporary world bridges and viaducts are required in the railway in order to cross valleys, water (rivers, river estuaries and flood plains), roads and other railway lines. Here the term "viaduct" refers to a longer elevated structure,composed of many consecutive spans. The majority of modern bridges and viaducts can be divided into three groups like Concrete box-section, Concrete-steel composite and all steel shown here in Fig.1
(i) Concrete box section
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(ii) Concrete steel composite
(iii) All steel Fig.1 Modern Bridge Structures (i) Concrete box section,(ii) Concrete steel composite,(iii) All steel [5]
However in the past, masonry, iron and steel bridges were built for the railway. Masonry bridges are normally regarded as very low-noise elevated structures [6]. As they have required less attention with regard to noise. So in contemporary world these types of structures are not made as of their highcosting. As with different configurations Iron and Steel bridges have been building. And these all are only constructed through beams and these will be referred here as open bridge. The most common configurations of iron and steel bridges are Fig.2
(i)
Side-deck I-beam
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Rajesh Purohit et al / Materials Today: Proceedings 4 (2017) 3745–3753
(ii) Under-deck I-beam
(iii) Side and under-deck I-beam Fig.2 Historical Design for Iron and Steel Railway Bridges:(i) Side-deck I-beam,(ii) Under-deck I-beam,(iii) Side and under-deck I-beam [6]
2.2.1. Railway Bridge tracks with Ballast layer Large numbers of railway tracks are ballasted. That means the rails are fastened to sleepers, which are supported by a layer of ballast. A cross-sectional view of a typical ballasted track arrangement on a railway bridge is shown Fig.3
Fig.3 Typical Ballast Track Arrangement on a Railway-Bridge [7]
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2.2.2Railway Bridge tracks without Ballast Layer In some of the conditions track structures do not include a ballast Layer or sleepers. So thesetypes of tracks are called as directly-fastened track. The only reason to use this type of track us that it requires less maintenance than ballasted track. The use of ballasted track is the major part of the running costs onrailway [8]. Though construction costs for directly-fastened track are greater than those for ballasted tracks. As bridges considered the use directly fastened track in preference to ballasted also brings the reduction in the total weight of the structure. And therefore it must support the bearing strength requirements. More and more use of directlyfastened track can lead tothe reduction in the overall depth of the bridge rail height. Modern rail fasteners on directly-fastened track are referred to as base plate-type rail, fasteners or base plates. A different base plate range is used. 3. Noise Reduction 3.1. Railway Bridge Noise All kind of bridges have the same noise characteristics. Among all the structures the lowest noise level are for concrete bridges with ballast track and can be compared with the at-grade track for given train speed [4]. And the highest noise level if for steel bridges with directly-fastened track. For bridges, ballast tracks the noise levels are lesser than those for the directly-fastened tracks. As the weight added on the bridge deck in case of ballast tracks, the vibration damping and sound absorption is more. In some of the report on noise generation due to different kind of bridges it was found that a concrete bridge produce noise mainly in the range up to about 500Hz, while steel bridges produce significant noise about 2kHz. 3.2. Noise control measures for Railway Bridges There are different approaches to reduce the noise for railway bridges [5]. Those are: i. ii. iii. iv. v. vi. vii.
Source reduction Vibration Isolation Vibration Damping Mass Addition Acoustic Isolation Acoustic Absorption Reduction of Radiating Area.
Here, Source reduction means improving the quality of the wheel and rail running surfaces. But as we talk there is very less and limited scope for such improvements [9].This vibration isolation principle and its application to Railway Bridges describe the use of this approach to achieve significant reductions in the noise radiated by the bridge/ Vibration Isolation using resilient base-plates found to be one of the most effective noise control measures for railway bridges. 3.3. Predictive models for bridge noise There have been many studies on the Railway bridge noise reduction. As the most effective model is Finite Element Model (FEM). The difficulty in using FEM is to predict bridge vibration and noise is the enormous number of modes expected in the frequency range of interest for bridge noise up to approximately 1500Hz. On another hand we have Statically Energy Analysis (SEA) method seems to address the difficulty of using the FE method for
Rajesh Purohit et al / Materials Today: Proceedings 4 (2017) 3745–3753
3750
Railway bridges. The input power to each significant component of the structure or in SEA terms, each subsystem of the SEA network is equated to the power dissipated within it and the power flow to other subsystems (the coupling power). SEA has been widely used to predict the bridge noise and vibration [11]. 4. Vibration Reduction 4.1. Source of vibration in Railway bridges The vibration generated by the train as it crosses a bridge, the hammer blow caused due to the balance-weight which is attached to the driving wheels of a locomotive for the purpose of minimizing the inertia effect of its reciprocating parts. Due to the fact that the moving load is more or less suddenly applied. But oscillations of this character are very short-lived and relatively insignificant in magnitude. Vibrations also are caused by the rail-joints. 4.2. Natural frequencies This structure may be modeled as simply supported beam [12]. We know a beam has different modes of vibrations. The natural frequency of different modes of vibrations is given by equation, 𝒇𝒋 =
(i) First Bending Mode
𝒋𝟐
𝟐𝑳𝟐
𝑬𝑰
(1)
�µ
(ii) Second Bending Mode
Fig.3 First two Natural Modes of Vibration for a Simply Supported Beam: (i) First Bending Mode,(ii) Second Bending Mode [12]
4.3. Excitation at the Wheel-Rail Interface The component velocities at the contact point and the excitation force applied to the rail can be found the wheel-rail interaction calculation of each frequency [9].
𝒗𝒘,𝒐 = �
𝒗𝒓,𝒐 = �
𝒊𝝎𝒓𝒀𝒘
𝒀𝒓 +𝒀𝒘 +𝒀
𝑪
�
F=�
𝒊𝝎𝒓𝒀𝒓
𝒀𝒓 +𝒀𝒘 +𝒀𝑪
𝒊𝒘𝒓
𝒀𝒓 +𝒀𝒘 +𝒀𝑪
�
(2)
�
(4)
(3)
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Nowconsider, Vertical motion, which is expected to be adequate for the case for straight track. Though lateral excitation forces may be important for curved track. The wheel mobility is found from a two degree-offreedommodel for each wheel shown in Fig.4
Fig.4 Two degree freedom system for each wheel of train [10]
So the conclusion of this is that the rail mobility is found from a model of the rail as a beam continuously connected to another beam for the bridge by up to three continuous resilient layers end up to two continuous mass layers. This referred to as coupled beam model. 4.4. Vibration response of the bridge This vibration of the bridge is determined by the simplified SEA Scheme. As the equations state.
𝑷𝒃𝒓𝒊𝒅𝒈𝒆 = 𝑷𝒅𝒊𝒔𝒔𝒊𝒑𝒂𝒕𝒆𝒅 + 𝑷𝒓𝒂𝒅𝒊𝒂𝒕𝒊𝒐𝒏 ⩭ 𝑷𝒅𝒊𝒔𝒔𝒊𝒑𝒂𝒕𝒆𝒅
(5)
As it is assumed that the Radiated Power is small relative to dissipated power. [13].
Now, the power dissipated within each plate subsystem is related to its mean-square velocity as follows
𝑷𝒅𝒊𝒔𝒔,𝒊 = 𝟐𝝅𝒇𝒏𝒊 𝝆𝒊 𝒉𝒊 𝑨𝒊 < 𝒗𝒊 𝟐 >
(6)
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The equipartition of modal energy, ratio of mean-square velocities in two subsystems equals,
<𝒗𝒊 𝟐 >
<𝒗𝒋 𝟐 >
=
𝑹𝒆(𝒀𝒊 )
(7)
𝑹𝒆(𝒀𝒋 )
The situation when all the subsystems of the bridge have the same material properties and damping loss factor. The spatially averaged mean square velocity of subsystem j is obtained by equation [1],
< 𝒗𝒋 𝟐 >=
𝑷𝒃𝒓𝒊𝒅𝒈𝒆
(8)
𝑨 𝟐𝝅𝒇𝒏𝝆𝒉𝒋 𝟐 ∑ 𝒊 𝒉𝒊
On further solving, the power low between the two networks is then given by equations [14].
𝑷𝒆𝒅𝒈𝒆 = 𝑳𝒆𝒙 𝒗𝟏 𝟐 𝑹𝒆(𝒁′ )
(9)
4.5. Vibration control
4.5.1. Using fluid viscous dampers As fast trains induce more resonance situations in railway bridges, especially when structure is a simply supported beam type. The cause of resonance is when the time interval between the passages of repeated groups of loads over a particular section of the railway bridge comes out to be one of its natural periods. These resonant vibrations can be resolved by the use of Linear Fluid Viscous Dampers (FVD). These dampers have to be connected in the railway tracks. 4.5.2. Using Tuned Mass Dampers The use of Tuned Mass Dampers (TMDs) has maximally reduced the vertical bridge displacement by 21%, whereas the vertical acceleration remains virtually unchanged. Likewise the dampers are configured as in figure 5.
Fig.5 Retrofit configuration for a concrete girder bridge [15]
Rajesh Purohit et al / Materials Today: Proceedings 4 (2017) 3745–3753
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The final installation consists of two main elements. The first element is an auxiliary, simply supported beam which is located underneath the main beam. The second element is a set of FVDs joining the vertical motion of certain sections of the main beam and the auxiliary one. Here our main focus is on the flexural vibrations of the main beam when the train of moving loads induces a resonance situation. So here we are analyzing a retrofit configuration as shown in fig.5.1. 5. Long span suspension bridges The long span bridge is playing a critical link in the transportation system and hence these are being under regular monitor for the purpose of both traffic and structural performance. The method of monitoring the structure using vibration measurements has been really attractive. By inversely solving the structural parameters that are obtained by the vibration response. The vibration can be used to examine the performance of structures. As the long span bridges are very flexible and dynamic properties are also very important as long span bridges can become unstable due to dynamic wind effects. 6. Conclusions When the simply supported beams are subjected to the moving loads, high resonant vibrations are produced. With the help of damping system proposed here, the resonant vibrations can be reduced. The damping system can also be applied to various situations when beams start vibrating at resonance due to different causes. The Finite Element Modeling (FEM) are used for only some lower range of frequencies. Since there are immense numbers of modes awaited in the frequency range of interest for bridge noise, therefore more difficulties arise using this model. One of the other methods to predict bridge noise and vibration is through Statistical Energy Analysis (SEA) method. This method is better sued for complex systems at high frequencies, where there are larger numbers of effective modes. Statistical Energy Analysis (SEA) method involves analogously lesser computational cost. Hence Statistical Energy Analysis (SEA) methodis widely used. Normal regular monitoring of Long Span Suspension Bridges are essential for better structural performance. References [1] M.H.A. and Thompson, D.J. Journal of Sound and Vibration, 1996, 193(1), 295-306. [2] Poisson and Margiocchi, Journal of sound and vibration, 2006, 51(3), 944-952. [3] Hardy, Noise from Railway Bridges, 1999, 213(3), 161-172. [4] L.G. Kurzweil, Prediction and Control of noise from railway bridges and tracked transit elevated structures, Journal of sound and vibration, 51, 418-438 [5] O.G. Bewes, Engineering Doctorate Thesis, University of Southampton, 2006, [6] Shield, Roberts and Vuillermoz, Noise on Docklands Light Railway, 1989, 26, 305-314 [7] Zhai, W.M., Wang and Lin J.H., Modeling and Experiment of Railway Ballast Vibrations, 2004, 270, 673-683. [8] Ban, Miyanmoto, Noise Control of High-Speed Railways, 1975, 43, 273-280 [9] A. Wang, O.G. Bewes, Cox, SJ Jones, Measurement and Modelingof Noise from the Arsta Bridge in Stockholm, 2007. [10] Fitzgerald B.M., Journal of sound and vibration, 193(1), 377-385. [11] Lyon, R.H. and Dejong, Theory and Application of Statistical Energy Analysis, 2nd Edition, 1995. [12] Fryba L, A rough assessment of railway bridges for high speed train engineering structures, 2000. [13] Cremer L., Heckl M.,Ungar E.E., Strucute-Borne Sound, Springer Verlag, 2nd Edition, 1998. [14] Beranek L.L, and Ver I.L., Noise nad Vibration Control Engineering, John Wiley and Sons, New Yord, 1992. [15] Kwon H.C., Kim M.C., Lee I.W., Vibration control of bridges under moving loads, Computers and Strucutres,1998, 66, 473-480.