PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Verification of Accuracy Using Measured Values of Low Frequency
Noise Numerical Analysis Generated from Expressway Bridge
Hiroshi IWABUKI1; Osamu FUNAHASHI2; Masayuki SHIMURA3; Noboru KAMIAKITO4
1

Nippon Expressway Research Institute Company Limited., Japan

2

Nippon Expressway Research Institute Company Limited., Japan

3

Civil Engineering And Eco-Technology Consultants Company Limited., Japan

4

Civil Engineering And Eco-Technology Consultants Company Limited., Japan

ABSTRACTIn Japan, road managers including expressway may respond to complaints such as road traffic noise,
vibration, low frequency noise, and so on from residents along the road. Among these countermeasures, noiseand vibration and so on complaints are identified and countermeasures are further examined and constructed,
but on the other hand, in the case of low frequency noise caused by bridges, many examinations on theoccurrence mechanism are required. Therefore, in this study, unsteady analysis was proposed by threedimensional finite element method on responses of a bridge due to vehicle load running on a bridge. The
numerical simulation of the low frequency noise field was carried out by calculating the three dimensional
wave equations with this unsteady analysis result as an unsteady boundary condition. By this method, it
became possible to quantitatively investigate to which part of the bridge the cause of the low frequency noise
originates. In this paper, identification of the cause of occurrence and simulation accuracy of the propagation
path were verified by using the measured results of low frequency noise and vibration acceleration.
Keywords: Low Frequency Noise, Sound, Expressway Bridge, Numerical Analysis

1. INTRODUCTION
With the promotion of public works, environmental problems, especially low frequency noiseproblems may occur. In recent years, many low frequency noise problems have arisen in wind power
facilities in each country, and guidelines are shown and operated in Australia, New Zealand, Canada
and Norway. [1-8] In Japan, the Ministry of Environment has established the "Manual for measuringlow-frequency sound" [9], and this manual has been in operation since October 2000. In this manual,
it is shown that the generation mechanism of low frequency sound and the generation source according
to the generation mechanism are a) due to flat plate vibration, b) due to pulsation of air flow, c) due
to unsteady excitation of gas, d) rapid of air compression and release.
In Japan, the vibration of girders and slabs by the road traffic vibration spreads in the air, andproduces low frequency noises in a land bridge particularly expressway bridge, and may receive acomplaint from inhabitants to live in near expressways. It is necessary identifying an outbreak source
and to examine an effective measures mechanic to cope with this complaint. What I install a lot of
sensors in each part and material and belonging of the bridge, and many points measure at the sametime is necessary, and there are great labor and the problem to cost of the expense in the preparations,
measurement, analysis to measure the vibration of a figure and the floor version of the bridge, and toanalyze it. It is intended that they estimate vibration and the quantity of the bridge by the simulation
outbreak of the low frequency sound in substitution for the measurement in the true bridge, and thewriters study technique analyzing the sound of the low frequency sound from dynamic reply analysisof the bridge upper part mechanic by the three dimensions finite element method to solve these. I
became able to consider which part of the viaduct the cause of the low frequency sound was greatly
1h.iwabuki.aa@ri-nexco.co.jp
o.funahashi.aa@ri-nexco.co.jp
3
shimura@kensetsukankyo.co.jp
4kamiakit@kensetsukankyo.co.jp
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caused by by past results of research [10] quantitatively. In this article, I report the result thatexamined identification of the origin and the simulation precision of the spread course using an actual
survey result of a low frequency sound and the vibration acceleration.

2. Research bridge and conditions of measurement and analysis
Here, the outline of the bridge measured in this research, and the measurement conditions and analysis
conditions are described.
2.1

Bridge outline
The target bridge of measurement and analysis of this research is 10 span continuous steel 2
main girder bridge among continuous viaducts. The main girder height is 4 m, the width is 10.9 m,
the span length is 35 m, and a noise insulation wall with a height of 4 m is installed on the roadshoulder side. A side view is shown in Fig. 1 and a cross-sectional view is shown in Fig.2
35m × 10 ＝ 350m

35m × 10 ＝ 350m
4m
6m

P20 P21 P22 P23 P24 P25 P26 P27 P28 P29 P30 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

Fig.1 Side view
2.2

Measurement condition
Low frequency noise pressure levels were measured
near the target bridge. The layout of the measurement
points is shown in Fig.3and Fig.4. Four points were
measured at a distance of 10 m from the bridge in the
direction perpendicular to the bridge axis. In the bridge
axis direction, S1 was set at P30, S2 was set at the middleof the span between P30 and P1, S3 was set at P1, and S4
was set at the middle of the span between P1 and P2. The
measurement was performed at a sampling frequency of
200 Hz using a low frequency sound level meter NA-18
manufactured by RION.

4m
1m
2.5m
2m

6.9m

2m

Fig.2 Cross-sectional view

Bridge: Measurement
point
17.5m
17.5m
17.5m

2m

P3

S2
S1

1m

P1

2.5m

Expansion
P30 Device

6m

P29
10m

2m

4m

P2

S4
S3

6.9m

1.2m
10.9m

Fig.3 Plan view

10m

Fig.4

Cross-sectional view

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2.3

Analysis condition
The sound field space to be analyzed covered four spans from P29 to P3 including the expansion
device of P30. The dynamic response analysis of the bridge used the existing commercial code DALIA(KOZO KEIKAKU ENGINEERING Inc.). The motion equation was discretized by the finite element
method, and time integration was sequentially performed on the unsteady external force (vehicle
travel) to perform unsteady response analysis. By setting the vibration velocity waveform of the entire
bridge calculated from the dynamic response analysis of the bridge as the load velocity, the soundfield analysis is performed by FEM, with the entire bridge modeled in the dynamic response analysis
as the target of sound pressure radiation. The conditions of the model were changed and analysis was
performed in seven cases. Case 1 is the basis. Case 2, 3 and 4 were set in which the mesh spacing ofCase 1 was changed. Cases 5, 6, and 7 were set in which the sound field space of Case 1 was changed.
It is shown in Table 1. The analysis time was 5 seconds from the time when the vehicle passes P29.
Table.1
Sound Field [m]itemdirectionxyz

Analysis condition
Mesh [m]xzconditions

case 1

35

140

20

1

0.5

basis

case 2

35

140

20

2

0.5

Mesh: 2x in x direction

case 3

35

140

20

1

1

Mesh: 2x in z direction

case 4

35

140

20

1

2

Mesh: 4x in z direction

case 5

35

105

20

1

0.5

from P29 to P2

case 6

35

70

20

1

0.5

from P29 to P1

case 7

35

105

20

1

0.5

from P30 to P3

2.4

running conditions of the test vehicle
The measurement of low frequency noise was performed by driving a large test vehicle (Nissan
Diesel: KL-CD48ZWH, 3-axis large vehicle, gross weight 245kN) with the general vehicle runningexcluded. The traveling position was in the traveling lane, and the traveling speed was 80 km / h.
Analysis was performed by modeling this vehicle.

3. ANALYSIS METHOD OF LOW FREQUENCY NOISE
Here, a method of analyzing low frequency sound is described. In this research, in order tosolve the dynamic response calculation of the structure by the three-dimensional finite element
method and transmit it to the sound field space, the sound field analysis is also solved by the threedimensional finite element method so that stress transfer of boundary conditions becomes easy. It was.
[11] The excitation source was a driving excitation of a large test vehicle (Nissan Diesel: KLCD48ZWH, 3-axle large vehicle, gross weight 245 kN) [12].
3.1

Primitive equation
In order to carry out the numeric simulation for the sound propagation in the air, the primitive
variable equations are described in continuous system and equation of motion, as follows



u p

0
t  xv p
  0   w  p  0t yt  z u v w p  0 C 2   
t

x

y

z



(1)

(2)

Where x, y, z are three dimensional coordinate system in space, and u, v, and w are acoustic

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particulate velocity for each direction. While p, ρ, C and t are sound pressure, the density of air, soundspeed and time respectively. Unknown parameters are u, v, w, and p.
3.2

Derivation of a wave equation
For efficient calculation, velocity potential φ is introduced to derive wave equation below with
one unknown parameter, thus


t

p

u


x

v


y

w


z

(3)

Where p is differentiated by time and u, v, and w are differentiated by each space coordinates. The
derivative formulas become,

p
 2
 2
t
t

u
 2
 2
x
x

v
 2
 2
y
y

w
 2
 2
z
z

(4)

Then wave equation can be obtained by substitute these equations into continuous system.
2
 2
 2  2  
2  
C  x 2  y 2   z 2   0
t 2



(5)

3.3

Finite element equation and Boundary condition
The finite element method is applied to the wave equation to obtain matrix equation. However,linear shape function is used for unknown values on the peak of hexahedral element .
3.3.1 Finite element equation
Finite element equation is described as follows

 2
M 2  C 2 S xx  S yy  S zz   C 2 Nunt(6)Then, each matrix is introduced by following integrationM   N  N  dS xx  N   N  N  dN  N 
N N N N d S yy   d S zz   
d
x x
y y
z z

(7)

(8)

Where dΩ and dΓ are the analysis domain and the boundary, respectively.
3.3.2 Handling of a time differentiation clause
Time derivative of φ can be differentiated as follows, 2  m1  2 m   m1

t 2
t 2

(9)

Where m means time step.
3.3.3 Boundary condition* The definition for particle velocity (e.g. the slab plate, the sound barriers, and the back acoustic
board) is given by4671

un  


n

(10)

* Sound penetration condition (i.e. impedance conditions: with open boundary) is presented byun p 1 1 Ct C C t(11)

* Sound reflection condition (for solid surfaces, such as the ground surface and a building used as
natural boundary conditions in FEM) can be defined as

un  


0
n

(12)

Where n is the normal direction of coordinate system.
With the application of lumped mass finite element equation, inverse-matrix calculation of M
becomes unnecessary, thus improve calculation speed.

4. Analysis of measurements and results
4.1

Time history waveforms
The time history waveform of the measured value and the analyzed value is compared andanalyzed. The respective time history waveforms of S1 to S4 are shown in Fig.5 to Fig.8.

2.0

case2
case3

0.0

case4
case5
case6
case7

-4.0
0.0

2.5
Time [s]Sound Pressure [Pa]

case1

-2.0

Sound Pressure [Pa]4.0

measuremeasure
case1

2.0

case2
case3

0.0

case4
case5

-2.0

case6
case7

-4.0

5.0

0.0

2.5
Time [s]5.0

Fig.5 Time history waveforms of S1

Fig.6 Time history waveforms of S2

4.0

4.0

measure
case1

2.0

case2
case3

0.0

case4
case5

-2.0

case6
case7

-4.0
0.0

2.5
Time [s]5.0

Fig.7 Time history waveforms of S3

Sound Pressure [Pa]Sound Pressure [Pa]4.0

measure
case1

2.0

case2
case3

0.0

case4
case5

-2.0

case6
case7

-4.0
0.0

2.5
Time [s]5.0

Fig.8 Time history waveforms of S4

The vehicle is reached at P30 (Time = 1.575[s]) having an expansion device, passing P29 (Time= 0.0 [s]). After that, it can be seen that the value of the low frequency noise increases. This tendency
is also observed with measured values and analyzed values. In the analysis values, Case 2 and 4 tend4672

to have a slightly different amplitude. It is assumed that changing the mesh spacing in the direction
perpendicular to the bridge axis has an influence on the amplitude. On the other hand, even if themesh spacing in the bridge axis direction is changed, the influence on the amplitude is small. It is
assumed that the contribution from the nearest bridge member is high, and that the low frequency
sound propagates radially but has a certain directivity. On the other hand, no major difference is seen
except Case 2. Therefore, even if the mesh spacing in the bridge axis direction is changed, theinfluence on the amplitude is small.
4.2

Frequency characteristics
The frequency characteristics were calculated by FFT analysis of time history waveform data.
The condition of the FFT analysis was that the number of output points was 1,024 points, the windowfunction was a Hamming function, the sampling time was 0.005 [s], and the frequency resolution was
0.0976625 [Hz]. The frequency characteristics were calculated under these conditions for bothmeasured and analyzed values, and comparison and analysis were performed. In the vertical axis, theleft side is the measured value, and the right side is the analyzed value.

100.0

210.0
measure
case2
case3

40.0

70.0

case4
case5

20.0
0.0

0.0
0.0

10.0 20.0 30.0
Frequency [Hz]case6

Spectrum [Pa]

50.0

300.0

40.0

240.0

measure
case1

30.0

180.0

case2

20.0

120.0

10.0

60.0

0.0

0.0
0.0

10.0 20.0 30.0
Frequency [Hz]

case3
case4
case5
case6
case7

Fig.12 Frequency characteristics of S3

210.0

60.0
140.0
40.0
70.0

20.0
0.0

case7

Fig.10 Frequency characteristics of S1

280.0

80.0
Spectrum [Pa]

140.0

60.0

case1

0.0
0.0

10.0 20.0 30.0
Frequency [Hz]measure
case1
case2
case3
case4
case5
case6
case7

Fig.11 Frequency characteristics of S2Spectrum [Pa]80.0

Spectrum [Pa]

100.0

200.0

100.0

160.0

80.0

120.0

60.0

80.0

40.0

40.0

20.0

0.0

0.0

measurecase1

0.0

10.0 20.0 30.0
Frequency [Hz]

case2
case3
case4
case5
case6
case7

Fig.13 Frequency characteristics of S4

The respective frequency characteristics of S1 to S4 are shown in Fig 10 to Fig.13. The mostprominent frequency is 3 to 4 [Hz] in the actual measurement value, while the analysis value isapproximately 2 to 3 [Hz], though it is slightly smaller, but it is almost the same. Although the degreeof excellence are different in the tens of Hz band, the peak values are almost the same. Focusing only
on analysis, Case 2 shows slightly different characteristics from the other cases. This is similar to thetime history waveform. Changing the mesh spacing in the direction perpendicular to the bridge axis
affects the frequency characteristics, while changing the mesh spacing in the bridge axis direction
reduces the effects on the frequency characteristics. Focusing only on analysis, S2 and S4 on the sideof the center of the span have almost no difference in frequency characteristics in each case, while S1and S3 on the side of the bridge pier have differences in frequency characteristics in each case. In an
actual phenomenon, it is possible that structures such as girder ends, supports, and bridge piers4673

influenced the propagation of low frequency sound, and it is assumed that the analysis value deviatesfrom the actual measurement value. Also, in the frequency band above 20 Hz, the analysis value tends
to deviate from the measured value. It is conceivable that as the frequency band becomes higher, thewavelength becomes shorter, and when the mesh spacing is large, the waveform cannot be captured.
In order to increase the accuracy of this frequency band by this method, it is considered necessary to
reduce the mesh spacing.
From the above, the present method is in a situation where it is difficult to make the analysis
value coincide with the measurement value at present, but it is possible to derive the tendency of thefrequency characteristic of the measurement value from the analysis value. Therefore, environmental
problems relating to low frequency noise occur, and it is considered to be effective in investigating
the cause and taking measures.

5. CONCLUSIONSIn this paper, we developed a method to analyze the acoustics of low frequency noise with theaim of estimating the vibration and low frequency noise of the bridge by simulation without measuring
the actual bridge. In addition, low frequency noise was measured when a test vehicle was run without
a general vehicle traveling on a bridge in service, and the measurement results were compared withthe analysis results. As a result, the following was shown.
The actual measurement value and the analysis value by the present method differ in the
degree of excellence of the amplitude value of the time history waveform and thefrequency characteristic. However, almost the same tendency was obtained for thefrequency characteristics. Therefore, it is considered effective in investigating the causesof environmental problems and taking measures.
The mesh spacing of the sound field space needs to set the spacing necessary for analysisof the target frequency band.

These acquired findings are considered to be useful for coping with environmental problems
that occur in various projects such as expressway projects.
In the future, it is an issue to expand the application range of this method by conducting similar
analysis with different types of bridges.

ACKNOWLEDGEMENTS
In this research, the members of the Road Traffic Vibration Estimation Subcommittee of theInstitute of Noise Control Engineering of Japan (INCE/J) received a great deal of cooperation inexperiments and analysis. I express my gratitude to this.

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Noise Limits，3rd International Conference on Wind Turbine Noise （WTN2009）.
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9. Manual on how to measure low frequency sound : Ministry of Environment, 2000.10.
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