assessment of traffic-induced low frequency noise radiated...

Steel Structures 8 (2008) 305-314 www.ijoss.org

Assessment of Traffic-induced Low Frequency Noise Radiated

from Steel Box Girder Bridge

Mitsuo Kawatani1, Chul-Woo Kim2*, Naoki Kawada3, and Shohei Koga4

1Professor, Dept. of Civil Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan2Research Scientist, Dept. of Civil Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan

3Structural Engineer, ACE Co., Ltd., Kyoto 600-8133, Japan4Structural Engineer, Obayashi Co., Shinagawa Intercity Tower, 2-15-2 Konan, Minato, Tokyo108-8502, Japan

Abstract

This study intends to investigate traffic-induced low frequency noises radiated from a seven span continuous steel box girderbridge which adopts steel decks and steel piers integrated with the superstructure rigidly. The low frequency sound pressurelevel (SPL) is estimated by means of the boundary element method (BEM) using velocity responses of the bridge. The velocityresponse is estimated from a three dimensional bridge-vehicle interactive analysis. The influence of the sound wave reflectedby ground is also considered in the analysis using the image method. Observations demonstrate that the vehicle moving on theouter lane (slow traffic lane) gives higher SPL than running on inner lane (passing lane) because of the torsional effect.Increasing the number of vehicles increases SPL as expected.

Keywords: boundary element method, low frequency noise, steel box girder bridge, traffic-induced vibration

1. Introduction

Low frequency noise radiated from highway bridges

due to moving vehicles has been one of environmental

vibration problems in Japan. Especially in some land

scarce major cities of Japan, viaducts have been

constructed even near to the residential zone, and as a

result a number of complaints about the noise from those

viaducts have been reported. Usually the noise radiated

from engines and tires of heavy vehicles are one of the

most typical environmental problems (e.g. Eberhardt

1988). The ground vibration is also categorized as a

major environmental vibration problem (e.g. Sheng et al.,

2006). In comparing to those ground vibrations and

noises from vehicles, the problem relating to the low

frequency vibration radiated from bridge vibrations under

moving vehicles has been a minor problem. However, the

increase of truck weight and heavy traffic volume as well

as adopting light structures with a simplified bridge

system give rise to the low frequency vibration problems

(e.g. Kim and Kawatani, 2003; Kim et al., 2004).

Very restricted numbers of the research were performed

focusing on the low frequency noise radiated from

highway bridges (e.g. Goromaru et al., 1987). It means

that effective countermeasure as well as systematic

approaches to reduce the vibration of bridges has not

been established yet. An important breakthrough in the

low frequency environmental problem radiated from

bridges, preliminary investigations using analytical tools

will be a solution if proper numerical and simulation

methods to examine the low-frequency noise problem of

highway bridges are available.

This study intends to assess the low frequency noise

radiated from a viaduct analytically. Analytical methods

for the bridge-vehicle interactive system and sound

propagation from the bridge are briefly described. The

sound propagation is estimated using boundary integral

equations which are solved by the boundary element

method (BEM) (Kawada and Kawatani, 2006). Dynamic

responses of the bridge are taken from a three-

dimensional traffic-induced vibration analysis (Kawatani

et al., 2005; Kim et al., 2005). The sound pressure level

at an observation point is estimated from the velocity of

steel decks and lower flanges of box girders which is

taken from the dynamic response analysis. The influence

of the sound wave reflected by ground is also considered

in the analysis using the image method (Ciskowski and

Brebbia, 1991; Wrobel, 2002).

2. Analytical Method

In this study, dynamic responses of a bridge are firstly

taken from the traffic-induced vibration analysis of a

Note.-Discussion open until May 1, 2009. This manuscript for thispaper was submitted for review and possible publication on October1, 2008; approved on December 1, 2008

*Corresponding authorTel: +81-78-803-6383; Fax: +81-78-803-6069E-mail: [email protected]

306 Mitsuo Kawatani et al.

bridge based on the modal analysis. Low frequency

noises are then investigated by means of the boundary

element method (BEM) (Cikawski and Brebbia, 1991;

Wrobel, 2002).

2.1. Traffic-induced vibration of bridge

A great number of analytical studies have been devoted

to the vibration of girder bridges under moving vehicles

(e.g. Green and Cebon, 1994; Yang and Wu, 2001;

Kawatani et al., 2005; Kim et al., 2005). The work

reported in this paper is based on the analytical procedure

developed for analysis of girder bridges, which was

validated through the comparison to the field-test data

(Kawatani et al., 2005; Kim et al., 2005). It is based on

the finite element method for the modal analysis using

three-dimensional models for both vehicle and bridge. To

improve the calculation efficiency, a process known as

Guyan reduction is performed (Guyan, 1965). The lumped

mass and Rayleigh damping are adopted to form mass

and damping matrices of the bridge model, respectively.

The equation of the forced vibration of a bridge system

subjected to moving vehicular loadings can be defined as

Eq. (1).

(1)

where, Mb, Cb and Kb indicate mass, damping and

stiffness matrices of the bridge, respectively; wb indicates

displacement vector of the bridge, which can be

expressed in terms of the normal coordinate qi and mode

vector φi as defined in Eq. (2); (·) represents the

derivative with respect to time.

(2)

The load vector due to moving vehicles in Eq. (1) is

defined as shown in Eq. (3).

(3)

where, is the distribution vector delivering wheel

loads through a plate element to each node of the

element; is the vehicle wheel load as defined in

Eq.(4); the subscript v indicates the vehicle number on the

bridge; nveh, the total number of vehicles; the subscript m

is the index for the axle/tire position; subscript u, the left

and right sides of a vehicle (u=1, 2 indicating left and

right side, respectively).

m = 1, 2, 3 (4)

where, Kvm2u and Cvm2u are spring constant and damping

coefficient of each tire, respectively; Rvm2u, the elastic

deformation of each tire; Z0vmu, the relative vertical

displacement between the tire and bridge deck defined in

Eq. (5).

(5)

where, w(t, xvmu) is the elastic deformation of the bridge

at time t and at the tire positioned at xvmu along the

direction of the wheel load; Zrvmu, the pavement

roughness at each axle.

The relative deformation Rvmku is as follows.

(6)

where, Zv11, Zv12, Zv22, θxv11, θxv12, θxv22, θyv11 and θyv22 refer

to the bounce of vehicle body, the parallel hop of front

and rear axle respectively, the rolling of vehicle body, the

axle tramp of the front and rear axles, the pitching of

vehicle body and the axle windup motion of the rear axle

of the vehicle model, respectively; the subscript k is the

index for indicating vehicle body and axle (k=1, 2

indicating vehicle body and axle, respectively). The sign

is taken to be positive if the deformation occurs in a

downward direction, pitching occurs from the rear to the

front axle and the rolling is generated from the right to

left side.

The governing equation of a vehicle system (see Fig. 1)

is derived from the energy method with Lagrange

equation of motion as shown in Eq. (7) (Kim et al.,

2005).

(7)

where, T is kinetic energy of the system; V, potential

energy of the system; Ud, dissipation energy of the

system; ai, the i-th generalized co-ordinate.

(8)

Mbw··b Cbw

·b Kbwb+ + fb=

wb φiqii

∑ Φ q⋅= =

fb Ψvmu t( )Pvmu t( )

u 1=

2

∑m 1=

3

∑v 1=

nveh

∑=

Ψvmu t( )

Pvmu t( )

Pvmu t( ) Wvmu Cvm2u Rvm2u Z0vmu–( ) Kvm2u Rvm2u Z

0vmu–( )+ +=

Z0vmu w t xvmu,( ) Zrvmu–=

Rvmku

Zv11 1–( )mλxvmθyv11 1–( )m λyv1θxv11 λyv m 1+( )θxvm2–( ) Zvm2–––

Zv12 1–( )uλyv2θxv12–

Zv22 1–( )mλxv3θyv2 1–( )mλyv3θxv22–+

0⎩⎪⎪⎨⎪⎪⎧

=

m 1 2,= k 1= u 1 2,=;;

m 1= k 2= u 1 2,=;;

m 2 3,= k 2= u 1 2,=;;

otherwise

d

dt----

∂T

∂a· i-------⎝ ⎠⎛ ⎞ ∂T

∂ai-------–

∂V∂ai-------

∂Ud

∂a· i---------+ + 0=

T1

2--- mv1kZ

·v1k

2

Jyvkkθ·yvkk2

Jxv1kθ·xv1k2

+ +( ) mv22Z·v22

2

Jxv22Z·xv22

2

+ +

k 1=

2

∑v 1=

nveh

∑=

Assessment of Traffic-induced Low Frequency Noise Radiated from Steel Box Girder Bridge 307

where, mv11, mv12 and mv22 indicate the concentrated mass

of the vehicle body, front and tandem axles, respectively;

Jxv11, Jxv12 and Jxv22 are inertia moment of vehicle body and

axles around x-axis, respectively; Jyv11 and Jyv22

respectively denote inertia moment of vehicle body and

tandem axle around y-axis.

(9)

(10)

The equations of motion for the vehicle-bridge interaction

are a non-stationary dynamic problem since the

coefficient matrices of the equation varying to the vehicle

position. An alternative step-by-step solution using

Newmark’s β method is applied to solve the derived

system of governing equations of motion. The value of

0.25 is used for β. The solution can be obtained within

the relative margin of error of less than 0.001.

The final formulation of the dynamic equation of

motion for a bridge-vehicle interactive system is written

as Eq. (11).

(11)

where, Mb, Cb and Kb respectively stand for the mass,

damping and stiffness matrices of bridge. Those for

vehicles are denoted as Mv, Cv and Kv. Cbv and Kbv

respectively indicate coupling damping and stiffness

matrices of the bridge-vehicle interactive system, which

will be time-dependent when the vehicle starts to move.

fb is the external load vector caused by the moving

vehicles on a bridge. fv is the vector for the dynamic

wheel load of vehicles. wb indicates displacement of the

bridge, which can be expressed in terms of the normal

coordinate q and mode matrix Φ as defined in Eq. (2).

2.2. Boundary integral equation for sound propagation

Integral equation methods have been applied to investigate

wave propagation to obtain analytical solutions to very

simplified problems. The use of boundary integral solutions

which are known as the Green’s third identity to solve

problems relating to acoustics numerically started in the

1960s (Wrobel, 2002). Noise propagation is an ideal

application area of the BEM because of its applicability

to infinite domain. Chandler-Wilde (1997) gives a detailed

review of the noise propagation by means of BEM.

The major goal of the BEM in this study is to estimate

the velocity potential at a field point P. If the velocity

potential φ(P, t) is estimated, then the sound pressure at a

field point P is obtained using the relation in Eq.(12).

(12)

where ρ indicates the density of air.

The propagation of noise through air is described by

the linear wave equation

(13)

where indicates Laplacian operator, φ is a velocity

potential, and c indicates the speed of sound in air

(=340 m/s). When the motion is assumed to be time-

harmonic as shown in Eq. (14), the function φ in a

domain Ω is expandable as shown in Eq. (15)

(14)

(15)

where φ(P) is a reduced velocity potential, and the

velocity potential φ(P) between a field point P and a

source point Q is the fundamental solution of the

Helmholtz equation as

(16)

Equation (16) satisfies the property

(17)

where δ is the Dirac delta function, and k is the wave

number (=ω/c) if ω indicates the angular frequency of

wave.

The low frequency noise radiated from a bridge is an

exterior problem defined over unbounded regions. The

derivation of the boundary integral equation for the

problem, however, can be found by starting from Green’s

second identity considering bounded domain Ω0 (see Fig.

2), which is written in the form

=

(18)

V1

2--- k

vm1uRvm1u

2kvm2u

Rvm2u

Z0vmu

–( )2+[ ]

u 1=

2

∑m 1=

3

∑v 1=

nveh

∑=

Ud

1

2--- c

vm1uR·vm1u

2

cvm2u

R·vm2u Z

·0vmu–( )

2

+[ ]

u 1=

2

∑m 1=

3

∑v 1=

nveh

∑=

Mb

Sym.

0

Mv

w··b

w··v⎩ ⎭

⎨ ⎬⎧ ⎫ C

b

Sym.

Cbv

Cv

w·b

w·v⎩ ⎭

⎨ ⎬⎧ ⎫ K

b

Sym.

Kbv

Kv

wb

wv⎩ ⎭

⎨ ⎬⎧ ⎫

+ +

fb

fv⎩ ⎭

⎨ ⎬⎧ ⎫

=

p ρ∂φ P t,( )

∂t-----------------=

∇2φ P t,( )1

c2----∂2φ

∂t2--------=

∇

φ P t,( ) φ P( )eiωt=

∇2φ P( ) k2φ P( )+ 0= P Ω∈( )

G P Q,( )eikr

4πr--------=

∇2G P Q,( ) k

2G P Q,( ) δ Q P–( )+ + 0=

φ q( )∇2G P q,( ) G P q,( )∇2φ q( )– vd

Ω0

∫∫∫

φ q( )∂G P q,( )

∂n--------------------

∂φ q( )∂n

-------------G P q,( )–

⎩ ⎭⎨ ⎬⎧ ⎫

sdΣ σ

sF+ +∫∫

Figure 1. Idealized vehicle model with 8DOF.


where Σ, σs and F are respectively the surface (or

boundary) of domain Ω0, field point P and subdomain Ωi.

denotes the normal derivative. For a finite domain Ωi

bounded by the actual surface F and the fictitious surface

Σ, Eq.(18) can be written as

(19)

where c(P) is the free coefficient definable as

(20)

The low frequency noise radiated from the vibrating

bridge is a kind of problems considering the scattering of

sound waves by a thin body. Usually for the very thin

body near-singularities and a degenerate system of equation

may arise if the standard integral equation such as Eq.

(19) is used alone. The formulation by Kawai and Terai

(1990) is useful to deviate from this kind of singularity

problem, which uses the normal derivative form instead

using the basic form shown in Eq. (19) by differentiating

the Eq. (19) with .

(21)

Next applying Eq. (21) to the vibrating bridge by

assuming no noise source except that from the bridge,

and considering the Sommerfeld’s radiation condition

(e.g. Baker and Copson, 1968), following equation for

velocity potential from the surface of the thin body (see

Fig. 3) is obtainable as

(22)

where φ1(p) and φ2(p) indicate the velocity potential at the

surface F1 and F2 respectively as shown in Fig. 3. It is

noteworthy that the directions normal to surfaces F1 and

F2 are opposite with each other. The velocity potential at

a field point within the boundary Ω0 is described as

= (23)

If the thin body of bridges is considered to be rigid,

then the boundary conditions of the type are

applied over the entire surface F. Moreover using the

relation, which is a velocity

at a boundary, Eq. (22) is rewritable as

(24)

It is noteworthy that the second term of the left part of

Eq. (22) takes zero value for surrounding structures

without having any noise source. The second order

derivative terms has the solution as

.

(25)

∂n

φD Ps P,( ) φ q( )∂G P q,( )

∂nq--------------------

∂φ q( )∂nq-------------G P q,( )–

⎩ ⎭⎨ ⎬⎧ ⎫

sdΣ F+∫∫+

c P( )φ P( )=

c P( )

φ P( ):P Ω0

∈=

1

2---φ P( ):P F Σ,∈=

0:P Ω0

∈=⎩⎪⎪⎨⎪⎪⎧

∂np

φD Ps p,( )np

-------------------- φ q( )∂2G p q,( )∂np∂nq---------------------

∂φ q( )∂nq-------------

∂G p q,( )∂np

-------------------–⎩ ⎭⎨ ⎬⎧ ⎫

sdF∫∫+

1

2---∂φ q( )∂np-------------=

P F∈( )

φ1q( ) φ

2q( )–

∂2G p q,( )∂np∂nq---------------------

∂φ1q( )

∂nq---------------

∂φ2q( )

∂nq---------------–

⎩ ⎭⎨ ⎬⎧ ⎫∂G p q,( )

∂np-------------------– sqd

F∫∫

1

2---

∂φ1p( )

∂np---------------

∂φ2p( )

∂np---------------+

⎩ ⎭⎨ ⎬⎧ ⎫

= P F∈( )

φ1q( ) φ

2q( )–

∂G P q,( )∂nq

--------------------∂φ

1q( )

∂nq---------------

∂φ2q( )

∂nq---------------–

⎩ ⎭⎨ ⎬⎧ ⎫

G P q,( )– sqdF∫∫

φ P( ) P Ω0

∈( )

∂φ ∂n⁄ 0=

∂φ1∂n⁄ ∂φ

1∂n⁄ v–= = p F∈( )

φ1q( ) φ

2q( )–

∂2G p q,( )∂np∂nq--------------------- sqd

F∫∫

Φ q( )∂2G p q,( )∂np∂nq--------------------- sqd

F∫∫ v p( )–== P F∈( )

∂2G p q,( )∂np∂nq---------------------

∂2

∂np∂nq----------------

exp ikr( )4πr

-------------------exp ikr( )

4πr3-------------------= =

1 ikr–( )cos nq np,( ) 3 ikr 1–( ) k2r2

+ cos r nq,( )cos r np,( )+[ ]

Figure 2. Geometry of exterior problem.

Figure 3. Geometry of thin body problem.


The velocity potential at a field point within the

boundary Ω0 is obtainable using the solution of Eq. (23)

and Eq. (24) as.

(26)

where is the solution of Eq. (24) for .

The boundary integral equation is solved by means of

the BEM based on a discretization procedure. The

boundary is divided into M segments of 1/5 (or 1/6) of the

wave length considering. The matrix form of the discrete

boundary equations for the surface F and domain Ω0 are

shown in Eq. (27) and Eq. (28), respectively.

(27a)

where,

(27b)

Therein, Eq. (27b) for p=q is introduced to avoid the

singularity at the point of p=q.

Using the which is a solution for of

Eq.(27a), the velocity potential at a field point P thus is

obtainable from the following relation.

(28a)

where,

(28b)

The validity of the method for low frequency noises of

bridges has been already verified (Kawada and Kawatani,

2006), and verification of the method is omitted in this

paper.

3. Analytical Model

3.1. Bridge model

The general layout and cross-sectional view of the

observation bridge are shown in Fig. 4 and Fig. 5,

respectively. The observation point in Fig. 4 indicates the

location where the low-frequency noise is estimated

through this study. The bridge comprises steel decks and

rigid frame piers which are rigidly connected with box

girders. The span length and width of the bridge are

respectively 265.0 m long and 17.25 m wide. Figure 6

illustrates the finite element model for the dynamic

response analysis, in which V2, V3 and V4 are the

observation points for bridge responses. The FE model

consists of 478 nodes and 548 beam elements. Since the

bridge has T-type piers, torsional vibrations occur during

vehicles running on the outer lane (slow traffic lane).

Brackets supporting cantilevered decks are also considered

in FE model to consider those torsional vibrations.

A part of natural modes and frequencies of the bridge

estimated from the eigenvalue analysis are summarized in

Φ q( )∂2G p q,( )∂np∂nq--------------------- sqd

F∫∫ φ p( )= P Ω0

∈

Φ q( ) Φ q( )

a11

a12

aM1

a21

a22

aM2

…

…

O

…

a2M

a1M

aMM

Φ p1

( )

Φ p2

( )

Φ pM

( )⎩ ⎭⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎧ ⎫ v p

1( )

v p2

( )

v pM

( )⎩ ⎭⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎧ ⎫

–=.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

apq

exp ikr( )

4πr3------------------- 1 ikr–( )cos nq np,( ) 3 ikr 1–( ) k

2r2

+ cos r nq,( )cos r np,( )+[ ] ∆sq⋅

exp ikr θ( ) 4πR θ( )

-----------------------------∫° dθik

2----+–

⎩⎪⎪⎨⎪⎪⎧

=

p q≠( )

p q=( )

Φ pi( ) Φ pi( )

b1b2… b

M

Φ p1

( )

Φ p2

( )

Φ pM

( )⎩ ⎭⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎧ ⎫

φ P( )=.

.

.

bq∂G P q,( )

∂nq--------------------

1

4πr--------

1

r---– ik+⎝ ⎠

⎛ ⎞ ikr( )exp cos r np,( )= =

Figure 4. General view of bridge.


Fig. 7. Therein, the out-of-plane bending mode of the

entire bridge is found in the first mode (1.692 Hz). The

third mode (2.600 Hz) and the eighth mode (3.600 Hz)

correspond to the second and fourth torsional mode of the

bridge superstructure, respectively. The fourth mode (2.704

Hz) is the first bending mode of the bridge superstructure.

Those frequencies are very similar to the bounce motion

of vehicles, and are expected to one of sources of the low

frequency noise. The 11th mode (4.388 Hz) is the fifth

bending mode of the bridge superstructure.

In the analysis of low frequency noise using BEM,

webs of the box girder is modeled only as the reflection

surface. The image method is applied to simulate

reflection of sound waves by the ground surface.

3.2. Vehicle model

The vehicle is composed of the body, tires and

suspension systems. Details of the vehicle idealization are

shown in Fig. 1 along with the eight degrees of freedom

to describe its movement. Properties of the vehicle are

summarized in Table 1 and Fig. 8.

In analysis three traffic scenarios according to vehicles’

position are considered as,

Figure 5. Cross-sectional view of bridge.

Figure 6. Analytical model of bridge.

Figure 7. Natural mode shapes and frequencies.


CASE1: Single vehicle running on the passing lane

with speed of 60 km/h,

CASE2: Single vehicle running on the slow traffic lane

with speed of 60 km/h, and

CASE3: Three vehicles running on the slow traffic lane

with speed of 60 km/h.

It is noteworthy that the headway of the vehicles for

CASE3 is estimated using the resonance headway

defined as

Ln

= n · v · T (29)

where, n is an appropriate integer, v is the vehicle speed,

T denotes the natural period considering. The headway

used in this study is 25.15 m based on the values of

v=16.67 m/s (60 km/h), T = 1/3.6 (Hz) and n=5.

4. Analytical Results

4.1. Traffic-induced vibration of bridge

Vertical acceleration responses at the observation points

V2, V3 and V4 (see Fig. 6) of the scenario CASE2 are

shown in Fig. 9, which demonstrates that the peak

acceleration of V3 point is the greatest value among three

observation points. Similar results are observed under

other scenarios, and omitted in this paper. Therefore, only

the third span is considered for low frequency noise

analysis using BEM to reduce computation time.

Effects of the traffic scenario to vertical acceleration

responses are readable from Fig. 10. Comparing the

responses under the scenario CASE2 with CASE1 shows

that the vehicle running on outer lane (or slow traffic

lane: CASE2) gives more critical dynamic responses than

running on the inner lane (or passing lane: CASE1). Of

course, the traffic scenario of three vehicles running on

the slow traffic lane (CASE3) results the most severe

dynamic responses.

Fourier spectra estimated from acceleration responses

of the bridge at V3 according to the traffic scenario such

as CASE1, CASE2 and CASE3 are also shown in Fig.

10. The dominant frequency near 3.6Hz is the effect of

the eighth natural frequency of the bridge (see Fig. 7(d)).

Another peak near 4.4Hz which is very apparent in

CASE3 is the contribution of the 11th mode (see Fig.

7(e)) coincident with the fifth bending mode of the

superstructure. The dominant frequency near 25 Hz is

contribution of the bending mode of brackets. Those

dominant frequencies are also appeared in SPL with

respect to frequency band, and will be discussed in the

next session 4.2.

4.2. Low frequency noise

The observation point for low frequency vibration is

adjacent to the third span (see also Fig. 4) which is

located near a residential zone: 10m apart from the edge

of the bridge; and 1.2 m above the ground. As previously

Figure 8. Dimension of moving vehicle.

Table 1. Dynamic properties of vehicle

Total weight 196.0 kN

Axle weightFront 49.0 kN

Rear 147.0 kN

Logarithmicdecrement

Front 0.66

Rear 0.33

Natural frequency(bounce motion)

Front 1.9 Hz

Rear 3.2 Hz

Figure 9. Acceleration responses at three observation pointsV2, V3 and V4 under traffic scenario CASE2 (Singlevehicle running on the slow traffic lane with speed of60 km/h).


stated, only the third span is considered to assess the low

frequency noise. In addition to the reason of the peak

response at the third span, to reduce the computation time

is another reason adopting only the third span for BEM.

It is noteworthy that a preliminary investigation shows

that the low frequency noise at the observation point

estimated using the one span model (third span) gives

very similar results comparing with those of model

considering even neighboring spans.

Contours of over all sound pressure (SPL) level

obtained from BEM across the cross section at the span

center of the third span are summarized in Fig. 11. It

demonstrates that the most severe SPL is observed under

the CASE3 of three vehicles running. Another important

point worth to comment is that the noisiest place is

between the superstructure and the ground of sound

reflecting. Contours also show that the sound pressure

occurring between the bridge and ground tends to

propagate farther along the ground than through the air

above the bridge.

The SPL at the observation point with noise criterion is

plotted as shown in Fig. 12, where the vertical and

horizontal axes denote the SPL in dB and 1/3 octave band

frequency, respectively. As expected the CASE3 of three

vehicles running gives the most severe SPL across the

frequency band. Figure 12 also indicates that the sound

radiated from the bridge is categorized as Area III and

Area IV. In other words, rattle of door or windows and

low frequency noise may occur due to the sound pressure

radiated from the bridge under moving heavy vehicles.

5. Conclusions

In this study, traffic-induced vibrations of a continuous

steel box girder bridge and sound pressures radiated from

the bridge are simulated to assess the low frequency

noise. The sound pressure is analyzed by means of BEM

using dynamic responses estimated from the traffic-

induced vibration analysis of the bridge.

Observations from this study demonstrate that the SPL

tends to increase with increasing number of vehicles. The

traffic scenario of vehicles running on the slow traffic

(outer lane) lane induces more severe noises than that

running on passing traffic lane (inner lane) because of the

torsional effect. It indicates importance of the three-

dimensional analysis which considers even torsional motion

for simulating this kind of traffic-induced environmental

vibration problems. Contours of the over all SPL shows

Figure 10. Acceleration responses and Fourier spectra at V3 under traffic scenarios.


that the place between the superstructure and the ground

of sound reflecting is the noisiest place. Contours also

demonstrate that the sound pressure occurring between

the bridge and ground tends to propagate farther along the

ground than through the air above the bridge.

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